extern "C" magma_int_t
magma_zlaqps_gpu(magma_int_t m, magma_int_t n, magma_int_t offset,
magma_int_t nb, magma_int_t *kb,
magmaDoubleComplex *A, magma_int_t lda,
magma_int_t *jpvt, magmaDoubleComplex *tau,
double *vn1, double *vn2,
magmaDoubleComplex *auxv,
magmaDoubleComplex *F, magma_int_t ldf)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
ZLAQPS computes a step of QR factorization with column pivoting
of a complex M-by-N matrix A by using Blas-3. It tries to factorize
NB columns from A starting from the row OFFSET+1, and updates all
of the matrix with Blas-3 xGEMM.
In some cases, due to catastrophic cancellations, it cannot
factorize NB columns. Hence, the actual number of factorized
columns is returned in KB.
Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
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
OFFSET (input) INTEGER
The number of rows of A that have been factorized in
previous steps.
NB (input) INTEGER
The number of columns to factorize.
KB (output) INTEGER
The number of columns actually factorized.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, block A(OFFSET+1:M,1:KB) is the triangular
factor obtained and block A(1:OFFSET,1:N) has been
accordingly pivoted, but no factorized.
The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has
been updated.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
JPVT (input/output) INTEGER array, dimension (N)
JPVT(I) = K <==> Column K of the full matrix A has been
permuted into position I in AP.
TAU (output) COMPLEX*16 array, dimension (KB)
The scalar factors of the elementary reflectors.
VN1 (input/output) DOUBLE PRECISION array, dimension (N)
The vector with the partial column norms.
VN2 (input/output) DOUBLE PRECISION array, dimension (N)
The vector with the exact column norms.
AUXV (input/output) COMPLEX*16 array, dimension (NB)
Auxiliar vector.
F (input/output) COMPLEX*16 array, dimension (LDF,NB)
Matrix F' = L*Y'*A.
LDF (input) INTEGER
The leading dimension of the array F. LDF >= max(1,N).
===================================================================== */
#define A(i, j) (A + (i) + (j)*(lda ))
#define F(i, j) (F + (i) + (j)*(ldf ))
magmaDoubleComplex c_zero = MAGMA_Z_MAKE( 0.,0.);
magmaDoubleComplex c_one = MAGMA_Z_MAKE( 1.,0.);
magmaDoubleComplex c_neg_one = MAGMA_Z_MAKE(-1.,0.);
magma_int_t ione = 1;
magma_int_t i__1, i__2;
//double d__1;
magmaDoubleComplex z__1;
//magma_int_t j;
magma_int_t k, rk;
//magmaDoubleComplex Akk;
magmaDoubleComplex *Aks;
magmaDoubleComplex tauk;
magma_int_t pvt;
//double temp, temp2;
double tol3z;
magma_int_t itemp;
double lsticc, *lsticcs;
magma_int_t lastrk;
magma_dmalloc( &lsticcs, 1+256*(n+255)/256 );
lastrk = min( m, n + offset );
tol3z = magma_dsqrt( lapackf77_dlamch("Epsilon"));
lsticc = 0;
k = 0;
magma_zmalloc( &Aks, nb );
while( k < nb && lsticc == 0 ) {
rk = offset + k;
/* Determine ith pivot column and swap if necessary */
// Fortran: pvt, k, idamax are all 1-based; subtract 1 from k.
// C: pvt, k, idamax are all 0-based; don't subtract 1.
pvt = k - 1 + magma_idamax( n-k, &vn1[k], ione );
if (pvt != k) {
/*if (pvt >= nb) {
// 1. Start copy from GPU
magma_zgetmatrix_async( m - offset - nb, 1,
dA(offset + nb, pvt), ldda,
A (offset + nb, pvt), lda, stream );
}*/
/* F gets swapped so F must be sent at the end to GPU */
i__1 = k;
/*if (pvt < nb){
// no need of transfer if pivot is within the panel
blasf77_zswap( &m, A(0, pvt), &ione, A(0, k), &ione );
}
else {
// 1. Finish copy from GPU
magma_queue_sync( stream );
// 2. Swap as usual on CPU
blasf77_zswap(&m, A(0, pvt), &ione, A(0, k), &ione);
// 3. Restore the GPU
magma_zsetmatrix_async( m - offset - nb, 1,
A (offset + nb, pvt), lda,
dA(offset + nb, pvt), ldda, stream);
}*/
magmablas_zswap( m, A(0, pvt), ione, A(0, k), ione );
//blasf77_zswap( &i__1, F(pvt,0), &ldf, F(k,0), &ldf );
magmablas_zswap( i__1, F(pvt, 0), ldf, F(k, 0), ldf);
itemp = jpvt[pvt];
jpvt[pvt] = jpvt[k];
jpvt[k] = itemp;
//vn1[pvt] = vn1[k];
//vn2[pvt] = vn2[k];
#if defined(PRECISION_d) || defined(PRECISION_z)
//magma_dswap( 1, &vn1[pvt], 1, &vn1[k], 1 );
//magma_dswap( 1, &vn2[pvt], 1, &vn2[k], 1 );
magma_dswap( 2, &vn1[pvt], n+offset, &vn1[k], n+offset );
#else
//magma_sswap( 1, &vn1[pvt], 1, &vn1[k], 1 );
//magma_sswap( 1, &vn2[pvt], 1, &vn2[k], 1 );
magma_sswap(2, &vn1[pvt], n+offset, &vn1[k], n+offset);
#endif
}
/* Apply previous Householder reflectors to column K:
A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)'.
Optimization: multiply with beta=0; wait for vector and subtract */
if (k > 0) {
/*#if (defined(PRECISION_c) || defined(PRECISION_z))
for (j = 0; j < k; ++j){
*F(k,j) = MAGMA_Z_CNJG( *F(k,j) );
}
#endif*/
//#define RIGHT_UPDATE
#ifdef RIGHT_UPDATE
i__1 = m - offset - nb;
i__2 = k;
magma_zgemv( MagmaNoTrans, i__1, i__2,
c_neg_one, A(offset+nb, 0), lda,
F(k, 0), ldf,
c_one, A(offset+nb, k), ione );
#else
i__1 = m - rk;
i__2 = k;
/*blasf77_zgemv( MagmaNoTransStr, &i__1, &i__2,
&c_neg_one, A(rk, 0), &lda,
F(k, 0), &ldf,
&c_one, A(rk, k), &ione );*/
magma_zgemv( MagmaNoTrans, i__1, i__2,
c_neg_one, A(rk, 0), lda,
F(k, 0), ldf,
c_one, A(rk, k), ione );
#endif
/*#if (defined(PRECISION_c) || defined(PRECISION_z))
for (j = 0; j < k; ++j) {
*F(k,j) = MAGMA_Z_CNJG( *F(k,j) );
}
#endif*/
}
/* Generate elementary reflector H(k). */
magma_zlarfg_gpu(m-rk, A(rk, k), A(rk + 1, k), &tau[k], &vn1[k], &Aks[k]);
//Akk = *A(rk, k);
//*A(rk, k) = c_one;
//magma_zgetvector( 1, &Aks[k], 1, &Akk, 1 );
/* needed to avoid the race condition */
if (k == 0) magma_zsetvector( 1, &c_one, 1, A(rk, k), 1 );
else magma_zcopymatrix( 1, 1, A(offset, 0), 1, A(rk, k), 1 );
/* Compute Kth column of F:
Compute F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)'*A(RK:M,K) on the GPU */
if (k < n-1 || k > 0) magma_zgetvector( 1, &tau[k], 1, &tauk, 1 );
if (k < n-1) {
i__1 = m - rk;
i__2 = n - k - 1;
/* Send the vector to the GPU */
//magma_zsetmatrix( i__1, 1, A(rk, k), lda, dA(rk,k), ldda );
/* Multiply on GPU */
// was CALL ZGEMV( 'Conjugate transpose', M-RK+1, N-K,
// TAU( K ), A( RK, K+1 ), LDA,
// A( RK, K ), 1,
// CZERO, F( K+1, K ), 1 )
//magma_zgetvector( 1, &tau[k], 1, &tauk, 1 );
magma_zgemv( MagmaConjTrans, m-rk, n-k-1,
tauk, A( rk, k+1 ), lda,
A( rk, k ), 1,
c_zero, F( k+1, k ), 1 );
//magma_zscal( m-rk, tau[k], F( k+1, k), 1 );
//magma_int_t i__3 = nb-k-1;
//magma_int_t i__4 = i__2 - i__3;
//magma_int_t i__5 = nb-k;
//magma_zgemv( MagmaConjTrans, i__1 - i__5, i__2 - i__3,
// tau[k], dA(rk +i__5, k+1+i__3), ldda,
// dA(rk +i__5, k ), ione,
// c_zero, dF(k+1+i__3, k ), ione );
//magma_zgetmatrix_async( i__2-i__3, 1,
// dF(k + 1 +i__3, k), i__2,
// F (k + 1 +i__3, k), i__2, stream );
//blasf77_zgemv( MagmaConjTransStr, &i__1, &i__3,
// &tau[k], A(rk, k+1), &lda,
// A(rk, k ), &ione,
// &c_zero, F(k+1, k ), &ione );
//magma_queue_sync( stream );
//blasf77_zgemv( MagmaConjTransStr, &i__5, &i__4,
// &tau[k], A(rk, k+1+i__3), &lda,
// A(rk, k ), &ione,
// &c_one, F(k+1+i__3, k ), &ione );
}
/* Padding F(1:K,K) with zeros.
for (j = 0; j <= k; ++j) {
magma_zsetvector( 1, &c_zero, 1, F(j, k), 1 );
}*/
/* Incremental updating of F:
F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)'*A(RK:M,K).
F(1:N,K) := tau(K)*A(RK:M,K+1:N)'*A(RK:M,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)'*A(RK:M,K)
:= tau(K)(A(RK:M,K+1:N)' - F(1:N,1:K-1)*A(RK:M,1:K-1)') A(RK:M,K)
so, F is (updated A)*V */
//if (k > 0 && k<n-1) {
if (k > 0) {
//magma_zgetvector( 1, &tau[k], 1, &tauk, 1 );
z__1 = MAGMA_Z_NEGATE( tauk );
#ifdef RIGHT_UPDATE
i__1 = m - offset - nb;
i__2 = k;
magma_zgemv( MagmaConjTrans, i__1, i__2,
z__1, A(offset+nb, 0), lda,
A(offset+nb, k), ione,
c_zero, auxv, ione );
i__1 = k;
magma_zgemv( MagmaNoTrans, n-k-1, i__1,
c_one, F(k+1,0), ldf,
auxv, ione,
c_one, F(k+1,k), ione );
#else
i__1 = m - rk;
i__2 = k;
//blasf77_zgemv( MagmaConjTransStr, &i__1, &i__2,
// &z__1, A(rk, 0), &lda,
// A(rk, k), &ione,
// &c_zero, auxv, &ione );
magma_zgemv( MagmaConjTrans, i__1, i__2,
z__1, A(rk, 0), lda,
A(rk, k), ione,
c_zero, auxv, ione );
//i__1 = k;
//blasf77_zgemv( MagmaNoTransStr, &n, &i__1,
// &c_one, F(0,0), &ldf,
// auxv, &ione,
// &c_one, F(0,k), &ione );
/*magma_zgemv( MagmaNoTrans, n, i__1,
c_one, F(0,0), ldf,
auxv, ione,
c_one, F(0,k), ione );*/
/* I think we only need stricly lower-triangular part :) */
magma_zgemv( MagmaNoTrans, n-k-1, i__2,
c_one, F(k+1,0), ldf,
auxv, ione,
c_one, F(k+1,k), ione );
#endif
}
/* Optimization: On the last iteration start sending F back to the GPU */
/* Update the current row of A:
A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)'. */
if (k < n-1) {
i__1 = n - k - 1;
i__2 = k + 1;
//blasf77_zgemm( MagmaNoTransStr, MagmaConjTransStr, &ione, &i__1, &i__2,
// &c_neg_one, A(rk, 0 ), &lda,
// F(k+1,0 ), &ldf,
// &c_one, A(rk, k+1), &lda );
#ifdef RIGHT_UPDATE
/* right-looking update of rows, */
magma_zgemm( MagmaNoTrans, MagmaConjTrans, nb-k, i__1, ione,
c_neg_one, A(rk, k ), lda,
F(k+1, k ), ldf,
c_one, A(rk, k+1), lda );
#else
/* left-looking update of rows, *
* since F=A'v with original A, so no right-looking */
magma_zgemm( MagmaNoTrans, MagmaConjTrans, ione, i__1, i__2,
c_neg_one, A(rk, 0 ), lda,
F(k+1,0 ), ldf,
c_one, A(rk, k+1), lda );
#endif
}
/* Update partial column norms. */
if (rk < min(m, n+offset)-1 ) {
magmablas_dznrm2_row_check_adjust(n-k-1, tol3z, &vn1[k+1], &vn2[k+1], A(rk,k+1), lda, lsticcs);
magma_device_sync();
#if defined(PRECISION_d) || defined(PRECISION_z)
magma_dgetvector( 1, &lsticcs[0], 1, &lsticc, 1 );
#else
magma_sgetvector( 1, &lsticcs[0], 1, &lsticc, 1 );
#endif
}
/*if (rk < lastrk) {
for (j = k + 1; j < n; ++j) {
if (vn1[j] != 0.) {
// NOTE: The following 4 lines follow from the analysis in
// Lapack Working Note 176.
temp = MAGMA_Z_ABS( *A(rk,j) ) / vn1[j];
temp = max( 0., ((1. + temp) * (1. - temp)) );
d__1 = vn1[j] / vn2[j];
temp2 = temp * (d__1 * d__1);
if (temp2 <= tol3z) {
vn2[j] = (double) lsticc;
lsticc = j;
} else {
vn1[j] *= magma_dsqrt(temp);
}
}
}
}*/
//*A(rk, k) = Akk;
//magma_zsetvector( 1, &Akk, 1, A(rk, k), 1 );
//magma_zswap( 1, &Aks[k], 1, A(rk, k), 1 );
++k;
}
magma_zcopymatrix( 1, k, Aks, 1, A(offset, 0), lda+1 );
// leave k as the last column done
--k;
*kb = k + 1;
rk = offset + *kb - 1;
/* Apply the block reflector to the rest of the matrix:
A(OFFSET+KB+1:M,KB+1:N) := A(OFFSET+KB+1:M,KB+1:N) - A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)' */
if (*kb < min(n, m - offset)) {
i__1 = m - rk - 1;
i__2 = n - *kb;
/* Send F to the GPU
magma_zsetmatrix( i__2, *kb,
F (*kb, 0), ldf,
dF(*kb, 0), i__2 );*/
magma_zgemm( MagmaNoTrans, MagmaConjTrans, i__1, i__2, *kb,
c_neg_one, A(rk+1, 0 ), lda,
F(*kb, 0 ), ldf,
c_one, A(rk+1, *kb), lda );
}
/* Recomputation of difficult columns. */
if( lsticc > 0 ) {
printf( " -- recompute dnorms --\n" );
magmablas_dznrm2_check(m-rk-1, n-*kb, A(rk+1,*kb), lda,
&vn1[*kb], lsticcs);
#if defined(PRECISION_d) || defined(PRECISION_z)
magma_dcopymatrix( n-*kb, 1, &vn1[*kb], *kb, &vn2[*kb], *kb);
#else
magma_scopymatrix( n-*kb, 1, &vn1[*kb], *kb, &vn2[*kb], *kb);
#endif
/*while( lsticc > 0 ) {
itemp = (magma_int_t)(vn2[lsticc] >= 0. ? floor(vn2[lsticc] + .5) : -floor(.5 - vn2[lsticc]));
i__1 = m - rk - 1;
if (lsticc <= nb)
vn1[lsticc] = cblas_dznrm2(i__1, A(rk + 1, lsticc), ione);
else {
// Where is the data, CPU or GPU ?
double r1, r2;
r1 = cblas_dznrm2(nb-k, A(rk + 1, lsticc), ione);
r2 = magma_dznrm2(m-offset-nb, dA(offset + nb + 1, lsticc), ione);
vn1[lsticc] = magma_dsqrt(r1*r1+r2*r2);
}
// NOTE: The computation of VN1( LSTICC ) relies on the fact that
// SNRM2 does not fail on vectors with norm below the value of SQRT(DLAMCH('S'))
vn2[lsticc] = vn1[lsticc];
lsticc = itemp;*/
}
magma_free(Aks);
magma_free(lsticcs);
return MAGMA_SUCCESS;
} /* magma_zlaqps */
/**
@deprecated
Purpose
-------
ZLAQPS computes a step of QR factorization with column pivoting
of a complex M-by-N matrix A by using Blas-3. It tries to factorize
NB columns from A starting from the row OFFSET+1, and updates all
of the matrix with Blas-3 xGEMM.
In some cases, due to catastrophic cancellations, it cannot
factorize NB columns. Hence, the actual number of factorized
columns is returned in KB.
Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
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]
offset INTEGER
The number of rows of A that have been factorized in
previous steps.
@param[in]
nb INTEGER
The number of columns to factorize.
@param[out]
kb INTEGER
The number of columns actually factorized.
@param[in,out]
dA COMPLEX_16 array, dimension (LDDA,N), on the GPU.
On entry, the M-by-N matrix A.
On exit, block A(OFFSET+1:M,1:KB) is the triangular
factor obtained and block A(1:OFFSET,1:N) has been
accordingly pivoted, but no factorized.
The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has
been updated.
@param[in]
ldda INTEGER
The leading dimension of the array A. LDDA >= max(1,M).
@param[in,out]
jpvt INTEGER array, dimension (N)
JPVT(I) = K <==> Column K of the full matrix A has been
permuted into position I in AP.
@param[out]
tau COMPLEX_16 array, dimension (KB)
The scalar factors of the elementary reflectors.
@param[in,out]
vn1 DOUBLE PRECISION array, dimension (N)
The vector with the partial column norms.
@param[in,out]
vn2 DOUBLE PRECISION array, dimension (N)
The vector with the exact column norms.
@param[in,out]
dauxv COMPLEX_16 array, dimension (NB), on the GPU
Auxiliary vector.
@param[in,out]
dF COMPLEX_16 array, dimension (LDDF,NB), on the GPU
Matrix F' = L*Y'*A.
@param[in]
lddf INTEGER
The leading dimension of the array F. LDDF >= max(1,N).
@ingroup magma_zgeqp3_aux
********************************************************************/
extern "C" magma_int_t
magma_zlaqps_gpu(
magma_int_t m, magma_int_t n, magma_int_t offset,
magma_int_t nb, magma_int_t *kb,
magmaDoubleComplex_ptr dA, magma_int_t ldda,
magma_int_t *jpvt, magmaDoubleComplex *tau,
double *vn1, double *vn2,
magmaDoubleComplex_ptr dauxv,
magmaDoubleComplex_ptr dF, magma_int_t lddf)
{
#define dA(i, j) (dA + (i) + (j)*(ldda))
#define dF(i, j) (dF + (i) + (j)*(lddf))
magmaDoubleComplex c_zero = MAGMA_Z_MAKE( 0.,0.);
magmaDoubleComplex c_one = MAGMA_Z_MAKE( 1.,0.);
magmaDoubleComplex c_neg_one = MAGMA_Z_MAKE(-1.,0.);
magma_int_t ione = 1;
magma_int_t i__1, i__2;
//double d__1;
magmaDoubleComplex z__1;
//magma_int_t j;
magma_int_t k, rk;
//magmaDoubleComplex Akk;
magmaDoubleComplex_ptr dAks;
magmaDoubleComplex tauk = MAGMA_Z_ZERO;
magma_int_t pvt;
//double temp, temp2;
double tol3z;
magma_int_t itemp;
double lsticc;
magmaDouble_ptr dlsticcs;
magma_dmalloc( &dlsticcs, 1+256*(n+255)/256 );
//lastrk = min( m, n + offset );
tol3z = magma_dsqrt( lapackf77_dlamch("Epsilon"));
lsticc = 0;
k = 0;
magma_zmalloc( &dAks, nb );
while( k < nb && lsticc == 0 ) {
rk = offset + k;
/* Determine ith pivot column and swap if necessary */
// subtract 1 from Fortran/CUBLAS idamax; pvt, k are 0-based.
pvt = k + magma_idamax( n-k, &vn1[k], ione ) - 1;
if (pvt != k) {
/*if (pvt >= nb) {
// 1. Start copy from GPU
magma_zgetmatrix_async( m - offset - nb, 1,
dA(offset + nb, pvt), ldda,
A (offset + nb, pvt), lda, stream );
}*/
/* F gets swapped so F must be sent at the end to GPU */
i__1 = k;
/*if (pvt < nb) {
// no need of transfer if pivot is within the panel
blasf77_zswap( &m, A(0, pvt), &ione, A(0, k), &ione );
}
else {
// 1. Finish copy from GPU
magma_queue_sync( stream );
// 2. Swap as usual on CPU
blasf77_zswap(&m, A(0, pvt), &ione, A(0, k), &ione);
// 3. Restore the GPU
magma_zsetmatrix_async( m - offset - nb, 1,
A (offset + nb, pvt), lda,
dA(offset + nb, pvt), ldda, stream);
}*/
magmablas_zswap( m, dA(0, pvt), ione, dA(0, k), ione );
//blasf77_zswap( &i__1, F(pvt,0), &ldf, F(k,0), &ldf );
magmablas_zswap( i__1, dF(pvt, 0), lddf, dF(k, 0), lddf);
itemp = jpvt[pvt];
jpvt[pvt] = jpvt[k];
jpvt[k] = itemp;
//vn1[pvt] = vn1[k];
//vn2[pvt] = vn2[k];
#if defined(PRECISION_d) || defined(PRECISION_z)
//magma_dswap( 1, &vn1[pvt], 1, &vn1[k], 1 );
//magma_dswap( 1, &vn2[pvt], 1, &vn2[k], 1 );
magma_dswap( 2, &vn1[pvt], n+offset, &vn1[k], n+offset );
#else
//magma_sswap( 1, &vn1[pvt], 1, &vn1[k], 1 );
//magma_sswap( 1, &vn2[pvt], 1, &vn2[k], 1 );
magma_sswap(2, &vn1[pvt], n+offset, &vn1[k], n+offset);
#endif
}
/* Apply previous Householder reflectors to column K:
A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)'.
Optimization: multiply with beta=0; wait for vector and subtract */
if (k > 0) {
/*#if (defined(PRECISION_c) || defined(PRECISION_z))
for (j = 0; j < k; ++j) {
*F(k,j) = MAGMA_Z_CNJG( *F(k,j) );
}
#endif*/
//#define RIGHT_UPDATE
#ifdef RIGHT_UPDATE
i__1 = m - offset - nb;
i__2 = k;
magma_zgemv( MagmaNoTrans, i__1, i__2,
c_neg_one, A(offset+nb, 0), lda,
F(k, 0), ldf,
c_one, A(offset+nb, k), ione );
#else
i__1 = m - rk;
i__2 = k;
/*blasf77_zgemv( MagmaNoTransStr, &i__1, &i__2,
&c_neg_one, A(rk, 0), &lda,
F(k, 0), &ldf,
&c_one, A(rk, k), &ione ); */
magma_zgemv( MagmaNoTrans, i__1, i__2,
c_neg_one, dA(rk, 0), ldda,
dF(k, 0), lddf,
c_one, dA(rk, k), ione );
#endif
/*#if (defined(PRECISION_c) || defined(PRECISION_z))
for (j = 0; j < k; ++j) {
*F(k,j) = MAGMA_Z_CNJG( *F(k,j) );
}
#endif*/
}
/* Generate elementary reflector H(k). */
magma_zlarfg_gpu( m-rk, dA(rk, k), dA(rk + 1, k), &tau[k], &vn1[k], &dAks[k]);
//Akk = *A(rk, k);
//*A(rk, k) = c_one;
//magma_zgetvector( 1, &dAks[k], 1, &Akk, 1 );
/* needed to avoid the race condition */
if (k == 0) magma_zsetvector( 1, &c_one, 1, dA(rk, k), 1 );
else magma_zcopymatrix( 1, 1, dA(offset, 0), 1, dA(rk, k), 1 );
/* Compute Kth column of F:
Compute F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)'*A(RK:M,K) on the GPU */
if (k < n-1 || k > 0) magma_zgetvector( 1, &tau[k], 1, &tauk, 1 );
if (k < n-1) {
i__1 = m - rk;
i__2 = n - k - 1;
/* Send the vector to the GPU */
//magma_zsetmatrix( i__1, 1, A(rk, k), lda, dA(rk,k), ldda );
/* Multiply on GPU */
// was CALL ZGEMV( 'Conjugate transpose', M-RK+1, N-K,
// TAU( K ), A( RK, K+1 ), LDA,
// A( RK, K ), 1,
// CZERO, F( K+1, K ), 1 )
//magma_zgetvector( 1, &tau[k], 1, &tauk, 1 );
magma_zgemv( MagmaConjTrans, m-rk, n-k-1,
tauk, dA( rk, k+1 ), ldda,
dA( rk, k ), 1,
c_zero, dF( k+1, k ), 1 );
//magma_zscal( m-rk, tau[k], F( k+1, k), 1 );
//magma_int_t i__3 = nb-k-1;
//magma_int_t i__4 = i__2 - i__3;
//magma_int_t i__5 = nb-k;
//magma_zgemv( MagmaConjTrans, i__1 - i__5, i__2 - i__3,
// tau[k], dA(rk +i__5, k+1+i__3), ldda,
// dA(rk +i__5, k ), ione,
// c_zero, dF(k+1+i__3, k ), ione );
//magma_zgetmatrix_async( i__2-i__3, 1,
// dF(k + 1 +i__3, k), i__2,
// F (k + 1 +i__3, k), i__2, stream );
//blasf77_zgemv( MagmaConjTransStr, &i__1, &i__3,
// &tau[k], A(rk, k+1), &lda,
// A(rk, k ), &ione,
// &c_zero, F(k+1, k ), &ione );
//magma_queue_sync( stream );
//blasf77_zgemv( MagmaConjTransStr, &i__5, &i__4,
// &tau[k], A(rk, k+1+i__3), &lda,
// A(rk, k ), &ione,
// &c_one, F(k+1+i__3, k ), &ione );
}
/* Padding F(1:K,K) with zeros.
for (j = 0; j <= k; ++j) {
magma_zsetvector( 1, &c_zero, 1, F(j, k), 1 );
}*/
/* Incremental updating of F:
F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)'*A(RK:M,K).
F(1:N,K) := tau(K)*A(RK:M,K+1:N)'*A(RK:M,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)'*A(RK:M,K)
:= tau(K)(A(RK:M,K+1:N)' - F(1:N,1:K-1)*A(RK:M,1:K-1)') A(RK:M,K)
so, F is (updated A)*V */
//if (k > 0 && k < n-1) {
if (k > 0) {
//magma_zgetvector( 1, &tau[k], 1, &tauk, 1 );
z__1 = MAGMA_Z_NEGATE( tauk );
#ifdef RIGHT_UPDATE
i__1 = m - offset - nb;
i__2 = k;
magma_zgemv( MagmaConjTrans, i__1, i__2,
z__1, dA(offset+nb, 0), lda,
dA(offset+nb, k), ione,
c_zero, dauxv, ione );
i__1 = k;
magma_zgemv( MagmaNoTrans, n-k-1, i__1,
c_one, F(k+1,0), ldf,
dauxv, ione,
c_one, F(k+1,k), ione );
#else
i__1 = m - rk;
i__2 = k;
//blasf77_zgemv( MagmaConjTransStr, &i__1, &i__2,
// &z__1, A(rk, 0), &lda,
// A(rk, k), &ione,
// &c_zero, auxv, &ione );
magma_zgemv( MagmaConjTrans, i__1, i__2,
z__1, dA(rk, 0), ldda,
dA(rk, k), ione,
c_zero, dauxv, ione );
//i__1 = k;
//blasf77_zgemv( MagmaNoTransStr, &n, &i__1,
// &c_one, F(0,0), &ldf,
// auxv, &ione,
// &c_one, F(0,k), &ione );
/*magma_zgemv( MagmaNoTrans, n, i__1,
c_one, F(0,0), ldf,
auxv, ione,
c_one, F(0,k), ione ); */
/* I think we only need stricly lower-triangular part :) */
magma_zgemv( MagmaNoTrans, n-k-1, i__2,
c_one, dF(k+1,0), lddf,
dauxv, ione,
c_one, dF(k+1,k), ione );
#endif
}
/* Optimization: On the last iteration start sending F back to the GPU */
/* Update the current row of A:
A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)'. */
if (k < n-1) {
i__1 = n - k - 1;
i__2 = k + 1;
//blasf77_zgemm( MagmaNoTransStr, MagmaConjTransStr, &ione, &i__1, &i__2,
// &c_neg_one, A(rk, 0 ), &lda,
// F(k+1,0 ), &ldf,
// &c_one, A(rk, k+1), &lda );
#ifdef RIGHT_UPDATE
/* right-looking update of rows, */
magma_zgemm( MagmaNoTrans, MagmaConjTrans, nb-k, i__1, ione,
c_neg_one, dA(rk, k ), ldda,
dF(k+1, k ), lddf,
c_one, dA(rk, k+1), ldda );
#else
/* left-looking update of rows, *
* since F=A'v with original A, so no right-looking */
magma_zgemm( MagmaNoTrans, MagmaConjTrans, ione, i__1, i__2,
c_neg_one, dA(rk, 0 ), ldda,
dF(k+1,0 ), lddf,
c_one, dA(rk, k+1), ldda );
#endif
}
/* Update partial column norms. */
if (rk < min(m, n+offset)-1 ) {
magmablas_dznrm2_row_check_adjust(n-k-1, tol3z, &vn1[k+1], &vn2[k+1], dA(rk,k+1), ldda, dlsticcs);
magma_device_sync();
#if defined(PRECISION_d) || defined(PRECISION_z)
magma_dgetvector( 1, &dlsticcs[0], 1, &lsticc, 1 );
#else
magma_sgetvector( 1, &dlsticcs[0], 1, &lsticc, 1 );
#endif
}
/*if (rk < lastrk) {
for (j = k + 1; j < n; ++j) {
if (vn1[j] != 0.) {
// NOTE: The following 4 lines follow from the analysis in
// Lapack Working Note 176.
temp = MAGMA_Z_ABS( *A(rk,j) ) / vn1[j];
temp = max( 0., ((1. + temp) * (1. - temp)) );
d__1 = vn1[j] / vn2[j];
temp2 = temp * (d__1 * d__1);
if (temp2 <= tol3z) {
vn2[j] = (double) lsticc;
lsticc = j;
} else {
vn1[j] *= magma_dsqrt(temp);
}
}
}
}*/
//*A(rk, k) = Akk;
//magma_zsetvector( 1, &Akk, 1, A(rk, k), 1 );
//magma_zswap( 1, &dAks[k], 1, A(rk, k), 1 );
++k;
}
magma_zcopymatrix( 1, k, dAks, 1, dA(offset, 0), ldda+1 );
// leave k as the last column done
--k;
*kb = k + 1;
rk = offset + *kb - 1;
/* Apply the block reflector to the rest of the matrix:
A(OFFSET+KB+1:M,KB+1:N) := A(OFFSET+KB+1:M,KB+1:N) - A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)' */
if (*kb < min(n, m - offset)) {
i__1 = m - rk - 1;
i__2 = n - *kb;
/* Send F to the GPU
magma_zsetmatrix( i__2, *kb,
F (*kb, 0), ldf,
dF(*kb, 0), i__2 ); */
magma_zgemm( MagmaNoTrans, MagmaConjTrans, i__1, i__2, *kb,
c_neg_one, dA(rk+1, 0 ), ldda,
dF(*kb, 0 ), lddf,
c_one, dA(rk+1, *kb), ldda );
}
/* Recomputation of difficult columns. */
if ( lsticc > 0 ) {
// printf( " -- recompute dnorms --\n" );
magmablas_dznrm2_check( m-rk-1, n-*kb, dA(rk+1,*kb), ldda,
&vn1[*kb], dlsticcs );
magma_dcopymatrix( n-*kb, 1, &vn1[*kb], *kb, &vn2[*kb], *kb );
/*while( lsticc > 0 ) {
itemp = (magma_int_t)(vn2[lsticc] >= 0. ? floor(vn2[lsticc] + .5) : -floor(.5 - vn2[lsticc]));
i__1 = m - rk - 1;
if (lsticc <= nb)
vn1[lsticc] = magma_cblas_dznrm2( i__1, A(rk+1,lsticc), ione );
else {
// Where is the data, CPU or GPU ?
double r1, r2;
r1 = magma_cblas_dznrm2( nb-k, A(rk+1,lsticc), ione );
r2 = magma_dznrm2(m-offset-nb, dA(offset + nb + 1, lsticc), ione);
vn1[lsticc] = magma_dsqrt(r1*r1+r2*r2);
}
// NOTE: The computation of VN1( LSTICC ) relies on the fact that
// SNRM2 does not fail on vectors with norm below the value of SQRT(DLAMCH('S'))
vn2[lsticc] = vn1[lsticc];
lsticc = itemp; */
}
magma_free(dAks);
magma_free(dlsticcs);
return MAGMA_SUCCESS;
} /* magma_zlaqps */
extern "C" magma_int_t
magma_zgeqr2_gpu(magma_int_t *m, magma_int_t *n, cuDoubleComplex *dA,
magma_int_t *ldda, cuDoubleComplex *dtau, double *dwork,
magma_int_t *info)
{
/* -- MAGMA (version 1.3.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
November 2012
Purpose
=======
ZGEQR2 computes a QR factorization of a complex 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.
A (input/output) COMPLEX*16 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 unitary matrix Q as a
product of elementary reflectors (see Further Details).
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (output) COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace) COMPLEX*16 array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Further Details
===============
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
===================================================================== */
#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))
static magma_int_t i, k;
*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;
}
/* Compute the norms of the trailing columns */
k = min(*m,*n);
magmablas_dznrm2(*m, k, da_ref(0,0), *ldda, dwork);
for (i = 0; i < k; ++i) {
/* Generate elementary reflector H(i) to annihilate A(i+1:m,i) */
magma_zlarfg_gpu(*m-i, da_ref(i, i), da_ref(min(i+1,*m), i), dtau+i, dwork+i);
if (i <= *n) {
/* Apply H(i)' to A(i:m,i+1:n) from the left */
magma_zlarf_gpu(*m-i, *n-i-1, da_ref(i, i), dtau+i, da_ref(i, i+1), *ldda,
dwork+i+1);
}
}
return *info;
} /* magma_zgeqr2 */
/**
@deprecated
Purpose
-------
ZLAQPS computes a step of QR factorization with column pivoting
of a complex M-by-N matrix A by using Blas-3. It tries to factorize
NB columns from A starting from the row OFFSET+1, and updates all
of the matrix with Blas-3 xGEMM.
In some cases, due to catastrophic cancellations, it cannot
factorize NB columns. Hence, the actual number of factorized
columns is returned in KB.
Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
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]
offset INTEGER
The number of rows of A that have been factorized in
previous steps.
@param[in]
nb INTEGER
The number of columns to factorize.
@param[out]
kb INTEGER
The number of columns actually factorized.
@param[in,out]
dA COMPLEX_16 array, dimension (LDDA,N), on the GPU.
On entry, the M-by-N matrix A.
On exit, block A(OFFSET+1:M,1:KB) is the triangular
factor obtained and block A(1:OFFSET,1:N) has been
accordingly pivoted, but no factorized.
The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has
been updated.
@param[in]
ldda INTEGER
The leading dimension of the array A. LDDA >= max(1,M).
@param[in,out]
jpvt INTEGER array, dimension (N)
JPVT(I) = K <==> Column K of the full matrix A has been
permuted into position I in AP.
@param[out]
tau COMPLEX_16 array, dimension (KB)
The scalar factors of the elementary reflectors.
@param[in,out]
vn1 DOUBLE PRECISION array, dimension (N)
The vector with the partial column norms.
@param[in,out]
vn2 DOUBLE PRECISION array, dimension (N)
The vector with the exact column norms.
@param[in,out]
dauxv COMPLEX_16 array, dimension (NB), on the GPU
Auxiliary vector.
@param[in,out]
dF COMPLEX_16 array, dimension (LDDF,NB), on the GPU
Matrix F' = L*Y'*A.
@param[in]
lddf INTEGER
The leading dimension of the array F. LDDF >= max(1,N).
@ingroup magma_zgeqp3_aux
********************************************************************/
extern "C" magma_int_t
magma_zlaqps_gpu(
magma_int_t m, magma_int_t n, magma_int_t offset,
magma_int_t nb, magma_int_t *kb,
magmaDoubleComplex_ptr dA, magma_int_t ldda,
magma_int_t *jpvt, magmaDoubleComplex *tau,
double *vn1, double *vn2,
magmaDoubleComplex_ptr dauxv,
magmaDoubleComplex_ptr dF, magma_int_t lddf)
{
#define dA(i, j) (dA + (i) + (j)*(ldda))
#define dF(i, j) (dF + (i) + (j)*(lddf))
magmaDoubleComplex c_zero = MAGMA_Z_MAKE( 0.,0.);
magmaDoubleComplex c_one = MAGMA_Z_MAKE( 1.,0.);
magmaDoubleComplex c_neg_one = MAGMA_Z_MAKE(-1.,0.);
magma_int_t ione = 1;
magma_int_t i__1, i__2;
magmaDoubleComplex z__1;
magma_int_t k, rk;
magmaDoubleComplex_ptr dAks;
magmaDoubleComplex tauk = MAGMA_Z_ZERO;
magma_int_t pvt;
double tol3z;
magma_int_t itemp;
double lsticc;
magmaDouble_ptr dlsticcs;
magma_dmalloc( &dlsticcs, 1+256*(n+255)/256 );
tol3z = magma_dsqrt( lapackf77_dlamch("Epsilon"));
lsticc = 0;
k = 0;
magma_zmalloc( &dAks, nb );
magma_queue_t queue;
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queue );
while( k < nb && lsticc == 0 ) {
rk = offset + k;
/* Determine ith pivot column and swap if necessary */
// subtract 1 from Fortran/CUBLAS idamax; pvt, k are 0-based.
pvt = k + magma_idamax( n-k, &vn1[k], ione, queue ) - 1;
if (pvt != k) {
/* F gets swapped so F must be sent at the end to GPU */
i__1 = k;
magmablas_zswap( m, dA(0, pvt), ione, dA(0, k), ione, queue );
magmablas_zswap( i__1, dF(pvt, 0), lddf, dF(k, 0), lddf, queue );
itemp = jpvt[pvt];
jpvt[pvt] = jpvt[k];
jpvt[k] = itemp;
magma_dswap( 2, &vn1[pvt], n+offset, &vn1[k], n+offset, queue );
}
/* Apply previous Householder reflectors to column K:
A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)'.
Optimization: multiply with beta=0; wait for vector and subtract */
if (k > 0) {
//#define RIGHT_UPDATE
#ifdef RIGHT_UPDATE
i__1 = m - offset - nb;
i__2 = k;
magma_zgemv( MagmaNoTrans, i__1, i__2,
c_neg_one, A(offset+nb, 0), lda,
F(k, 0), ldf,
c_one, A(offset+nb, k), ione, queue );
#else
i__1 = m - rk;
i__2 = k;
magma_zgemv( MagmaNoTrans, i__1, i__2,
c_neg_one, dA(rk, 0), ldda,
dF(k, 0), lddf,
c_one, dA(rk, k), ione, queue );
#endif
}
/* Generate elementary reflector H(k). */
magma_zlarfg_gpu( m-rk, dA(rk, k), dA(rk + 1, k), &tau[k], &vn1[k], &dAks[k], queue );
/* needed to avoid the race condition */
if (k == 0) magma_zsetvector( 1, &c_one, 1, dA(rk, k), 1, queue );
else magma_zcopymatrix( 1, 1, dA(offset, 0), 1, dA(rk, k), 1, queue );
/* Compute Kth column of F:
Compute F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)'*A(RK:M,K) on the GPU */
if (k < n-1 || k > 0) magma_zgetvector( 1, &tau[k], 1, &tauk, 1, queue );
if (k < n-1) {
i__1 = m - rk;
i__2 = n - k - 1;
/* Multiply on GPU */
magma_zgemv( MagmaConjTrans, m-rk, n-k-1,
tauk, dA( rk, k+1 ), ldda,
dA( rk, k ), 1,
c_zero, dF( k+1, k ), 1, queue );
}
/* Incremental updating of F:
F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)'*A(RK:M,K).
F(1:N,K) := tau(K)*A(RK:M,K+1:N)'*A(RK:M,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)'*A(RK:M,K)
:= tau(K)(A(RK:M,K+1:N)' - F(1:N,1:K-1)*A(RK:M,1:K-1)') A(RK:M,K)
so, F is (updated A)*V */
if (k > 0) {
z__1 = MAGMA_Z_NEGATE( tauk );
#ifdef RIGHT_UPDATE
i__1 = m - offset - nb;
i__2 = k;
magma_zgemv( MagmaConjTrans, i__1, i__2,
z__1, dA(offset+nb, 0), lda,
dA(offset+nb, k), ione,
c_zero, dauxv, ione, queue );
i__1 = k;
magma_zgemv( MagmaNoTrans, n-k-1, i__1,
c_one, F(k+1,0), ldf,
dauxv, ione,
c_one, F(k+1,k), ione, queue );
#else
i__1 = m - rk;
i__2 = k;
magma_zgemv( MagmaConjTrans, i__1, i__2,
z__1, dA(rk, 0), ldda,
dA(rk, k), ione,
c_zero, dauxv, ione, queue );
/* I think we only need stricly lower-triangular part :) */
magma_zgemv( MagmaNoTrans, n-k-1, i__2,
c_one, dF(k+1,0), lddf,
dauxv, ione,
c_one, dF(k+1,k), ione, queue );
#endif
}
/* Optimization: On the last iteration start sending F back to the GPU */
/* Update the current row of A:
A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)'. */
if (k < n-1) {
i__1 = n - k - 1;
i__2 = k + 1;
#ifdef RIGHT_UPDATE
/* right-looking update of rows, */
magma_zgemm( MagmaNoTrans, MagmaConjTrans, nb-k, i__1, ione,
c_neg_one, dA(rk, k ), ldda,
dF(k+1, k ), lddf,
c_one, dA(rk, k+1), ldda, queue );
#else
/* left-looking update of rows, *
* since F=A'v with original A, so no right-looking */
magma_zgemm( MagmaNoTrans, MagmaConjTrans, ione, i__1, i__2,
c_neg_one, dA(rk, 0 ), ldda,
dF(k+1,0 ), lddf,
c_one, dA(rk, k+1), ldda, queue );
#endif
}
/* Update partial column norms. */
if (rk < min(m, n+offset)-1 ) {
magmablas_dznrm2_row_check_adjust( n-k-1, tol3z, &vn1[k+1], &vn2[k+1],
dA(rk,k+1), ldda, dlsticcs, queue );
//magma_device_sync();
magma_dgetvector( 1, &dlsticcs[0], 1, &lsticc, 1, queue );
}
++k;
}
magma_zcopymatrix( 1, k, dAks, 1, dA(offset, 0), ldda+1, queue );
// leave k as the last column done
--k;
*kb = k + 1;
rk = offset + *kb - 1;
/* Apply the block reflector to the rest of the matrix:
A(OFFSET+KB+1:M,KB+1:N) := A(OFFSET+KB+1:M,KB+1:N) - A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)' */
if (*kb < min(n, m - offset)) {
i__1 = m - rk - 1;
i__2 = n - *kb;
magma_zgemm( MagmaNoTrans, MagmaConjTrans, i__1, i__2, *kb,
c_neg_one, dA(rk+1, 0 ), ldda,
dF(*kb, 0 ), lddf,
c_one, dA(rk+1, *kb), ldda, queue );
}
/* Recomputation of difficult columns. */
if ( lsticc > 0 ) {
// printf( " -- recompute dnorms --\n" );
magmablas_dznrm2_check( m-rk-1, n-*kb, dA(rk+1,*kb), ldda,
&vn1[*kb], dlsticcs, queue );
magma_dcopymatrix( n-*kb, 1, &vn1[*kb], *kb, &vn2[*kb], *kb, queue );
}
magma_free( dAks );
magma_free( dlsticcs );
magma_queue_destroy( queue );
return MAGMA_SUCCESS;
} /* magma_zlaqps */
