int main( int argc, char** argv)
{
real_Double_t gflops, gpu_perf, cpu_perf, gpu_time, cpu_time;
float error, work[1];
int transA = MagmaNoTrans;
int transB = MagmaNoTrans;
float Cnorm;
magma_int_t istart = 1024;
magma_int_t iend = 8194;
magma_int_t M, M0 = 0;
magma_int_t N, N0 = 0;
magma_int_t K, K0 = 0;
magma_int_t i;
magma_int_t Am, An, Bm, Bn;
magma_int_t szeA, szeB, szeC;
magma_int_t lda, ldb, ldc, ldda, lddb, lddc;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magmaFloatComplex *h_A, *h_B, *h_C, *h_C2;
magmaFloatComplex_ptr d_A, d_B, d_C;
magmaFloatComplex mzone = MAGMA_C_NEG_ONE;
magmaFloatComplex alpha = MAGMA_C_MAKE( 0.29, -0.86 );
magmaFloatComplex beta = MAGMA_C_MAKE( -0.48, 0.38 );
if (argc != 1){
for(i=1; i<argc; i++){
if ( strcmp("-N", argv[i]) == 0 ){
N0 = atoi(argv[++i]);
}
else if ( strcmp("-M", argv[i]) == 0 ){
M0 = atoi(argv[++i]);
}
else if ( strcmp("-K", argv[i]) == 0 ){
K0 = atoi(argv[++i]);
}
else if (strcmp("-NN", argv[i])==0){
transA = transB = MagmaNoTrans;
}
else if (strcmp("-TT", argv[i])==0){
transA = transB = MagmaTrans;
}
else if (strcmp("-NT", argv[i])==0){
transA = MagmaNoTrans;
transB = MagmaTrans;
}
else if (strcmp("-TN", argv[i])==0){
transA = MagmaTrans;
transB = MagmaNoTrans;
}
#if defined(PRECISION_z) || defined(PRECISION_c)
else if (strcmp("-NC", argv[i])==0){
transA = MagmaNoTrans;
transB = MagmaConjTrans;
}
else if (strcmp("-TC", argv[i])==0){
transA = MagmaTrans;
transB = MagmaConjTrans;
}
else if (strcmp("-CN", argv[i])==0){
transA = MagmaConjTrans;
transB = MagmaNoTrans;
}
else if (strcmp("-CT", argv[i])==0){
transA = MagmaConjTrans;
transB = MagmaTrans;
}
else if (strcmp("-CC", argv[i])==0){
transA = transB = MagmaConjTrans;
}
#endif
}
}
if ( (M0 != 0) && (N0 != 0) && (K0 != 0) )
iend = istart + 1;
M = N = K = iend;
if ( M0 != 0 ) M = M0;
if ( N0 != 0 ) N = N0;
if ( K0 != 0 ) K = K0;
if( transA == MagmaNoTrans ) {
Am = M;
An = K;
} else {
Am = K;
An = M;
}
if( transB == MagmaNoTrans ) {
Bm = K;
Bn = N;
} else {
Bm = N;
Bn = K;
}
/* Initialize */
magma_queue_t queue;
magma_device_t device[ MagmaMaxGPUs ];
int num = 0;
magma_err_t err;
magma_init();
err = magma_get_devices( device, MagmaMaxGPUs, &num );
if ( err != 0 || num < 1 ) {
fprintf( stderr, "magma_get_devices failed: %d\n", err );
exit(-1);
}
err = magma_queue_create( device[0], &queue );
if ( err != 0 ) {
fprintf( stderr, "magma_queue_create failed: %d\n", err );
exit(-1);
}
lda = ldc = M;
ldb = Bm;
ldda = lddc = ((M+31)/32)*32;
lddb = ((ldb+31)/32)*32;
K+=32;
M+=32;
N +=32;
TESTING_MALLOC_CPU( h_A, magmaFloatComplex, lda*K );
TESTING_MALLOC_CPU( h_B, magmaFloatComplex, ldb*Bn );
TESTING_MALLOC_CPU( h_C, magmaFloatComplex, ldc*N );
TESTING_MALLOC_CPU( h_C2, magmaFloatComplex, ldc*N );
TESTING_MALLOC_DEV( d_A, magmaFloatComplex, ldda*K );
TESTING_MALLOC_DEV( d_B, magmaFloatComplex, lddb*Bn );
TESTING_MALLOC_DEV( d_C, magmaFloatComplex, lddc*N );
printf("\nUsage: \n");
printf(" testing_cgemm [-NN|NT|TN|TT] [-N %d] \n\n", 1024);
printf("\n");
printf("Testing transA = %c transB = %c\n", transA, transB);
printf(" M N K clAmdBlas GFLop/s (sec) CPU GFlop/s (sec) error\n");
printf("===========================================================================\n");
for(i=istart; i<iend; i = (int)(i*1.25) )
{
M = N = K = i;
if ( M0 != 0 ) M = M0;
if ( N0 != 0 ) N = N0;
if ( K0 != 0 ) K = K0;
if( transA == MagmaNoTrans ) {
lda = Am = M;
An = K;
} else {
lda = Am = K;
An = M;
}
if( transB == MagmaNoTrans ) {
ldb = Bm = K;
Bn = N;
} else {
ldb = Bm = N;
Bn = K;
}
gflops = FLOPS( (float)M, (float)N, (float)K ) * 1e-9;
ldc = M;
ldda = ((lda+31)/32)*32;
lddb = ((ldb+31)/32)*32;
lddc = ((ldc+31)/32)*32;
szeA = lda * An;
szeB = ldb * Bn;
szeC = ldc * N;
/* Initialize the matrices */
lapackf77_clarnv( &ione, ISEED, &szeA, h_A );
lapackf77_clarnv( &ione, ISEED, &szeB, h_B );
lapackf77_clarnv( &ione, ISEED, &szeC, h_C );
/* =====================================================================
Performs operation using MAGMA-BLAS
=================================================================== */
magma_csetmatrix( Am, An, h_A, 0, lda, d_A, 0, ldda, queue );
magma_csetmatrix( Bm, Bn, h_B, 0, ldb, d_B, 0, lddb, queue );
magma_csetmatrix( M, N, h_C, 0, ldc, d_C, 0, lddc, queue );
magma_cgemm( transA, transB, M, N, K,
alpha, d_A, 0, ldda,
d_B, 0, lddb,
beta, d_C, 0, lddc, queue );
magma_csetmatrix( M, N, h_C, 0, ldc, d_C, 0, lddc, queue );
magma_queue_sync( queue );
gpu_time = magma_wtime();
magma_cgemm( transA, transB, M, N, K,
alpha, d_A, 0, ldda,
d_B, 0, lddb,
beta, d_C, 0, lddc, queue );
magma_queue_sync( queue);
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
magma_cgetmatrix( M, N, d_C, 0, lddc, h_C2, 0, ldc, queue );
/* =====================================================================
Performs operation using CPU-BLAS
=================================================================== */
cpu_time = magma_wtime();
blasf77_cgemm( lapack_const(transA), lapack_const(transB),
&M, &N, &K,
&alpha, h_A, &lda,
h_B, &ldb,
&beta, h_C, &ldc );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
// |C_magma - C_lapack| / |C_lapack|
Cnorm = lapackf77_clange( "M", &M, &N, h_C, &ldc, work );
/* =====================================================================
Error Computation and Performance Compariosn
=================================================================== */
blasf77_caxpy(&szeC, &mzone, h_C, &ione, h_C2, &ione);
error = lapackf77_clange("M", &M, &N, h_C2, &ldc, work)/Cnorm;
printf("%5d %5d %5d %8.2f (%6.2f) %6.2f (%6.2f) %e\n",
M, N, K, gpu_perf, gpu_time, cpu_perf, cpu_time, error);
}
/* Memory clean up */
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_B );
TESTING_FREE_CPU( h_C );
TESTING_FREE_CPU( h_C2 );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_B );
TESTING_FREE_DEV( d_C );
magma_queue_destroy( queue );
magma_finalize();
}
extern "C" magma_int_t
magma_cgehrd2(magma_int_t n, magma_int_t ilo, magma_int_t ihi,
magmaFloatComplex *a, magma_int_t lda,
magmaFloatComplex *tau, magmaFloatComplex *work,
magma_int_t lwork, magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
CGEHRD2 reduces a COMPLEX general matrix A to upper Hessenberg form H by
an orthogonal similarity transformation: Q' * A * Q = H .
Arguments
=========
N (input) INTEGER
The order of the matrix A. N >= 0.
ILO (input) INTEGER
IHI (input) INTEGER
It is assumed that A is already upper triangular in rows
and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
set by a previous call to CGEBAL; otherwise they should be
set to 1 and N respectively. See Further Details.
1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
A (input/output) COMPLEX array, dimension (LDA,N)
On entry, the N-by-N general matrix to be reduced.
On exit, the upper triangle and the first subdiagonal of A
are overwritten with the upper Hessenberg matrix H, and the
elements below the first subdiagonal, with the array TAU,
represent the orthogonal matrix Q as a product of elementary
reflectors. See Further Details.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
TAU (output) COMPLEX array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to
zero.
WORK (workspace/output) COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The length of the array WORK. LWORK >= max(1,N).
For optimum performance LWORK >= N*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 by XERBLA.
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 (ihi-ilo) elementary
reflectors
Q = H(ilo) H(ilo+1) . . . H(ihi-1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
exit in A(i+2:ihi,i), and tau in TAU(i).
The contents of A are illustrated by the following example, with
n = 7, ilo = 2 and ihi = 6:
on entry, on exit,
( a a a a a a a ) ( a a h h h h a )
( a a a a a a ) ( a h h h h a )
( a a a a a a ) ( h h h h h h )
( a a a a a a ) ( v2 h h h h h )
( a a a a a a ) ( v2 v3 h h h h )
( a a a a a a ) ( v2 v3 v4 h h h )
( a ) ( a )
where a denotes an element of the original matrix A, h denotes a
modified element of the upper Hessenberg matrix H, and vi denotes an
element of the vector defining H(i).
This implementation follows the hybrid algorithm and notations described in
S. Tomov and J. Dongarra, "Accelerating the reduction to upper Hessenberg
form through hybrid GPU-based computing," University of Tennessee Computer
Science Technical Report, UT-CS-09-642 (also LAPACK Working Note 219),
May 24, 2009.
===================================================================== */
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_zero = MAGMA_C_ZERO;
magma_int_t nb = magma_get_cgehrd_nb(n);
magma_int_t N = n, ldda = n;
magma_int_t ib;
magma_int_t nh, iws;
magma_int_t nbmin, iinfo;
magma_int_t ldwork;
magma_int_t lquery;
--tau;
*info = 0;
MAGMA_C_SET2REAL( work[0], (float) n * nb );
lquery = lwork == -1;
if (n < 0) {
*info = -1;
} else if (ilo < 1 || ilo > max(1,n)) {
*info = -2;
} else if (ihi < min(ilo,n) || ihi > n) {
*info = -3;
} else if (lda < max(1,n)) {
*info = -5;
} else if (lwork < max(1,n) && ! lquery) {
*info = -8;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
/* Quick return if possible */
nh = ihi - ilo + 1;
if (nh <= 1) {
work[0] = c_one;
return *info;
}
magmaFloatComplex *da;
if (MAGMA_SUCCESS != magma_cmalloc( &da, N*ldda + 2*N*nb + nb*nb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magmaFloatComplex *d_A = da;
magmaFloatComplex *d_work = da + (N+nb)*ldda;
magma_int_t i__;
magmaFloatComplex *t, *d_t;
magma_cmalloc_cpu( &t, nb*nb );
if ( t == NULL ) {
magma_free( da );
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
d_t = d_work + nb * ldda;
czero_nbxnb_block(nb, d_A+N*ldda, ldda);
/* Set elements 1:ILO-1 and IHI:N-1 of TAU to zero */
for (i__ = 1; i__ < ilo; ++i__)
tau[i__] = c_zero;
for (i__ = max(1,ihi); i__ < n; ++i__)
tau[i__] = c_zero;
for(i__=0; i__< nb*nb; i__+=4)
t[i__] = t[i__+1] = t[i__+2] = t[i__+3] = c_zero;
nbmin = 2;
iws = 1;
if (nb > 1 && nb < nh) {
/* Determine when to cross over from blocked to unblocked code
(last block is always handled by unblocked code) */
if (nb < nh) {
/* Determine if workspace is large enough for blocked code */
iws = n * nb;
if (lwork < iws) {
/* Not enough workspace to use optimal NB: determine the
minimum value of NB, and reduce NB or force use of
unblocked code */
nbmin = nb;
if (lwork >= n * nbmin)
nb = lwork / n;
else
nb = 1;
}
}
}
ldwork = n;
if (nb < nbmin || nb >= nh) {
/* Use unblocked code below */
i__ = ilo;
}
else {
/* Use blocked code */
/* Copy the matrix to the GPU */
magma_csetmatrix( N, N-ilo+1, a+(ilo-1)*(lda), lda, d_A, ldda );
for (i__ = ilo; i__ < ihi - nb; i__ += nb) {
/* Computing MIN */
ib = min(nb, ihi - i__);
/* Reduce columns i:i+ib-1 to Hessenberg form, returning the
matrices V and T of the block reflector H = I - V*T*V'
which performs the reduction, and also the matrix Y = A*V*T */
/* Get the current panel (no need for the 1st iteration) */
magma_cgetmatrix( ihi-i__+1, ib,
d_A + (i__ - ilo)*ldda + i__ - 1, ldda,
a + (i__ - 1 )*lda + i__ - 1, lda );
magma_clahr2(ihi, i__, ib,
d_A + (i__ - ilo)*ldda,
d_A + N*ldda + 1,
a + (i__ - 1 )*(lda) , lda,
&tau[i__], t, nb, work, ldwork);
/* Copy T from the CPU to D_T on the GPU */
magma_csetmatrix( nb, nb, t, nb, d_t, nb );
magma_clahru(n, ihi, i__ - 1, ib,
a + (i__ - 1 )*(lda), lda,
d_A + (i__ - ilo)*ldda,
d_A + (i__ - ilo)*ldda + i__ - 1,
d_A + N*ldda, d_t, d_work);
}
}
/* Use unblocked code to reduce the rest of the matrix */
if (!(nb < nbmin || nb >= nh)) {
magma_cgetmatrix( n, n-i__+1,
d_A+ (i__-ilo)*ldda, ldda,
a + (i__-1)*(lda), lda );
}
lapackf77_cgehd2(&n, &i__, &ihi, a, &lda, &tau[1], work, &iinfo);
MAGMA_C_SET2REAL( work[0], (float) iws );
magma_free( da );
magma_free_cpu(t);
return *info;
} /* magma_cgehrd2 */
/**
Purpose
-------
CHEGVX computes selected eigenvalues, and optionally, eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be Hermitian and B is also positive definite.
Eigenvalues and eigenvectors can be selected by specifying either a
range of values or a range of indices for the desired eigenvalues.
Arguments
---------
@param[in]
itype INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x
@param[in]
jobz magma_vec_t
- = MagmaNoVec: Compute eigenvalues only;
- = MagmaVec: Compute eigenvalues and eigenvectors.
@param[in]
range magma_range_t
- = MagmaRangeAll: all eigenvalues will be found.
- = MagmaRangeV: all eigenvalues in the half-open interval (VL,VU]
will be found.
- = MagmaRangeI: the IL-th through IU-th eigenvalues will be found.
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangles of A and B are stored;
- = MagmaLower: Lower triangles of A and B are stored.
@param[in]
n INTEGER
The order of the matrices A and B. N >= 0.
@param[in,out]
A COMPLEX array, dimension (LDA, N)
On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = MagmaLower,
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
\n
On exit, the lower triangle (if UPLO=MagmaLower) or the upper
triangle (if UPLO=MagmaUpper) of A, including the diagonal, is
destroyed.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[in,out]
B COMPLEX array, dimension (LDB, N)
On entry, the Hermitian matrix B. If UPLO = MagmaUpper, the
leading N-by-N upper triangular part of B contains the
upper triangular part of the matrix B. If UPLO = MagmaLower,
the leading N-by-N lower triangular part of B contains
the lower triangular part of the matrix B.
\n
On exit, if INFO <= N, the part of B containing the matrix is
overwritten by the triangular factor U or L from the Cholesky
factorization B = U**H*U or B = L*L**H.
@param[in]
ldb INTEGER
The leading dimension of the array B. LDB >= max(1,N).
@param[in]
vl REAL
@param[in]
vu REAL
If RANGE=MagmaRangeV, the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeI.
@param[in]
il INTEGER
@param[in]
iu INTEGER
If RANGE=MagmaRangeI, the indices (in ascending order) of the
smallest and largest eigenvalues to be returned.
1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeV.
@param[in]
abstol REAL
The absolute error tolerance for the eigenvalues.
An approximate eigenvalue is accepted as converged
when it is determined to lie in an interval [a,b]
of width less than or equal to
\n
ABSTOL + EPS * max( |a|,|b| ),
\n
where EPS is the machine precision. If ABSTOL is less than
or equal to zero, then EPS*|T| will be used in its place,
where |T| is the 1-norm of the tridiagonal matrix obtained
by reducing A to tridiagonal form.
\n
Eigenvalues will be computed most accurately when ABSTOL is
set to twice the underflow threshold 2*SLAMCH('S'), not zero.
If this routine returns with INFO > 0, indicating that some
eigenvectors did not converge, try setting ABSTOL to
2*SLAMCH('S').
@param[out]
m INTEGER
The total number of eigenvalues found. 0 <= M <= N.
If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1.
@param[out]
w REAL array, dimension (N)
The first M elements contain the selected
eigenvalues in ascending order.
@param[out]
Z COMPLEX array, dimension (LDZ, max(1,M))
If JOBZ = MagmaNoVec, then Z is not referenced.
If JOBZ = MagmaVec, then if INFO = 0, the first M columns of Z
contain the orthonormal eigenvectors of the matrix A
corresponding to the selected eigenvalues, with the i-th
column of Z holding the eigenvector associated with W(i).
The eigenvectors are normalized as follows:
if ITYPE = 1 or 2, Z**T*B*Z = I;
if ITYPE = 3, Z**T*inv(B)*Z = I.
\n
If an eigenvector fails to converge, then that column of Z
contains the latest approximation to the eigenvector, and the
index of the eigenvector is returned in IFAIL.
Note: the user must ensure that at least max(1,M) columns are
supplied in the array Z; if RANGE = MagmaRangeV, the exact value of M
is not known in advance and an upper bound must be used.
@param[in]
ldz INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = MagmaVec, LDZ >= max(1,N).
@param[out]
work (workspace) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The length of the array WORK. LWORK >= max(1,2*N).
For optimal efficiency, LWORK >= (NB+1)*N,
where NB is the blocksize for CHETRD returned by ILAENV.
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
@param
rwork (workspace) REAL array, dimension (7*N)
@param
iwork (workspace) INTEGER array, dimension (5*N)
@param[out]
ifail INTEGER array, dimension (N)
If JOBZ = MagmaVec, then if INFO = 0, the first M elements of
IFAIL are zero. If INFO > 0, then IFAIL contains the
indices of the eigenvectors that failed to converge.
If JOBZ = MagmaNoVec, then IFAIL is not referenced.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: CPOTRF or CHEEVX returned an error code:
<= N: if INFO = i, CHEEVX failed to converge;
i eigenvectors failed to converge. Their indices
are stored in array IFAIL.
> N: if INFO = N + i, for 1 <= i <= N, then the leading
minor of order i of B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.
Further Details
---------------
Based on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
@ingroup magma_chegv_driver
********************************************************************/
extern "C" magma_int_t
magma_chegvx(
magma_int_t itype, magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *B, magma_int_t ldb,
float vl, float vu, magma_int_t il, magma_int_t iu, float abstol,
magma_int_t *m, float *w, magmaFloatComplex *Z, magma_int_t ldz,
magmaFloatComplex *work, magma_int_t lwork, float *rwork,
magma_int_t *iwork, magma_int_t *ifail,
magma_int_t *info)
{
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex *dA;
magmaFloatComplex *dB;
magmaFloatComplex *dZ;
magma_int_t ldda = n;
magma_int_t lddb = n;
magma_int_t lddz = n;
magma_int_t lower;
magma_trans_t trans;
magma_int_t wantz;
magma_int_t lquery;
magma_int_t alleig, valeig, indeig;
magma_int_t lwmin;
wantz = (jobz == MagmaVec);
lower = (uplo == MagmaLower);
alleig = (range == MagmaRangeAll);
valeig = (range == MagmaRangeV);
indeig = (range == MagmaRangeI);
lquery = (lwork == -1);
*info = 0;
if (itype < 1 || itype > 3) {
*info = -1;
} else if (! (alleig || valeig || indeig)) {
*info = -2;
} else if (! (wantz || (jobz == MagmaNoVec))) {
*info = -3;
} else if (! (lower || (uplo == MagmaUpper))) {
*info = -4;
} else if (n < 0) {
*info = -5;
} else if (lda < max(1,n)) {
*info = -7;
} else if (ldb < max(1,n)) {
*info = -9;
} else if (ldz < 1 || (wantz && ldz < n)) {
*info = -18;
} else {
if (valeig) {
if (n > 0 && vu <= vl) {
*info = -11;
}
} else if (indeig) {
if (il < 1 || il > max(1,n)) {
*info = -12;
} else if (iu < min(n,il) || iu > n) {
*info = -13;
}
}
}
magma_int_t nb = magma_get_chetrd_nb(n);
lwmin = n * (nb + 1);
work[0] = magma_cmake_lwork( lwmin );
if (lwork < lwmin && ! lquery) {
*info = -20;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info));
return *info;
} else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
return *info;
}
if (MAGMA_SUCCESS != magma_cmalloc( &dA, n*ldda ) ||
MAGMA_SUCCESS != magma_cmalloc( &dB, n*lddb ) ||
MAGMA_SUCCESS != magma_cmalloc( &dZ, n*lddz )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_queue_t queue;
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queue );
/* Form a Cholesky factorization of B. */
magma_csetmatrix( n, n, B, ldb, dB, lddb, queue );
magma_csetmatrix_async( n, n,
A, lda,
dA, ldda, queue );
magma_cpotrf_gpu(uplo, n, dB, lddb, info);
if (*info != 0) {
*info = n + *info;
return *info;
}
magma_queue_sync( queue );
magma_cgetmatrix_async( n, n,
dB, lddb,
B, ldb, queue );
/* Transform problem to standard eigenvalue problem and solve. */
magma_chegst_gpu(itype, uplo, n, dA, ldda, dB, lddb, info);
magma_cheevx_gpu(jobz, range, uplo, n, dA, ldda, vl, vu, il, iu, abstol, m, w, dZ, lddz, A, lda, Z, ldz, work, lwork, rwork, iwork, ifail, info);
if (wantz && *info == 0) {
/* Backtransform eigenvectors to the original problem. */
if (itype == 1 || itype == 2) {
/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
if (lower) {
trans = MagmaConjTrans;
} else {
trans = MagmaNoTrans;
}
magma_ctrsm( MagmaLeft, uplo, trans, MagmaNonUnit, n, *m, c_one, dB, lddb, dZ, lddz, queue );
}
else if (itype == 3) {
/* For B*A*x=(lambda)*x;
backtransform eigenvectors: x = L*y or U'*y */
if (lower) {
trans = MagmaNoTrans;
} else {
trans = MagmaConjTrans;
}
magma_ctrmm( MagmaLeft, uplo, trans, MagmaNonUnit, n, *m, c_one, dB, lddb, dZ, lddz, queue );
}
magma_cgetmatrix( n, *m, dZ, lddz, Z, ldz, queue );
}
magma_queue_sync( queue );
magma_queue_destroy( queue );
magma_free( dA );
magma_free( dB );
magma_free( dZ );
return *info;
} /* magma_chegvx */
/**
Purpose
-------
CHEEVD_GPU computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A. If eigenvectors are desired, it uses a
divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
---------
@param[in]
jobz magma_vec_t
- = MagmaNoVec: Compute eigenvalues only;
- = MagmaVec: Compute eigenvalues and eigenvectors.
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of A is stored;
- = MagmaLower: Lower triangle of A is stored.
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in,out]
dA COMPLEX array on the GPU,
dimension (LDDA, N).
On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = MagmaLower,
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
On exit, if JOBZ = MagmaVec, then if INFO = 0, A contains the
orthonormal eigenvectors of the matrix A.
If JOBZ = MagmaNoVec, then on exit the lower triangle (if UPLO=MagmaLower)
or the upper triangle (if UPLO=MagmaUpper) of A, including the
diagonal, is destroyed.
@param[in]
ldda INTEGER
The leading dimension of the array DA. LDDA >= max(1,N).
@param[out]
w REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
@param
wA (workspace) COMPLEX array, dimension (LDWA, N)
@param[in]
ldwa INTEGER
The leading dimension of the array wA. LDWA >= max(1,N).
@param[out]
work (workspace) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The length of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LWORK >= N + N*NB.
If JOBZ = MagmaVec and N > 1, LWORK >= max( N + N*NB, 2*N + N**2 ).
NB can be obtained through magma_get_chetrd_nb(N).
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
@param[out]
rwork (workspace) REAL array, dimension (LRWORK)
On exit, if INFO = 0, RWORK[0] returns the optimal LRWORK.
@param[in]
lrwork INTEGER
The dimension of the array RWORK.
If N <= 1, LRWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LRWORK >= N.
If JOBZ = MagmaVec and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
\n
If LRWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
@param[out]
iwork (workspace) INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK.
@param[in]
liwork INTEGER
The dimension of the array IWORK.
If N <= 1, LIWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LIWORK >= 1.
If JOBZ = MagmaVec and N > 1, LIWORK >= 3 + 5*N.
\n
If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: if INFO = i and JOBZ = MagmaNoVec, then the algorithm failed
to converge; i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero;
if INFO = i and JOBZ = MagmaVec, then the algorithm failed
to compute an eigenvalue while working on the submatrix
lying in rows and columns INFO/(N+1) through
mod(INFO,N+1).
Further Details
---------------
Based on contributions by
Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
Modified description of INFO. Sven, 16 Feb 05.
@ingroup magma_cheev_driver
********************************************************************/
extern "C" magma_int_t
magma_cheevd_gpu(magma_vec_t jobz, magma_uplo_t uplo,
magma_int_t n,
magmaFloatComplex *dA, magma_int_t ldda,
float *w,
magmaFloatComplex *wA, magma_int_t ldwa,
magmaFloatComplex *work, magma_int_t lwork,
float *rwork, magma_int_t lrwork,
magma_int_t *iwork, magma_int_t liwork,
magma_int_t *info)
{
const char* uplo_ = lapack_uplo_const( uplo );
const char* jobz_ = lapack_vec_const( jobz );
magma_int_t ione = 1;
float d__1;
float eps;
magma_int_t inde;
float anrm;
magma_int_t imax;
float rmin, rmax;
float sigma;
magma_int_t iinfo, lwmin;
magma_int_t lower;
magma_int_t llrwk;
magma_int_t wantz;
magma_int_t indwk2, llwrk2;
magma_int_t iscale;
float safmin;
float bignum;
magma_int_t indtau;
magma_int_t indrwk, indwrk, liwmin;
magma_int_t lrwmin, llwork;
float smlnum;
magma_int_t lquery;
float *dwork;
magmaFloatComplex *dC;
magma_int_t lddc = ldda;
wantz = (jobz == MagmaVec);
lower = (uplo == MagmaLower);
lquery = (lwork == -1 || lrwork == -1 || liwork == -1);
*info = 0;
if (! (wantz || (jobz == MagmaNoVec))) {
*info = -1;
} else if (! (lower || (uplo == MagmaUpper))) {
*info = -2;
} else if (n < 0) {
*info = -3;
} else if (ldda < max(1,n)) {
*info = -5;
} else if (ldwa < max(1,n)) {
*info = -8;
}
magma_int_t nb = magma_get_chetrd_nb( n );
if ( n <= 1 ) {
lwmin = 1;
lrwmin = 1;
liwmin = 1;
}
else if ( wantz ) {
lwmin = max( n + n*nb, 2*n + n*n );
lrwmin = 1 + 5*n + 2*n*n;
liwmin = 3 + 5*n;
}
else {
lwmin = n + n*nb;
lrwmin = n;
liwmin = 1;
}
// multiply by 1+eps (in Double!) to ensure length gets rounded up,
// if it cannot be exactly represented in floating point.
real_Double_t one_eps = 1. + lapackf77_slamch("Epsilon");
work[0] = MAGMA_C_MAKE( lwmin * one_eps, 0.);
rwork[0] = lrwmin * one_eps;
iwork[0] = liwmin;
if ((lwork < lwmin) && !lquery) {
*info = -10;
} else if ((lrwork < lrwmin) && ! lquery) {
*info = -12;
} else if ((liwork < liwmin) && ! lquery) {
*info = -14;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Check if matrix is very small then just call LAPACK on CPU, no need for GPU */
if (n <= 128) {
#ifdef ENABLE_DEBUG
printf("--------------------------------------------------------------\n");
printf(" warning matrix too small N=%d NB=%d, calling lapack on CPU \n", (int) n, (int) nb);
printf("--------------------------------------------------------------\n");
#endif
magmaFloatComplex *A;
magma_cmalloc_cpu( &A, n*n );
magma_cgetmatrix(n, n, dA, ldda, A, n);
lapackf77_cheevd(jobz_, uplo_,
&n, A, &n,
w, work, &lwork,
rwork, &lrwork,
iwork, &liwork, info);
magma_csetmatrix( n, n, A, n, dA, ldda);
magma_free_cpu(A);
return *info;
}
magma_queue_t stream;
magma_queue_create( &stream );
// dC and dwork are never used together, so use one buffer for both;
// unfortunately they're different types (complex and float).
// (this works better in dsyevd_gpu where they're both float).
// n*lddc for chetrd2_gpu, *2 for complex
// n for clanhe
magma_int_t ldwork = n*lddc*2;
if ( wantz ) {
// need 3n^2/2 for cstedx
ldwork = max( ldwork, 3*n*(n/2 + 1) );
}
if (MAGMA_SUCCESS != magma_smalloc( &dwork, ldwork )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
dC = (magmaFloatComplex*) dwork;
/* Get machine constants. */
safmin = lapackf77_slamch("Safe minimum");
eps = lapackf77_slamch("Precision");
smlnum = safmin / eps;
bignum = 1. / smlnum;
rmin = magma_ssqrt(smlnum);
rmax = magma_ssqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = magmablas_clanhe(MagmaMaxNorm, uplo, n, dA, ldda, dwork);
iscale = 0;
sigma = 1;
if (anrm > 0. && anrm < rmin) {
iscale = 1;
sigma = rmin / anrm;
} else if (anrm > rmax) {
iscale = 1;
sigma = rmax / anrm;
}
if (iscale == 1) {
magmablas_clascl(uplo, 0, 0, 1., sigma, n, n, dA, ldda, info);
}
/* Call CHETRD to reduce Hermitian matrix to tridiagonal form. */
// chetrd rwork: e (n)
// cstedx rwork: e (n) + llrwk (1 + 4*N + 2*N**2) ==> 1 + 5n + 2n^2
inde = 0;
indrwk = inde + n;
llrwk = lrwork - indrwk;
// chetrd work: tau (n) + llwork (n*nb) ==> n + n*nb
// cstedx work: tau (n) + z (n^2)
// cunmtr work: tau (n) + z (n^2) + llwrk2 (n or n*nb) ==> 2n + n^2, or n + n*nb + n^2
indtau = 0;
indwrk = indtau + n;
indwk2 = indwrk + n*n;
llwork = lwork - indwrk;
llwrk2 = lwork - indwk2;
magma_timer_t time=0;
timer_start( time );
#ifdef FAST_HEMV
magma_chetrd2_gpu(uplo, n, dA, ldda, w, &rwork[inde],
&work[indtau], wA, ldwa, &work[indwrk], llwork,
dC, n*lddc, &iinfo);
#else
magma_chetrd_gpu (uplo, n, dA, ldda, w, &rwork[inde],
&work[indtau], wA, ldwa, &work[indwrk], llwork, &iinfo);
#endif
timer_stop( time );
timer_printf( "time chetrd_gpu = %6.2f\n", time );
/* For eigenvalues only, call SSTERF. For eigenvectors, first call
CSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
tridiagonal matrix, then call CUNMTR to multiply it to the Householder
transformations represented as Householder vectors in A. */
if (! wantz) {
lapackf77_ssterf(&n, w, &rwork[inde], info);
}
else {
timer_start( time );
magma_cstedx( MagmaRangeAll, n, 0., 0., 0, 0, w, &rwork[inde],
&work[indwrk], n, &rwork[indrwk],
llrwk, iwork, liwork, dwork, info);
timer_stop( time );
timer_printf( "time cstedx = %6.2f\n", time );
timer_start( time );
magma_csetmatrix( n, n, &work[indwrk], n, dC, lddc );
magma_cunmtr_gpu(MagmaLeft, uplo, MagmaNoTrans, n, n, dA, ldda, &work[indtau],
dC, lddc, wA, ldwa, &iinfo);
magma_ccopymatrix( n, n, dC, lddc, dA, ldda );
timer_stop( time );
timer_printf( "time cunmtr_gpu + copy = %6.2f\n", time );
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
if (*info == 0) {
imax = n;
} else {
imax = *info - 1;
}
d__1 = 1. / sigma;
blasf77_sscal(&imax, &d__1, w, &ione);
}
work[0] = MAGMA_C_MAKE( lwmin * one_eps, 0.); // round up
rwork[0] = lrwmin * one_eps;
iwork[0] = liwmin;
magma_queue_destroy( stream );
magma_free( dwork );
return *info;
} /* magma_cheevd_gpu */
/**
Purpose
-------
CLAHRU is an auxiliary MAGMA routine that is used in CGEHRD to update
the trailing sub-matrices after the reductions of the corresponding
panels.
See further details below.
Arguments
---------
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in]
ihi INTEGER
Last row to update. Same as IHI in cgehrd.
@param[in]
k INTEGER
Number of rows of the matrix Am (see details below)
@param[in]
nb INTEGER
Block size
@param[out]
A COMPLEX array, dimension (LDA,N-K)
On entry, the N-by-(N-K) general matrix to be updated. The
computation is done on the GPU. After Am is updated on the GPU
only Am(1:NB) is transferred to the CPU - to update the
corresponding Am matrix. See Further Details below.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[in,out]
dA COMPLEX array on the GPU, dimension (LDDA,N-K).
On entry, the N-by-(N-K) general matrix to be updated.
On exit, the 1st K rows (matrix Am) of A are updated by
applying an orthogonal transformation from the right
Am = Am (I-V T V'), and sub-matrix Ag is updated by
Ag = (I - V T V') Ag (I - V T V(NB+1:)' )
where Q = I - V T V' represent the orthogonal matrix
(as a product of elementary reflectors V) used to reduce
the current panel of A to upper Hessenberg form. After Am
is updated Am(:,1:NB) is sent to the CPU.
See Further Details below.
@param[in]
ldda INTEGER
The leading dimension of the array dA. LDDA >= max(1,N).
@param[in,out]
dY (workspace) COMPLEX array on the GPU, dimension (LDDY, NB).
On entry the (N-K)-by-NB Y = A V. It is used internally
as workspace, so its value is changed on exit.
@param[in]
lddy INTEGER
The leading dimension of the array dY. LDDY >= max(1,N).
@param[in,out]
dV (workspace) COMPLEX array on the GPU, dimension (LDDV, NB).
On entry the (N-K)-by-NB matrix V of elementary reflectors
used to reduce the current panel of A to upper Hessenberg form.
The rest K-by-NB part is used as workspace. V is unchanged on
exit.
@param[in]
lddv INTEGER
The leading dimension of the array dV. LDDV >= max(1,N).
@param[in]
dT COMPLEX array on the GPU, dimension (NB, NB).
On entry the NB-by-NB upper trinagular matrix defining the
orthogonal Hessenberg reduction transformation matrix for
the current panel. The lower triangular part are 0s.
@param
dwork (workspace) COMPLEX array on the GPU, dimension N*NB.
@param[in]
queue magma_queue_t
Queue to execute in.
Further Details
---------------
This implementation follows the algorithm and notations described in:
S. Tomov and J. Dongarra, "Accelerating the reduction to upper Hessenberg
form through hybrid GPU-based computing," University of Tennessee Computer
Science Technical Report, UT-CS-09-642 (also LAPACK Working Note 219),
May 24, 2009.
The difference is that here Am is computed on the GPU.
M is renamed Am, G is renamed Ag.
@ingroup magma_cgeev_aux
********************************************************************/
extern "C" magma_int_t
magma_clahru(
magma_int_t n, magma_int_t ihi, magma_int_t k, magma_int_t nb,
magmaFloatComplex *A, magma_int_t lda,
magmaFloatComplex_ptr dA, magma_int_t ldda,
magmaFloatComplex_ptr dY, magma_int_t lddy,
magmaFloatComplex_ptr dV, magma_int_t lddv,
magmaFloatComplex_ptr dT,
magmaFloatComplex_ptr dwork,
magma_queue_t queue )
{
#define dA(i_,j_) (dA + (i_) + (j_)*ldda)
magmaFloatComplex c_zero = MAGMA_C_ZERO;
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex *dYm = dV + ihi - k;
magma_int_t info = 0;
if (n < 0) {
info = -1;
} else if (ihi < 0 || ihi > n) {
info = -2;
} else if (k < 0 || k > n) {
info = -3;
} else if (nb < 1 || nb > n) {
info = -4;
} else if (lda < max(1,n)) {
info = -6;
} else if (ldda < max(1,n)) {
info = -8;
} else if (lddy < max(1,n)) {
info = -10;
} else if (lddv < max(1,n)) {
info = -12;
}
if (info != 0) {
magma_xerbla( __func__, -(info) );
return info;
}
// top part of Y, above panel, hasn't been computed yet, so do that now
// Ym = Am V = A(0:k-1, 0:ihi-k-1) * V(0:ihi-k-1, 0:nb-1)
magma_cgemm( MagmaNoTrans, MagmaNoTrans, k, nb, ihi-k,
c_one, dA, ldda,
dV, lddv,
c_zero, dYm, ldda, queue );
// -----
// on right, A := A Q = A - A V T V'
// Update Am = Am - Am V T V' = Am - Ym W', with W = V T'
// W = V T' = V(0:ihi-k-1, 0:nb-1) * T(0:nb-1, 0:nb-1)'
magma_cgemm( MagmaNoTrans, MagmaConjTrans, ihi-k, nb, nb,
c_one, dV, lddv,
dT, nb,
c_zero, dwork, ldda, queue );
// Am = Am - Ym W' = A(0:k-1, 0:ihi-k-1) - Ym(0:k-1, 0:nb-1) * W(0:ihi-k-1, 0:nb-1)'
magma_cgemm( MagmaNoTrans, MagmaConjTrans, k, ihi-k, nb,
c_neg_one, dYm, ldda,
dwork, ldda,
c_one, dA, ldda, queue );
// copy first nb columns of Am, A(0:k-1, 0:nb-1), to host
magma_cgetmatrix( k, nb, dA, ldda, A, lda, queue );
// -----
// on right, A := A Q = A - A V T V'
// Update Ag = Ag - Ag V T V' = Ag - Y W'
// Ag = Ag - Y W' = A(k:ihi-1, nb:ihi-k-1) - Y(0:ihi-k-1, 0:nb-1) * W(nb:ihi-k-1, 0:nb-1)'
magma_cgemm( MagmaNoTrans, MagmaConjTrans, ihi-k, ihi-k-nb, nb,
c_neg_one, dY, ldda,
dwork + nb, ldda,
c_one, dA(k,nb), ldda, queue );
// -----
// on left, A := Q' A = A - V T' V' A
// Ag2 = Ag2 - V T' V' Ag2 = W Yg, with W = V T' and Yg = V' Ag2
// Note that Ag is A(k:ihi, nb+1:ihi-k)
// while Ag2 is A(k:ihi, nb+1: n -k)
// Z = V(0:ihi-k-1, 0:nb-1)' * A(k:ihi-1, nb:n-k-1); Z is stored over Y
magma_cgemm( MagmaConjTrans, MagmaNoTrans, nb, n-k-nb, ihi-k,
c_one, dV, lddv,
dA(k,nb), ldda,
c_zero, dY, nb, queue );
// Ag2 = Ag2 - W Z = A(k:ihi-1, nb:n-k-1) - W(nb:n-k-1, 0:nb-1) * Z(0:nb-1, nb:n-k-1)
magma_cgemm( MagmaNoTrans, MagmaNoTrans, ihi-k, n-k-nb, nb,
c_neg_one, dwork, ldda,
dY, nb,
c_one, dA(k,nb), ldda, queue );
return info;
}
/**
Purpose
-------
Solves a system of linear equations
A * X = B, A**T * X = B, or A**H * X = B
with a general N-by-N matrix A using the LU factorization computed by CGETRF_GPU.
Arguments
---------
@param[in]
trans magma_trans_t
Specifies the form of the system of equations:
- = MagmaNoTrans: A * X = B (No transpose)
- = MagmaTrans: A**T * X = B (Transpose)
- = MagmaConjTrans: A**H * X = B (Conjugate transpose)
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in]
nrhs INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
@param[in]
dA COMPLEX array on the GPU, dimension (LDA,N)
The factors L and U from the factorization A = P*L*U as computed
by CGETRF_GPU.
@param[in]
ldda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[in]
ipiv INTEGER array, dimension (N)
The pivot indices from CGETRF; for 1 <= i <= N, row i of the
matrix was interchanged with row IPIV(i).
@param[in,out]
dB COMPLEX array on the GPU, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
@param[in]
lddb INTEGER
The leading dimension of the array B. LDB >= max(1,N).
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_cgesv_comp
********************************************************************/
extern "C" magma_int_t
magma_cgetrs_gpu(magma_trans_t trans, magma_int_t n, magma_int_t nrhs,
magmaFloatComplex *dA, magma_int_t ldda,
magma_int_t *ipiv,
magmaFloatComplex *dB, magma_int_t lddb,
magma_int_t *info)
{
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex *work = NULL;
int notran = (trans == MagmaNoTrans);
magma_int_t i1, i2, inc;
*info = 0;
if ( (! notran) &&
(trans != MagmaTrans) &&
(trans != MagmaConjTrans) ) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (nrhs < 0) {
*info = -3;
} else if (ldda < max(1,n)) {
*info = -5;
} else if (lddb < max(1,n)) {
*info = -8;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (n == 0 || nrhs == 0) {
return *info;
}
magma_cmalloc_cpu( &work, n * nrhs );
if ( work == NULL ) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
i1 = 1;
i2 = n;
if (notran) {
inc = 1;
/* Solve A * X = B. */
magma_cgetmatrix( n, nrhs, dB, lddb, work, n );
lapackf77_claswp(&nrhs, work, &n, &i1, &i2, ipiv, &inc);
magma_csetmatrix( n, nrhs, work, n, dB, lddb );
if ( nrhs == 1) {
magma_ctrsv(MagmaLower, MagmaNoTrans, MagmaUnit, n, dA, ldda, dB, 1 );
magma_ctrsv(MagmaUpper, MagmaNoTrans, MagmaNonUnit, n, dA, ldda, dB, 1 );
} else {
magma_ctrsm(MagmaLeft, MagmaLower, MagmaNoTrans, MagmaUnit, n, nrhs, c_one, dA, ldda, dB, lddb );
magma_ctrsm(MagmaLeft, MagmaUpper, MagmaNoTrans, MagmaNonUnit, n, nrhs, c_one, dA, ldda, dB, lddb );
}
} else {
inc = -1;
/* Solve A**T * X = B or A**H * X = B. */
if ( nrhs == 1) {
magma_ctrsv(MagmaUpper, trans, MagmaNonUnit, n, dA, ldda, dB, 1 );
magma_ctrsv(MagmaLower, trans, MagmaUnit, n, dA, ldda, dB, 1 );
} else {
magma_ctrsm(MagmaLeft, MagmaUpper, trans, MagmaNonUnit, n, nrhs, c_one, dA, ldda, dB, lddb );
magma_ctrsm(MagmaLeft, MagmaLower, trans, MagmaUnit, n, nrhs, c_one, dA, ldda, dB, lddb );
}
magma_cgetmatrix( n, nrhs, dB, lddb, work, n );
lapackf77_claswp(&nrhs, work, &n, &i1, &i2, ipiv, &inc);
magma_csetmatrix( n, nrhs, work, n, dB, lddb );
}
magma_free_cpu(work);
return *info;
}
int main( int argc, char** argv)
{
real_Double_t gflops, gpu_perf, cpu_perf, gpu_time, cpu_time;
magmaFloatComplex *h_R = NULL, *h_P = NULL;
magmaFloatComplex_ptr d_lA[MagmaMaxSubs * MagmaMaxGPUs];
magma_int_t N = 0, n2, lda, ldda;
magma_int_t size[10] =
{ 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000 };
magma_int_t i, j, k, check = 0, info;
magmaFloatComplex mz_one = MAGMA_C_NEG_ONE;
magma_int_t ione = 1;
magma_int_t num_gpus0 = 1, num_gpus, num_subs0 = 1, num_subs, tot_subs, flag = 0;
int nb, n_local, nk;
magma_uplo_t uplo = MagmaLower;
if (argc != 1){
for(i = 1; i<argc; i++){
if (strcmp("-N", argv[i]) == 0){
N = atoi(argv[++i]);
if (N > 0) {
size[0] = size[9] = N;
flag = 1;
}
}
if(strcmp("-NGPU", argv[i]) == 0)
num_gpus0 = atoi(argv[++i]);
if(strcmp("-NSUB", argv[i]) == 0)
num_subs0 = atoi(argv[++i]);
if(strcmp("-UPLO", argv[i]) == 0)
uplo = (strcmp("L", argv[++i]) == 0 ? MagmaLower : MagmaUpper);
if(strcmp("-check", argv[i]) == 0)
check = 1;
}
}
/* Initialize */
magma_queue_t queues[2*MagmaMaxGPUs];
magma_device_t devices[ MagmaMaxGPUs ];
int num = 0;
magma_err_t err;
magma_init();
err = magma_get_devices( devices, MagmaMaxGPUs, &num );
if ( err != 0 || num < 1 ) {
fprintf( stderr, "magma_get_devices failed: %d\n", err );
exit(-1);
}
for(i=0;i<num_gpus0;i++){
err = magma_queue_create( devices[i], &queues[2*i] );
if ( err != 0 ) {
fprintf( stderr, "magma_queue_create failed: %d\n", err );
exit(-1);
}
err = magma_queue_create( devices[i], &queues[2*i+1] );
if ( err != 0 ) {
fprintf( stderr, "magma_queue_create failed: %d\n", err );
exit(-1);
}
}
printf("\nUsing %d GPUs:\n", num_gpus0);
printf(" testing_cpotrf_msub -N %d -NGPU %d -NSUB %d -UPLO %c %s\n\n", size[0], num_gpus0,num_subs0,
(uplo == MagmaLower ? 'L' : 'U'),(check == 1 ? "-check" : " "));
printf(" N CPU GFlop/s (sec) GPU GFlop/s (sec) ||R_magma-R_lapack||_F / ||R_lapack||_F\n");
printf("========================================================================================\n");
for(i=0; i<10; i++){
N = size[i];
lda = N;
n2 = lda*N;
gflops = FLOPS_CPOTRF( N ) / 1e9;;
nb = magma_get_cpotrf_nb(N);
if (num_subs0*num_gpus0 > N/nb) {
num_gpus = N/nb;
num_subs = 1;
if(N%nb != 0) num_gpus ++;
printf("too many GPUs for the matrix size, using %d GPUs\n", (int)num_gpus);
} else {
num_gpus = num_gpus0;
num_subs = num_subs0;
}
tot_subs = num_subs * num_gpus;
/* Allocate host memory for the matrix */
#ifdef USE_PINNED_CLMEMORY
cl_mem buffer1 = clCreateBuffer(gContext, CL_MEM_READ_WRITE | CL_MEM_ALLOC_HOST_PTR, n2*sizeof(magmaFloatComplex), NULL, NULL);
cl_mem buffer2 = clCreateBuffer(gContext, CL_MEM_READ_WRITE | CL_MEM_ALLOC_HOST_PTR, lda*nb*sizeof(magmaFloatComplex), NULL, NULL);
for (k=0; k<num_gpus; k++) {
h_R = (magmaFloatComplex*)clEnqueueMapBuffer(queues[2*k], buffer1, CL_TRUE, CL_MAP_READ | CL_MAP_WRITE, 0,
n2*sizeof(magmaFloatComplex), 0, NULL, NULL, NULL);
h_P = (magmaFloatComplex*)clEnqueueMapBuffer(queues[2*k], buffer2, CL_TRUE, CL_MAP_READ | CL_MAP_WRITE, 0,
lda*nb*sizeof(magmaFloatComplex), 0, NULL, NULL, NULL);
}
#else
TESTING_MALLOC_PIN( h_P, magmaFloatComplex, lda*nb );
TESTING_MALLOC_PIN( h_R, magmaFloatComplex, n2 );
#endif
/* Initialize the matrix */
init_matrix( N, h_R, lda );
/* Allocate GPU memory */
if (uplo == MagmaUpper) {
ldda = ((N+nb-1)/nb)*nb;
n_local = ((N+nb*tot_subs-1)/(nb*tot_subs))*nb;
} else {
ldda = ((N+nb*tot_subs-1)/(nb*tot_subs))*nb;
n_local = ((N+nb-1)/nb)*nb;
}
for (j=0; j<tot_subs; j++) {
TESTING_MALLOC_DEV( d_lA[j], magmaFloatComplex, n_local*ldda );
}
/* Warm up to measure the performance */
/* distribute matrix to gpus */
if (uplo == MagmaUpper) {
for (j=0; j<N; j+=nb) {
k = (j/nb)%tot_subs;
nk = min(nb, N-j);
magma_csetmatrix(j+nk, nk,
&h_R[j*lda], 0, lda,
d_lA[k], j/(nb*tot_subs)*nb*ldda, ldda,
queues[2*(k%num_gpus)]);
}
} else {
for (j=0; j<N; j+=nb) {
nk = min(nb, N-j);
for (int kk = 0; kk<tot_subs; kk++) {
int mk = 0;
for (int ii=j+kk*nb; ii<N; ii+=nb*tot_subs) {
int mii = min(nb, N-ii);
lapackf77_clacpy( MagmaFullStr, &mii, &nk, &h_R[ii+j*lda], &lda, &h_P[mk], &lda );
mk += mii;
}
k = ((j+kk*nb)/nb)%tot_subs;
if (mk > 0 && nk > 0) {
magma_csetmatrix(mk, nk,
h_P, 0, lda,
d_lA[k], j*ldda+(j+kk*nb)/(nb*tot_subs)*nb, ldda,
queues[2*(k%num_gpus)]);
}
}
}
/*for (j=0; j<N; j+=nb) {
k = (j/nb)%tot_subs;
nk = min(nb, N-j);
magma_csetmatrix(nk, j+nk, &h_R[j], 0, lda,
d_lA[k], j/(nb*tot_subs)*nb, ldda,
queues[2*(k%num_gpus)]);
}*/
}
magma_cpotrf_msub( num_subs, num_gpus, uplo, N, d_lA, 0, ldda, &info, queues );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
/* distribute matrix to gpus */
if (uplo == MagmaUpper) {
for (j=0; j<N; j+=nb) {
k = (j/nb)%tot_subs;
nk = min(nb, N-j);
magma_csetmatrix(j+nk, nk,
&h_R[j*lda], 0, lda,
d_lA[k], j/(nb*tot_subs)*nb*ldda, ldda,
queues[2*(k%num_gpus)]);
}
} else {
for (j=0; j<N; j+=nb) {
nk = min(nb, N-j);
for (int kk = 0; kk<tot_subs; kk++) {
int mk = 0;
for (int ii=j+kk*nb; ii<N; ii+=nb*tot_subs) {
int mii = min(nb, N-ii);
lapackf77_clacpy( MagmaFullStr, &mii, &nk, &h_R[ii+j*lda], &lda, &h_P[mk], &lda );
mk += mii;
}
k = ((j+kk*nb)/nb)%tot_subs;
if (mk > 0 && nk > 0) {
magma_csetmatrix(mk, nk,
h_P, 0, lda,
d_lA[k], j*ldda+(j+kk*nb)/(nb*tot_subs)*nb, ldda,
queues[2*(k%num_gpus)]);
}
}
}
/*for (j=0; j<N; j+=nb) {
k = (j/nb)%tot_subs;
nk = min(nb, N-j);
magma_csetmatrix(nk, j+nk, &h_R[j], 0, lda,
d_lA[k], (j/(nb*tot_subs)*nb), ldda,
queues[2*(k%num_gpus)]);
}*/
}
gpu_time = magma_wtime();
magma_cpotrf_msub( num_subs, num_gpus, uplo, N, d_lA, 0, ldda, &info, queues );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf( "magma_cpotrf had error %d.\n", info );
/* gather matrix from gpus */
if (uplo==MagmaUpper) {
for (j=0; j<N; j+=nb) {
k = (j/nb)%tot_subs;
nk = min(nb, N-j);
magma_cgetmatrix(j+nk, nk,
d_lA[k], j/(nb*tot_subs)*nb*ldda, ldda,
&h_R[j*lda], 0, lda, queues[2*(k%num_gpus)]);
}
} else {
for (j=0; j<N; j+=nb) {
nk = min(nb, N-j);
for (int kk = 0; kk<tot_subs; kk++) {
k = ((j+kk*nb)/nb)%tot_subs;
int mk = 0;
mk = 0;
for (int ii=j+kk*nb; ii<N; ii+=nb*tot_subs) {
mk += min(nb, N-ii);
}
if (mk > 0 && nk > 0) {
magma_cgetmatrix(mk, nk,
d_lA[k], j*ldda+(j+kk*nb)/(nb*tot_subs)*nb, ldda,
h_P, 0, lda,
queues[2*(k%num_gpus)]);
}
mk = 0;
for (int ii=j+kk*nb; ii<N; ii+=nb*tot_subs) {
int mii = min(nb, N-ii);
lapackf77_clacpy( MagmaFullStr, &mii, &nk, &h_P[mk], &lda, &h_R[ii+j*lda], &lda );
mk += mii;
}
}
}
/*for (j=0; j<N; j+=nb) {
k = (j/nb)%tot_subs;
nk = min(nb, N-j);
magma_cgetmatrix( nk, j+nk,
d_lA[k], (j/(nb*tot_subs)*nb), ldda,
&h_R[j], 0, lda, queues[2*(k%num_gpus)] );
}*/
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if (check == 1) {
float work[1], matnorm, diffnorm;
magmaFloatComplex *h_A;
TESTING_MALLOC_PIN( h_A, magmaFloatComplex, n2 );
init_matrix( N, h_A, lda );
cpu_time = magma_wtime();
if (uplo == MagmaLower) {
lapackf77_cpotrf( MagmaLowerStr, &N, h_A, &lda, &info );
} else {
lapackf77_cpotrf( MagmaUpperStr, &N, h_A, &lda, &info );
}
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf( "lapackf77_cpotrf had error %d.\n", info );
/* =====================================================================
Check the result compared to LAPACK
|R_magma - R_lapack| / |R_lapack|
=================================================================== */
matnorm = lapackf77_clange("f", &N, &N, h_A, &lda, work);
blasf77_caxpy(&n2, &mz_one, h_A, &ione, h_R, &ione);
diffnorm = lapackf77_clange("f", &N, &N, h_R, &lda, work);
printf( "%5d %6.2f (%6.2f) %6.2f (%6.2f) %e\n",
N, cpu_perf, cpu_time, gpu_perf, gpu_time, diffnorm / matnorm );
TESTING_FREE_PIN( h_A );
} else {
printf( "%5d - - (- -) %6.2f (%6.2f) - -\n",
N, gpu_perf, gpu_time );
}
// free memory
#ifdef USE_PINNED_CLMEMORY
for (k=0; k<num_gpus; k++) {
clEnqueueUnmapMemObject(queues[2*k], buffer1, h_R, 0, NULL, NULL);
clEnqueueUnmapMemObject(queues[2*k], buffer2, h_P, 0, NULL, NULL);
}
clReleaseMemObject(buffer1);
clReleaseMemObject(buffer2);
#else
TESTING_FREE_PIN( h_P );
TESTING_FREE_PIN( h_R );
#endif
for (j=0; j<tot_subs; j++) {
TESTING_FREE_DEV( d_lA[j] );
}
if (flag != 0)
break;
}
/* clean up */
for (i=0; i<num_gpus; i++) {
magma_queue_destroy( queues[2*i] );
magma_queue_destroy( queues[2*i+1] );
}
magma_finalize();
return 0;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing cgetrf_batched
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, magma_perf, magma_time, cublas_perf=0., cublas_time=0., cpu_perf=0, cpu_time=0;
float error;
magma_int_t cublas_enable = 0;
magmaFloatComplex *h_A, *h_R;
magmaFloatComplex *dA_magma;
magmaFloatComplex **dA_array = NULL;
magma_int_t **dipiv_array = NULL;
magma_int_t *ipiv, *cpu_info;
magma_int_t *dipiv_magma, *dinfo_magma;
magma_int_t M, N, n2, lda, ldda, min_mn, info;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t batchCount;
magma_int_t status = 0;
magma_opts opts( MagmaOptsBatched );
opts.parse_opts( argc, argv );
//opts.lapack |= opts.check;
batchCount = opts.batchcount;
magma_int_t columns;
float tol = opts.tolerance * lapackf77_slamch("E");
printf("%% BatchCount M N CPU Gflop/s (ms) MAGMA Gflop/s (ms) CUBLAS Gflop/s (ms) ||PA-LU||/(||A||*N)\n");
printf("%%==========================================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[itest];
N = opts.nsize[itest];
min_mn = min(M, N);
lda = M;
n2 = lda*N * batchCount;
ldda = magma_roundup( M, opts.align ); // multiple of 32 by default
gflops = FLOPS_CGETRF( M, N ) / 1e9 * batchCount;
TESTING_MALLOC_CPU( cpu_info, magma_int_t, batchCount );
TESTING_MALLOC_CPU( ipiv, magma_int_t, min_mn * batchCount );
TESTING_MALLOC_CPU( h_A, magmaFloatComplex, n2 );
TESTING_MALLOC_CPU( h_R, magmaFloatComplex, n2 );
TESTING_MALLOC_DEV( dA_magma, magmaFloatComplex, ldda*N * batchCount );
TESTING_MALLOC_DEV( dipiv_magma, magma_int_t, min_mn * batchCount );
TESTING_MALLOC_DEV( dinfo_magma, magma_int_t, batchCount );
TESTING_MALLOC_DEV( dA_array, magmaFloatComplex*, batchCount );
TESTING_MALLOC_DEV( dipiv_array, magma_int_t*, batchCount );
/* Initialize the matrix */
lapackf77_clarnv( &ione, ISEED, &n2, h_A );
// make A diagonally dominant, to not need pivoting
for( int s=0; s < batchCount; ++s ) {
for( int i=0; i < min_mn; ++i ) {
h_A[ i + i*lda + s*lda*N ] = MAGMA_C_MAKE(
MAGMA_C_REAL( h_A[ i + i*lda + s*lda*N ] ) + N,
MAGMA_C_IMAG( h_A[ i + i*lda + s*lda*N ] ));
}
}
columns = N * batchCount;
lapackf77_clacpy( MagmaFullStr, &M, &columns, h_A, &lda, h_R, &lda );
magma_csetmatrix( M, columns, h_R, lda, dA_magma, ldda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
magma_cset_pointer( dA_array, dA_magma, ldda, 0, 0, ldda*N, batchCount, opts.queue );
magma_time = magma_sync_wtime( opts.queue );
info = magma_cgetrf_nopiv_batched( M, N, dA_array, ldda, dinfo_magma, batchCount, opts.queue);
magma_time = magma_sync_wtime( opts.queue ) - magma_time;
magma_perf = gflops / magma_time;
// check correctness of results throught "dinfo_magma" and correctness of argument throught "info"
magma_getvector( batchCount, sizeof(magma_int_t), dinfo_magma, 1, cpu_info, 1);
for (int i=0; i < batchCount; i++)
{
if (cpu_info[i] != 0 ) {
printf("magma_cgetrf_batched matrix %d returned internal error %d\n", i, (int)cpu_info[i] );
}
}
if (info != 0) {
printf("magma_cgetrf_batched returned argument error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
for (int i=0; i < batchCount; i++) {
lapackf77_cgetrf(&M, &N, h_A + i*lda*N, &lda, ipiv + i * min_mn, &info);
assert( info == 0 );
}
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0) {
printf("lapackf77_cgetrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
}
/* =====================================================================
Check the factorization
=================================================================== */
if ( opts.lapack ) {
printf("%10d %5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %7.2f (%7.2f)",
(int) batchCount, (int) M, (int) N, cpu_perf, cpu_time*1000., magma_perf, magma_time*1000., cublas_perf*cublas_enable, cublas_time*1000.*cublas_enable );
}
else {
printf("%10d %5d %5d --- ( --- ) %7.2f (%7.2f) %7.2f (%7.2f)",
(int) batchCount, (int) M, (int) N, magma_perf, magma_time*1000., cublas_perf*cublas_enable, cublas_time*1000.*cublas_enable );
}
if ( opts.check ) {
// initialize ipiv to 1, 2, 3, ...
for (int i=0; i < batchCount; i++)
{
for (int k=0; k < min_mn; k++) {
ipiv[i*min_mn+k] = k+1;
}
}
magma_cgetmatrix( M, N*batchCount, dA_magma, ldda, h_A, lda );
error = 0;
for (int i=0; i < batchCount; i++)
{
float err;
err = get_LU_error( M, N, h_R + i * lda*N, lda, h_A + i * lda*N, ipiv + i * min_mn);
if ( isnan(err) || isinf(err) ) {
error = err;
break;
}
error = max( err, error );
}
bool okay = (error < tol);
status += ! okay;
printf(" %8.2e %s\n", error, (okay ? "ok" : "failed") );
}
else {
printf(" --- \n");
}
TESTING_FREE_CPU( cpu_info );
TESTING_FREE_CPU( ipiv );
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_R );
TESTING_FREE_DEV( dA_magma );
TESTING_FREE_DEV( dinfo_magma );
TESTING_FREE_DEV( dipiv_magma );
TESTING_FREE_DEV( dipiv_array );
TESTING_FREE_DEV( dA_array );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing clarfb_gpu
*/
int main( int argc, char** argv )
{
TESTING_CUDA_INIT();
cuFloatComplex c_zero = MAGMA_C_ZERO;
cuFloatComplex c_one = MAGMA_C_ONE;
cuFloatComplex c_neg_one = MAGMA_C_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
cuFloatComplex *C, *R, *V, *T, *W;
TESTING_MALLOC( C, cuFloatComplex, ldc*n );
TESTING_MALLOC( R, cuFloatComplex, ldc*n );
TESTING_MALLOC( V, cuFloatComplex, ldv*k );
TESTING_MALLOC( T, cuFloatComplex, ldt*k );
TESTING_MALLOC( W, cuFloatComplex, ldw*k );
cuFloatComplex *dC, *dV, *dT, *dW;
TESTING_DEVALLOC( dC, cuFloatComplex, ldc*n );
TESTING_DEVALLOC( dV, cuFloatComplex, ldv*k );
TESTING_DEVALLOC( dT, cuFloatComplex, ldt*k );
TESTING_DEVALLOC( dW, cuFloatComplex, ldw*k );
magma_int_t size;
magma_int_t iseed[4] = { 1, 2, 3, 4 };
float error, work[1];
// test all combinations of input parameters
const char* side[] = { MagmaLeftStr, MagmaRightStr };
const char* trans[] = { MagmaConjTransStr, 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_clarnv( &ione, iseed, &size, C );
//printf( "C=" ); magma_cprint( 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_clarnv( &ione, iseed, &size, V );
if ( *storev[istor] == MagmaColumnwise ) {
if ( *direct[idir] == MagmaForward ) {
lapackf77_claset( MagmaUpperStr, &k, &k, &c_zero, &c_one, V, &ldv );
}
else {
lapackf77_claset( 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_claset( MagmaLowerStr, &k, &k, &c_zero, &c_one, V, &ldv );
}
else {
lapackf77_claset( MagmaUpperStr, &k, &k, &c_zero, &c_one, &V[(nv-k)*ldv], &ldv );
}
}
//printf( "# ldv %d, nv %d\n", ldv, nv );
//printf( "V=" ); magma_cprint( 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_clarnv( &ione, iseed, &size, T );
if ( *direct[idir] == MagmaForward ) {
lapackf77_claset( MagmaLowerStr, &k1, &k1, &c_zero, &c_zero, &T[1], &ldt );
}
else {
lapackf77_claset( MagmaUpperStr, &k1, &k1, &c_zero, &c_zero, &T[1*ldt], &ldt );
}
//printf( "T=" ); magma_cprint( k, k, T, ldt );
magma_csetmatrix( m, n, C, ldc, dC, ldc );
magma_csetmatrix( ldv, nv, V, ldv, dV, ldv );
magma_csetmatrix( k, k, T, ldt, dT, ldt );
lapackf77_clarfb( side[iside], trans[itran], direct[idir], storev[istor],
&m, &n, &k,
V, &ldv, T, &ldt, C, &ldc, W, &ldw );
//printf( "HC=" ); magma_cprint( m, n, C, ldc );
magma_clarfb_gpu( *side[iside], *trans[itran], *direct[idir], *storev[istor],
m, n, k,
dV, ldv, dT, ldt, dC, ldc, dW, ldw );
magma_cgetmatrix( m, n, dC, ldc, R, ldc );
//printf( "dHC=" ); magma_cprint( m, n, R, ldc );
// compute relative error |HC_magma - HC_lapack| / |HC_lapack|
error = lapackf77_clange( "Fro", &m, &n, C, &ldc, work );
size = ldc*n;
blasf77_caxpy( &size, &c_neg_one, C, &ione, R, &ione );
error = lapackf77_clange( "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;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing cgegqr
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
float e, e1, e2, e3, e4, e5, *work;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_zero = MAGMA_C_ZERO;
magmaFloatComplex *h_A, *h_R, *tau, *dtau, *h_work, *h_rwork, tmp[1];
magmaFloatComplex_ptr d_A, dwork;
magma_int_t M, N, n2, lda, ldda, lwork, info, min_mn;
magma_int_t ione = 1, ldwork;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
opts.lapack |= opts.check; // check (-c) implies lapack (-l)
// versions 1...4 are valid
if (opts.version < 1 || opts.version > 4) {
printf("Unknown version %d; exiting\n", (int) opts.version );
return -1;
}
float tol = 10. * opts.tolerance * lapackf77_slamch("E");
printf("version %d\n", (int) opts.version );
printf(" M N CPU GFlop/s (ms) GPU GFlop/s (ms) ||I-Q'Q||_F / M ||I-Q'Q||_I / M ||A-Q R||_I\n");
printf(" MAGMA / LAPACK MAGMA / LAPACK\n");
printf("==========================================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[itest];
N = opts.nsize[itest];
if (N > 128) {
printf("%5d %5d skipping because cgegqr requires N <= 128\n",
(int) M, (int) N);
continue;
}
if (M < N) {
printf("%5d %5d skipping because cgegqr requires M >= N\n",
(int) M, (int) N);
continue;
}
min_mn = min(M, N);
lda = M;
n2 = lda*N;
ldda = ((M+31)/32)*32;
gflops = FLOPS_CGEQRF( M, N ) / 1e9 + FLOPS_CUNGQR( M, N, N ) / 1e9;
// query for workspace size
lwork = -1;
lapackf77_cgeqrf(&M, &N, NULL, &M, NULL, tmp, &lwork, &info);
lwork = (magma_int_t)MAGMA_C_REAL( tmp[0] );
lwork = max(lwork, 3*N*N);
ldwork = N*N;
if (opts.version == 2) {
ldwork = 3*N*N + min_mn + 2;
}
TESTING_MALLOC_PIN( tau, magmaFloatComplex, min_mn );
TESTING_MALLOC_PIN( h_work, magmaFloatComplex, lwork );
TESTING_MALLOC_PIN(h_rwork, magmaFloatComplex, lwork );
TESTING_MALLOC_CPU( h_A, magmaFloatComplex, n2 );
TESTING_MALLOC_CPU( h_R, magmaFloatComplex, n2 );
TESTING_MALLOC_CPU( work, float, M );
TESTING_MALLOC_DEV( d_A, magmaFloatComplex, ldda*N );
TESTING_MALLOC_DEV( dtau, magmaFloatComplex, min_mn );
TESTING_MALLOC_DEV( dwork, magmaFloatComplex, ldwork );
/* Initialize the matrix */
lapackf77_clarnv( &ione, ISEED, &n2, h_A );
lapackf77_clacpy( MagmaUpperLowerStr, &M, &N, h_A, &lda, h_R, &lda );
magma_csetmatrix( M, N, h_R, lda, d_A, ldda );
// warmup
if ( opts.warmup ) {
magma_cgegqr_gpu( 1, M, N, d_A, ldda, dwork, h_work, &info );
magma_csetmatrix( M, N, h_R, lda, d_A, ldda );
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_sync_wtime( 0 );
magma_cgegqr_gpu( opts.version, M, N, d_A, ldda, dwork, h_rwork, &info );
gpu_time = magma_sync_wtime( 0 ) - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_cgegqr returned error %d: %s.\n",
(int) info, magma_strerror( info ));
magma_cgetmatrix( M, N, d_A, ldda, h_R, M );
// Regenerate R
// blasf77_cgemm("t", "n", &N, &N, &M, &c_one, h_R, &M, h_A, &M, &c_zero, h_rwork, &N);
// magma_cprint(N, N, h_work, N);
blasf77_ctrmm("r", "u", "n", "n", &M, &N, &c_one, h_rwork, &N, h_R, &M);
blasf77_caxpy( &n2, &c_neg_one, h_A, &ione, h_R, &ione );
e5 = lapackf77_clange("i", &M, &N, h_R, &M, work) /
lapackf77_clange("i", &M, &N, h_A, &lda, work);
magma_cgetmatrix( M, N, d_A, ldda, h_R, M );
if ( opts.lapack ) {
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
/* Orthogonalize on the CPU */
lapackf77_cgeqrf(&M, &N, h_A, &lda, tau, h_work, &lwork, &info);
lapackf77_cungqr(&M, &N, &N, h_A, &lda, tau, h_work, &lwork, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_cungqr returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Check the result compared to LAPACK
=================================================================== */
blasf77_cgemm("c", "n", &N, &N, &M, &c_one, h_R, &M, h_R, &M, &c_zero, h_work, &N);
for(int ii = 0; ii < N*N; ii += N+1 ) {
h_work[ii] = MAGMA_C_SUB(h_work[ii], c_one);
}
e1 = lapackf77_clange("f", &N, &N, h_work, &N, work) / N;
e3 = lapackf77_clange("i", &N, &N, h_work, &N, work) / N;
blasf77_cgemm("c", "n", &N, &N, &M, &c_one, h_A, &M, h_A, &M, &c_zero, h_work, &N);
for(int ii = 0; ii < N*N; ii += N+1 ) {
h_work[ii] = MAGMA_C_SUB(h_work[ii], c_one);
}
e2 = lapackf77_clange("f", &N, &N, h_work, &N, work) / N;
e4 = lapackf77_clange("i", &N, &N, h_work, &N, work) / N;
if (opts.version != 4)
e = e1;
else
e = e1 / (10.*max(M,N));
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e / %8.2e %8.2e / %8.2e %8.2e %s\n",
(int) M, (int) N, cpu_perf, 1000.*cpu_time, gpu_perf, 1000.*gpu_time,
e1, e2, e3, e4, e5,
(e < tol ? "ok" : "failed"));
status += ! (e < tol);
}
else {
printf("%5d %5d --- ( --- ) %7.2f (%7.2f) --- \n",
(int) M, (int) N, gpu_perf, 1000.*gpu_time );
}
TESTING_FREE_PIN( tau );
TESTING_FREE_PIN( h_work );
TESTING_FREE_PIN( h_rwork );
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_R );
TESTING_FREE_CPU( work );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( dtau );
TESTING_FREE_DEV( dwork );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/***************************************************************************//**
Purpose
-------
CGEQRF computes a QR factorization of a complex M-by-N matrix A:
A = Q * R. This is a GPU interface of the routine.
Arguments
---------
@param[in]
ngpu INTEGER
Number of GPUs to use. ngpu > 0.
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. N >= 0.
@param[in,out]
dlA COMPLEX array of pointers on the GPU, dimension (ngpu).
On entry, the M-by-N matrix A distributed over GPUs
(d_lA[d] points to the local matrix on d-th GPU).
It uses 1D block column cyclic format with the block size of nb,
and each local matrix is stored by column.
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 COMPLEX 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 complex scalar, and v is a complex vector with
v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
@ingroup magma_geqrf
*******************************************************************************/
extern "C" magma_int_t
magma_cgeqrf2_mgpu(
magma_int_t ngpu,
magma_int_t m, magma_int_t n,
magmaFloatComplex_ptr dlA[], magma_int_t ldda,
magmaFloatComplex *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.
magmaFloatComplex *dwork[MagmaMaxGPUs]={NULL}, *dpanel[MagmaMaxGPUs]={NULL};
magmaFloatComplex *hwork=NULL, *hpanel=NULL;
magma_queue_t queues[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 );
nb = magma_get_cgeqrf_nb( m, n );
/* dwork is (n*nb) --- for T (nb*nb) and clarfb work ((n-nb)*nb) ---
* + dpanel (ldda*nb), on each GPU.
* I think clarfb work could be smaller, max(n_local[:]).
* Oddly, T and clarfb 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 < ngpu; dev++ ) {
magma_setdevice( dev );
if ( MAGMA_SUCCESS != magma_cmalloc( &(dwork[dev]), (lddwork + ldda)*nb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
goto CLEANUP;
}
}
/* hwork is MAX( workspace for cgeqrf (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_cmalloc_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 < ngpu; dev++ ) {
n_local[dev] = ((n/nb)/ngpu)*nb;
if (dev < (n/nb) % ngpu)
n_local[dev] += nb;
else if (dev == (n/nb) % ngpu)
n_local[dev] += n % nb;
}
for( dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
magma_queue_create( dev, &queues[dev][0] );
magma_queue_create( dev, &queues[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) % ngpu;
/* Set the local index where the current panel is (j == i) */
i_local = i/(nb*ngpu)*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( queues[panel_dev][1], panel_event[panel_dev] );
magma_cgetmatrix_async( rows, ib,
dlA(panel_dev, i, i_local), ldda,
hpanel(i), ldhpanel,
queues[panel_dev][1] );
magma_queue_sync( queues[panel_dev][1] );
// Factor panel
lapackf77_cgeqrf( &rows, &ib, hpanel(i), &ldhpanel, tau+i,
hwork, &lhwork, info );
if ( *info != 0 ) {
fprintf( stderr, "error %lld\n", (long long) *info );
}
// Form the triangular factor of the block reflector
// H = H(i) H(i+1) . . . H(i+ib-1)
lapackf77_clarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib,
hpanel(i), &ldhpanel, tau+i, hwork, &ib );
magma_cpanel_to_q( MagmaUpper, ib, hpanel(i), ldhpanel, hwork + ib*ib );
// Send the current panel back to the GPUs
for( dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
if (dev == panel_dev)
dpanel[dev] = dlA(dev, i, i_local);
else
dpanel[dev] = dwork[dev] + dpanel_offset;
magma_csetmatrix_async( rows, ib,
hpanel(i), ldhpanel,
dpanel[dev], ldda,
queues[dev][0] );
}
for( dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
magma_queue_sync( queues[dev][0] );
}
// TODO: if magma_cpanel_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 */
magma_cq_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 < ngpu; dev++ ) {
magma_setdevice( dev );
magma_csetmatrix_async( ib, ib,
hwork, ib,
dwork[dev], lddwork,
queues[dev][0] );
}
la_dev = (panel_dev+1) % ngpu;
for( dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
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*ngpu)*nb;
magma_clarfb_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
queues[dev][0] );
magma_event_record( panel_event[dev], queues[dev][0] );
// for trailing matrix, apply H' to A(i:m,i+2*ib:n)
magma_clarfb_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
queues[dev][0] );
}
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_clarfb_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
queues[dev][0] );
}
}
// Restore top of panel (after larfb is done)
magma_setdevice( panel_dev );
magma_csetmatrix_async( ib, ib,
hpanel(i), ldhpanel,
dlA(panel_dev, i, i_local), ldda,
queues[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) % ngpu;
i_local = j/(nb*ngpu)*nb;
ib = min( n-j, nb );
magma_setdevice( panel_dev );
magma_cgetmatrix( rows, ib,
dlA(panel_dev, i, i_local), ldda,
hwork + (j-i)*rows, rows,
queues[panel_dev][0] );
}
// needs lwork >= 2*n*nb:
// needs (m-i)*(n-i) for last block row, bounded by nb*n.
// needs (n-i)*nb for cgeqrf work, bounded by n*nb.
ib = n-i; // total columns in block row
lhwork = lwork - ib*rows;
lapackf77_cgeqrf( &rows, &ib, hwork, &rows, tau+i, hwork + ib*rows, &lhwork, info );
if ( *info != 0 ) {
fprintf( stderr, "error %lld\n", (long long) *info );
}
for( j=i; j < n; j += nb ) {
panel_dev = (j/nb) % ngpu;
i_local = j/(nb*ngpu)*nb;
ib = min( n-j, nb );
magma_setdevice( panel_dev );
magma_csetmatrix( rows, ib,
hwork + (j-i)*rows, rows,
dlA(panel_dev, i, i_local), ldda,
queues[panel_dev][0] );
}
}
CLEANUP:
// free(NULL) does nothing.
for( dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
magma_queue_destroy( queues[dev][0] );
magma_queue_destroy( queues[dev][1] );
magma_event_destroy( panel_event[dev] );
magma_free( dwork[dev] );
}
magma_free_pinned( hwork );
magma_setdevice( orig_dev );
return *info;
} /* magma_cgeqrf2_mgpu */
/* ////////////////////////////////////////////////////////////////////////////
-- Testing csymmetrize
Code is very similar to testing_ctranspose.cpp
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gbytes, gpu_perf, gpu_time, cpu_perf, cpu_time;
float error, work[1];
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex *h_A, *h_R;
magmaFloatComplex_ptr d_A;
magma_int_t N, size, lda, ldda;
magma_int_t ione = 1;
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
printf("uplo = %s\n", lapack_uplo_const(opts.uplo) );
printf(" N CPU GByte/s (ms) GPU GByte/s (ms) check\n");
printf("=====================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
lda = N;
ldda = ((N+31)/32)*32;
size = lda*N;
// load strictly lower triangle, save strictly upper triangle
gbytes = sizeof(magmaFloatComplex) * 1.*N*(N-1) / 1e9;
TESTING_MALLOC_CPU( h_A, magmaFloatComplex, size );
TESTING_MALLOC_CPU( h_R, magmaFloatComplex, size );
TESTING_MALLOC_DEV( d_A, magmaFloatComplex, ldda*N );
/* Initialize the matrix */
for( int j = 0; j < N; ++j ) {
for( int i = 0; i < N; ++i ) {
h_A[i + j*lda] = MAGMA_C_MAKE( i + j/10000., j );
}
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
magma_csetmatrix( N, N, h_A, lda, d_A, ldda );
gpu_time = magma_sync_wtime( 0 );
//magmablas_csymmetrize( opts.uplo, N-2, d_A+1+ldda, ldda ); // inset by 1 row & col
magmablas_csymmetrize( opts.uplo, N, d_A, ldda );
gpu_time = magma_sync_wtime( 0 ) - gpu_time;
gpu_perf = gbytes / gpu_time;
/* =====================================================================
Performs operation using naive in-place algorithm
(LAPACK doesn't implement symmetrize)
=================================================================== */
cpu_time = magma_wtime();
//for( int j = 1; j < N-1; ++j ) { // inset by 1 row & col
// for( int i = 1; i < j; ++i ) {
for( int j = 0; j < N; ++j ) {
for( int i = 0; i < j; ++i ) {
if ( opts.uplo == MagmaLower ) {
h_A[i + j*lda] = MAGMA_C_CNJG( h_A[j + i*lda] );
}
else {
h_A[j + i*lda] = MAGMA_C_CNJG( h_A[i + j*lda] );
}
}
}
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gbytes / cpu_time;
/* =====================================================================
Check the result
=================================================================== */
magma_cgetmatrix( N, N, d_A, ldda, h_R, lda );
blasf77_caxpy(&size, &c_neg_one, h_A, &ione, h_R, &ione);
error = lapackf77_clange("f", &N, &N, h_R, &lda, work);
printf("%5d %7.2f (%7.2f) %7.2f (%7.2f) %s\n",
(int) N, cpu_perf, cpu_time*1000., gpu_perf, gpu_time*1000.,
(error == 0. ? "ok" : "failed") );
status += ! (error == 0.);
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_R );
TESTING_FREE_DEV( d_A );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
int main( int argc, char** argv )
{
magma_init();
cublasHandle_t handle;
cudaSetDevice( 0 );
cublasCreate( &handle );
magmaFloatComplex *A, *B, *C;
magmaFloatComplex *dA, *dB, *dC;
float error, work[1];
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magma_int_t ione = 1;
magma_int_t ISEED[4] = { 1, 2, 3, 4 };
magma_int_t n, lda, ldda, size, info;
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
float tol = opts.tolerance * lapackf77_slamch("E");
printf(" N |dC - C|/|C|\n");
printf("====================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
// for this simple case, all matrices are N-by-N
n = opts.nsize[itest];
lda = n;
ldda = ((n+31)/32)*32;
magma_cmalloc_cpu( &A, lda*n );
magma_cmalloc_cpu( &B, lda*n );
magma_cmalloc_cpu( &C, lda*n );
magma_cmalloc( &dA, ldda*n );
magma_cmalloc( &dB, ldda*n );
magma_cmalloc( &dC, ldda*n );
// initialize matrices
size = lda*n;
lapackf77_clarnv( &ione, ISEED, &size, A );
lapackf77_clarnv( &ione, ISEED, &size, B );
lapackf77_clarnv( &ione, ISEED, &size, C );
// increase diagonal to be SPD
for( int i=0; i < n; ++i ) {
C[i+i*lda] = MAGMA_C_ADD( C[i+i*lda], MAGMA_C_MAKE( n*n, 0 ));
}
magma_csetmatrix( n, n, A, lda, dA, ldda );
magma_csetmatrix( n, n, B, lda, dB, ldda );
magma_csetmatrix( n, n, C, lda, dC, ldda );
// compute with cublas
cublasCgemm( handle, CUBLAS_OP_N, CUBLAS_OP_N, n, n, n,
&c_neg_one, dA, ldda, dB, ldda, &c_one, dC, ldda );
magma_cpotrf_gpu( MagmaLower, n, dC, ldda, &info );
if (info != 0)
printf("magma_cpotrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
// compute with LAPACK
blasf77_cgemm( MagmaNoTransStr, MagmaNoTransStr, &n, &n, &n,
&c_neg_one, A, &lda, B, &lda, &c_one, C, &lda );
lapackf77_cpotrf( MagmaLowerStr, &n, C, &lda, &info );
if (info != 0)
printf("lapackf77_cpotrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
// compute difference, |dC - C| / |C|
magma_cgetmatrix( n, n, dC, ldda, A, lda );
blasf77_caxpy( &size, &c_neg_one, C, &ione, A, &ione );
error = lapackf77_clange( "F", &n, &n, A, &lda, work )
/ lapackf77_clange( "F", &n, &n, C, &lda, work );
printf( "%5d %8.2e %s\n",
(int) n, error, (error < tol ? "ok" : "failed"));
status += ! (error < tol);
magma_free( dA );
magma_free( dB );
magma_free( dC );
magma_free_cpu( A );
magma_free_cpu( B );
magma_free_cpu( C );
fflush( stdout );
}
}
cublasDestroy( handle );
magma_finalize();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing cunmqr_gpu
*/
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
float Cnorm, error, work[1];
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magma_int_t ione = 1;
magma_int_t mm, m, n, k, size, info;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t nb, ldc, lda, lwork, lwork_max, dt_size;
magmaFloatComplex *C, *R, *A, *hwork, *tau;
magmaFloatComplex_ptr dC, dA, dT;
magma_int_t status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
// need slightly looser bound (60*eps instead of 30*eps) for some tests
opts.tolerance = max( 60., opts.tolerance );
float tol = opts.tolerance * lapackf77_slamch("E");
// test all combinations of input parameters
magma_side_t side [] = { MagmaLeft, MagmaRight };
magma_trans_t trans[] = { Magma_ConjTrans, MagmaNoTrans };
printf("%% M N K side trans CPU Gflop/s (sec) GPU Gflop/s (sec) ||R||_F / ||QC||_F\n");
printf("%%==============================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iside = 0; iside < 2; ++iside ) {
for( int itran = 0; itran < 2; ++itran ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
m = opts.msize[itest];
n = opts.nsize[itest];
k = opts.ksize[itest];
ldc = magma_roundup( m, opts.align ); // multiple of 32 by default
// A is m x k (left) or n x k (right)
mm = (side[iside] == MagmaLeft ? m : n);
nb = magma_get_cgeqrf_nb( mm, k );
lda = magma_roundup( mm, opts.align ); // multiple of 32 by default
gflops = FLOPS_CUNMQR( m, n, k, side[iside] ) / 1e9;
if ( side[iside] == MagmaLeft && m < k ) {
printf( "%5d %5d %5d %4c %5c skipping because side=left and m < k\n",
(int) m, (int) n, (int) k,
lapacke_side_const( side[iside] ),
lapacke_trans_const( trans[itran] ) );
continue;
}
if ( side[iside] == MagmaRight && n < k ) {
printf( "%5d %5d %5d %4c %5c skipping because side=right and n < k\n",
(int) m, (int) n, (int) k,
lapacke_side_const( side[iside] ),
lapacke_trans_const( trans[itran] ) );
continue;
}
if ( side[iside] == MagmaLeft ) {
// side = left
lwork_max = (m - k + nb)*(n + nb) + n*nb;
dt_size = ( 2*min(m,k) + magma_roundup( max(m,n), 32) )*nb;
}
else {
// side = right
lwork_max = (n - k + nb)*(m + nb) + m*nb;
dt_size = ( 2*min(n,k) + magma_roundup( max(m,n), 32 ) )*nb;
}
// this rounds it up slightly if needed to agree with lwork query below
lwork_max = int( real( magma_cmake_lwork( lwork_max )));
TESTING_MALLOC_CPU( C, magmaFloatComplex, ldc*n );
TESTING_MALLOC_CPU( R, magmaFloatComplex, ldc*n );
TESTING_MALLOC_CPU( A, magmaFloatComplex, lda*k );
TESTING_MALLOC_CPU( hwork, magmaFloatComplex, lwork_max );
TESTING_MALLOC_CPU( tau, magmaFloatComplex, k );
TESTING_MALLOC_DEV( dC, magmaFloatComplex, ldc*n );
TESTING_MALLOC_DEV( dA, magmaFloatComplex, lda*k );
TESTING_MALLOC_DEV( dT, magmaFloatComplex, dt_size );
// C is full, m x n
size = ldc*n;
lapackf77_clarnv( &ione, ISEED, &size, C );
magma_csetmatrix( m, n, C, ldc, dC, ldc );
// A is m x k (left) or n x k (right)
size = lda*k;
lapackf77_clarnv( &ione, ISEED, &size, A );
// compute QR factorization to get Householder vectors in dA, tau, dT
magma_csetmatrix( mm, k, A, lda, dA, lda );
magma_cgeqrf_gpu( mm, k, dA, lda, tau, dT, &info );
magma_cgetmatrix( mm, k, dA, lda, A, lda );
if (info != 0) {
printf("magma_cgeqrf_gpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
lapackf77_cunmqr( lapack_side_const( side[iside] ), lapack_trans_const( trans[itran] ),
&m, &n, &k,
A, &lda, tau, C, &ldc, hwork, &lwork_max, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0) {
printf("lapackf77_cunmqr returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
// query for workspace size
lwork = -1;
magma_cunmqr_gpu( side[iside], trans[itran],
m, n, k,
dA, lda, tau, dC, ldc, hwork, lwork, dT, nb, &info );
if (info != 0) {
printf("magma_cunmqr_gpu (lwork query) returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
lwork = (magma_int_t) MAGMA_C_REAL( hwork[0] );
if ( lwork < 0 || lwork > lwork_max ) {
printf("Warning: optimal lwork %d > allocated lwork_max %d\n", (int) lwork, (int) lwork_max );
lwork = lwork_max;
}
// cunmqr2 takes a copy of dA in CPU memory
if ( opts.version == 2 ) {
magma_cgetmatrix( mm, k, dA, lda, A, lda );
}
magmablasSetKernelStream( opts.queue );
gpu_time = magma_sync_wtime( opts.queue ); // sync needed for L,N and R,T cases
if ( opts.version == 1 ) {
magma_cunmqr_gpu( side[iside], trans[itran],
m, n, k,
dA, lda, tau, dC, ldc, hwork, lwork, dT, nb, &info );
}
else if ( opts.version == 2 ) {
magma_cunmqr2_gpu( side[iside], trans[itran],
m, n, k,
dA, lda, tau, dC, ldc, A, lda, &info );
}
gpu_time = magma_sync_wtime( opts.queue ) - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0) {
printf("magma_cunmqr_gpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
magma_cgetmatrix( m, n, dC, ldc, R, ldc );
/* =====================================================================
compute relative error |QC_magma - QC_lapack| / |QC_lapack|
=================================================================== */
size = ldc*n;
blasf77_caxpy( &size, &c_neg_one, C, &ione, R, &ione );
Cnorm = lapackf77_clange( "Fro", &m, &n, C, &ldc, work );
error = lapackf77_clange( "Fro", &m, &n, R, &ldc, work ) / (magma_ssqrt(m*n) * Cnorm);
printf( "%5d %5d %5d %4c %5c %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %s\n",
(int) m, (int) n, (int) k,
lapacke_side_const( side[iside] ),
lapacke_trans_const( trans[itran] ),
cpu_perf, cpu_time, gpu_perf, gpu_time,
error, (error < tol ? "ok" : "failed") );
status += ! (error < tol);
TESTING_FREE_CPU( C );
TESTING_FREE_CPU( R );
TESTING_FREE_CPU( A );
TESTING_FREE_CPU( hwork );
TESTING_FREE_CPU( tau );
TESTING_FREE_DEV( dC );
TESTING_FREE_DEV( dA );
TESTING_FREE_DEV( dT );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}} // end iside, itran
printf( "\n" );
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
magmaFloatComplex *h_A, *h_R;
magmaFloatComplex *d_A;
magma_int_t N, n2, lda, ldda, info;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
float work[1], error;
magma_int_t status = 0;
magmaFloatComplex **d_A_array = NULL;
magma_int_t *dinfo_magma;
magma_int_t batchCount;
magma_queue_t queue = magma_stream;
magma_opts opts;
parse_opts( argc, argv, &opts );
opts.lapack |= opts.check; // check (-c) implies lapack (-l)
batchCount = opts.batchcount;
float tol = opts.tolerance * lapackf77_slamch("E");
printf("BatchCount N CPU GFlop/s (ms) GPU GFlop/s (ms) ||R_magma - R_lapack||_F / ||R_lapack||_F\n");
printf("========================================================\n");
for( int i = 0; i < opts.ntest; ++i ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[i];
ldda = lda = ((N+31)/32)*32;
n2 = lda* N * batchCount;
gflops = batchCount * FLOPS_CPOTRF( N ) / 1e9 ;
TESTING_MALLOC_CPU( h_A, magmaFloatComplex, n2);
TESTING_MALLOC_PIN( h_R, magmaFloatComplex, n2);
TESTING_MALLOC_DEV( d_A, magmaFloatComplex, ldda * N * batchCount);
TESTING_MALLOC_DEV( dinfo_magma, magma_int_t, batchCount);
magma_malloc((void**)&d_A_array, batchCount * sizeof(*d_A_array));
/* Initialize the matrix */
lapackf77_clarnv( &ione, ISEED, &n2, h_A );
for(int i=0; i<batchCount; i++)
{
magma_cmake_hpd( N, h_A + i * lda * N, lda );// need modification
}
magma_int_t columns = N * batchCount;
lapackf77_clacpy( MagmaUpperLowerStr, &N, &(columns), h_A, &lda, h_R, &lda );
magma_csetmatrix( N, columns, h_A, lda, d_A, ldda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
cset_pointer(d_A_array, d_A, ldda, 0, 0, ldda * N, batchCount, queue);
gpu_time = magma_sync_wtime(NULL);
info = magma_cpotrf_batched( opts.uplo, N, d_A_array, ldda, dinfo_magma, batchCount, queue);
gpu_time = magma_sync_wtime(NULL) - gpu_time;
gpu_perf = gflops / gpu_time;
magma_int_t *cpu_info = (magma_int_t*) malloc(batchCount*sizeof(magma_int_t));
magma_getvector( batchCount, sizeof(magma_int_t), dinfo_magma, 1, cpu_info, 1);
for(int i=0; i<batchCount; i++)
{
if(cpu_info[i] != 0 ){
printf("magma_cpotrf_batched matrix %d returned internal error %d\n",i, (int)cpu_info[i] );
}
}
if (info != 0)
printf("magma_cpotrf_batched returned argument error %d: %s.\n", (int) info, magma_strerror( info ));
if ( opts.lapack ) {
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
for(int i=0; i<batchCount; i++)
{
lapackf77_cpotrf( lapack_uplo_const(opts.uplo), &N, h_A + i * lda * N, &lda, &info );
}
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_cpotrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Check the result compared to LAPACK
=================================================================== */
magma_cgetmatrix( N, columns, d_A, ldda, h_R, lda );
magma_int_t NN = lda*N;
char const uplo = 'l'; // lapack_uplo_const(opts.uplo)
float err = 0.0;
for(int i=0; i<batchCount; i++)
{
error = lapackf77_clanhe("f", &uplo, &N, h_A + i * lda*N, &lda, work);
blasf77_caxpy(&NN, &c_neg_one, h_A + i * lda*N, &ione, h_R + i * lda*N, &ione);
error = lapackf77_clanhe("f", &uplo, &N, h_R + i * lda*N, &lda, work) / error;
if ( isnan(error) || isinf(error) ) {
err = error;
break;
}
err = max(fabs(error),err);
}
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %s\n",
(int)batchCount, (int) N, cpu_perf, cpu_time*1000., gpu_perf, gpu_time*1000., err, (error < tol ? "ok" : "failed"));
status += ! (err < tol);
}
else {
printf("%5d %5d --- ( --- ) %7.2f (%7.2f) --- \n",
(int)batchCount, (int) N, gpu_perf, gpu_time*1000. );
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_PIN( h_R );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_A_array );
TESTING_FREE_DEV( dinfo_magma );
free(cpu_info);
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/***************************************************************************//**
Purpose
-------
CGERFS improves the computed solution to a system of linear equations.
The iterative refinement process is stopped if
ITER > ITERMAX
or for all the RHS we have:
RNRM < SQRT(n)*XNRM*ANRM*EPS*BWDMAX
where
o ITER is the number of the current iteration in the iterative
refinement process
o RNRM is the infinity-norm of the residual
o XNRM is the infinity-norm of the solution
o ANRM is the infinity-operator-norm of the matrix A
o EPS is the machine epsilon returned by SLAMCH('Epsilon')
The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 respectively.
Arguments
---------
@param[in]
trans magma_trans_t
Specifies the form of the system of equations:
- = MagmaNoTrans: A * X = B (No transpose)
- = MagmaTrans: A**T * X = B (Transpose)
- = MagmaConjTrans: A**H * X = B (Conjugate transpose)
@param[in]
n INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.
@param[in]
nrhs INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
@param[in]
dA COMPLEX array on the GPU, dimension (ldda,N)
the N-by-N coefficient matrix A.
@param[in]
ldda INTEGER
The leading dimension of the array dA. ldda >= max(1,N).
@param[in]
dB COMPLEX array on the GPU, dimension (lddb,NRHS)
The N-by-NRHS right hand side matrix B.
@param[in]
lddb INTEGER
The leading dimension of the array dB. lddb >= max(1,N).
@param[in, out]
dX COMPLEX array on the GPU, dimension (lddx,NRHS)
On entry, the solution matrix X, as computed by
CGETRS_NOPIV. On exit, the improved solution matrix X.
@param[in]
lddx INTEGER
The leading dimension of the array dX. lddx >= max(1,N).
@param
dworkd (workspace) COMPLEX array on the GPU, dimension (N*NRHS)
This array is used to hold the residual vectors.
@param
dAF COMPLEX array on the GPU, dimension (ldda,n)
The factors L and U from the factorization A = L*U
as computed by CGETRF_NOPIV.
@param[out]
iter INTEGER
- < 0: iterative refinement has failed, real
factorization has been performed
+ -1 : the routine fell back to full precision for
implementation- or machine-specific reasons
+ -2 : narrowing the precision induced an overflow,
the routine fell back to full precision
+ -3 : failure of SGETRF
+ -31: stop the iterative refinement after the 30th iteration
- > 0: iterative refinement has been successfully used.
Returns the number of iterations
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if info = -i, the i-th argument had an illegal value
- > 0: if info = i, U(i,i) computed in REAL is
exactly zero. The factorization has been completed,
but the factor U is exactly singular, so the solution
could not be computed.
@ingroup magma_gerfs_nopiv
*******************************************************************************/
extern "C" magma_int_t
magma_cgerfs_nopiv_gpu(
magma_trans_t trans, magma_int_t n, magma_int_t nrhs,
magmaFloatComplex_ptr dA, magma_int_t ldda,
magmaFloatComplex_ptr dB, magma_int_t lddb,
magmaFloatComplex_ptr dX, magma_int_t lddx,
magmaFloatComplex_ptr dworkd, magmaFloatComplex_ptr dAF,
magma_int_t *iter,
magma_int_t *info)
{
#define dB(i,j) (dB + (i) + (j)*lddb)
#define dX(i,j) (dX + (i) + (j)*lddx)
#define dR(i,j) (dR + (i) + (j)*lddr)
/* Constants */
const magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
const magmaFloatComplex c_one = MAGMA_C_ONE;
const magma_int_t ione = 1;
/* Local variables */
magmaFloatComplex_ptr dR;
magmaFloatComplex Xnrmv, Rnrmv;
float Anrm, Xnrm, Rnrm, cte, eps;
magma_int_t i, j, iiter, lddsa, lddr;
/* Check arguments */
*iter = 0;
*info = 0;
if ( n < 0 )
*info = -1;
else if ( nrhs < 0 )
*info = -2;
else if ( ldda < max(1,n))
*info = -4;
else if ( lddb < max(1,n))
*info = -8;
else if ( lddx < max(1,n))
*info = -10;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
if ( n == 0 || nrhs == 0 )
return *info;
magma_queue_t queue = NULL;
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queue );
lddsa = n;
lddr = n;
dR = dworkd;
eps = lapackf77_slamch("Epsilon");
Anrm = magmablas_clange( MagmaInfNorm, n, n, dA, ldda, (magmaFloat_ptr)dworkd, n*nrhs, queue );
cte = Anrm * eps * magma_ssqrt( (float) n ) * BWDMAX;
// residual dR = dB - dA*dX in real
magmablas_clacpy( MagmaFull, n, nrhs, dB, lddb, dR, lddr, queue );
if ( nrhs == 1 ) {
magma_cgemv( trans, n, n,
c_neg_one, dA, ldda,
dX, 1,
c_one, dR, 1, queue );
}
else {
magma_cgemm( trans, MagmaNoTrans, n, nrhs, n,
c_neg_one, dA, ldda,
dX, lddx,
c_one, dR, lddr, queue );
}
// TODO: use MAGMA_C_ABS( dX(i,j) ) instead of clange?
for( j=0; j < nrhs; j++ ) {
i = magma_icamax( n, dX(0,j), 1, queue ) - 1;
magma_cgetmatrix( 1, 1, dX(i,j), 1, &Xnrmv, 1, queue );
Xnrm = lapackf77_clange( "F", &ione, &ione, &Xnrmv, &ione, NULL );
i = magma_icamax( n, dR(0,j), 1, queue ) - 1;
magma_cgetmatrix( 1, 1, dR(i,j), 1, &Rnrmv, 1, queue );
Rnrm = lapackf77_clange( "F", &ione, &ione, &Rnrmv, &ione, NULL );
//printf("Rnrm : %e, Xnrm*cte : %e\n", Rnrm, Xnrm*cte);
if ( Rnrm > Xnrm*cte ) {
goto refinement;
}
}
*iter = 0;
goto cleanup;
refinement:
for( iiter=1; iiter < ITERMAX; ) {
*info = 0;
// solve dAF*dX = dR
// it's okay that dR is used for both dB input and dX output.
magma_cgetrs_nopiv_gpu( trans, n, nrhs, dAF, lddsa, dR, lddr, info );
if (*info != 0) {
*iter = -3;
goto fallback;
}
// Add correction and setup residual
// dX += dR --and--
// dR = dB
// This saves going through dR a second time (if done with one more kernel).
// -- not really: first time is read, second time is write.
for( j=0; j < nrhs; j++ ) {
magmablas_caxpycp( n, dR(0,j), dX(0,j), dB(0,j), queue );
}
// residual dR = dB - dA*dX in real
if ( nrhs == 1 ) {
magma_cgemv( trans, n, n,
c_neg_one, dA, ldda,
dX, 1,
c_one, dR, 1, queue );
}
else {
magma_cgemm( trans, MagmaNoTrans, n, nrhs, n,
c_neg_one, dA, ldda,
dX, lddx,
c_one, dR, lddr, queue );
}
/* Check whether the nrhs normwise backward errors satisfy the
* stopping criterion. If yes, set ITER=IITER > 0 and return. */
for( j=0; j < nrhs; j++ ) {
i = magma_icamax( n, dX(0,j), 1, queue ) - 1;
magma_cgetmatrix( 1, 1, dX(i,j), 1, &Xnrmv, 1, queue );
Xnrm = lapackf77_clange( "F", &ione, &ione, &Xnrmv, &ione, NULL );
i = magma_icamax( n, dR(0,j), 1, queue ) - 1;
magma_cgetmatrix( 1, 1, dR(i,j), 1, &Rnrmv, 1, queue );
Rnrm = lapackf77_clange( "F", &ione, &ione, &Rnrmv, &ione, NULL );
if ( Rnrm > Xnrm*cte ) {
goto L20;
}
}
/* If we are here, the nrhs normwise backward errors satisfy
* the stopping criterion, we are good to exit. */
*iter = iiter;
goto cleanup;
L20:
iiter++;
}
/* If we are at this place of the code, this is because we have
* performed ITER=ITERMAX iterations and never satisified the
* stopping criterion. Set up the ITER flag accordingly. */
*iter = -ITERMAX - 1;
fallback:
/* Iterative refinement failed to converge to a
* satisfactory solution. */
cleanup:
magma_queue_destroy( queue );
return *info;
}
extern "C" magma_int_t
magma_cunmql(const char side, const char 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)
{
/* -- MAGMA (version 1.4.1) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
December 2013
Purpose
=======
CUNMQL overwrites the general complex M-by-N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'C': Q**H * C C * Q**H
where Q is a complex unitary matrix defined as the product of k
elementary reflectors
Q = H(k) . . . H(2) H(1)
as returned by CGEQLF. Q is of order M if SIDE = 'L' and of order N
if SIDE = 'R'.
Arguments
=========
SIDE (input) CHARACTER*1
= 'L': apply Q or Q**H from the Left;
= 'R': apply Q or Q**H from the Right.
TRANS (input) CHARACTER*1
= 'N': No transpose, apply Q;
= 'C': Transpose, apply Q**H.
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) COMPLEX array, dimension (LDA,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
CGEQLF in the last k columns of its array argument A.
A is modified by the routine but restored on exit.
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) COMPLEX array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by CGEQLF.
C (input/output) 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.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) 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
===================================================================== */
char side_[2] = {side, 0};
char trans_[2] = {trans, 0};
magma_int_t i__4, i__;
magmaFloatComplex *T;
magma_int_t i1, i2, i3, ib, nb, mi, ni, nq, nw;
magma_int_t iinfo, ldwork, lwkopt=0;
int lquery, left, notran;
*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 = max(1,n);
} else {
nq = n;
nw = max(1,m);
}
if (! left && ! lapackf77_lsame(side_, "R")) {
*info = -1;
} else if (! notran && ! lapackf77_lsame(trans_, "C")) {
*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;
}
if (*info == 0) {
if (m == 0 || n == 0) {
lwkopt = 1;
} else {
/* Determine the block size. NB may be at most NBMAX, where
NBMAX is used to define the local array T. */
nb = 64;
lwkopt = nw * nb;
}
work[0] = MAGMA_C_MAKE( lwkopt, 0 );
if (lwork < 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) {
return *info;
}
/* Allocate work space on the GPU */
magmaFloatComplex *dwork, *dc;
magma_cmalloc( &dc, (m)*(n) );
magma_cmalloc( &dwork, 2*(m + 64)*64 );
/* Copy matrix C from the CPU to the GPU */
magma_csetmatrix( m, n, c, ldc, dc, m );
/* work space on CPU */
if ( MAGMA_SUCCESS != magma_cmalloc_pinned( &T, 2*nb*nb ) ) {
magma_free( dc );
magma_free( dwork );
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
ldwork = nw;
if ( nb >= k ) {
/* Use CPU code */
lapackf77_cunmql(side_, trans_, &m, &n, &k, a, &lda, tau,
c, &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;
}
// silence "uninitialized" warnings
mi = 0;
ni = 0;
if (left) {
ni = n;
} else {
mi = m;
}
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+ib-1) . . . H(i+1) H(i) */
i__4 = nq - k + i__ + ib - 1;
lapackf77_clarft("Backward", "Columnwise", &i__4, &ib,
&a[(i__-1) * lda], &lda, &tau[i__-1], T, &ib);
/* 1) Put 0s in the lower triangular part of A;
2) copy the panel from A to the GPU, and
3) restore A */
cpanel_to_q('L', ib, &a[i__-1 + (i__-1) * lda], lda, T+ib*ib);
magma_csetmatrix( i__4, ib, &a[(i__-1) * lda], lda, dwork, i__4 );
cq_to_panel('L', ib, &a[i__-1 + (i__-1) * lda], lda, T+ib*ib);
if (left) {
/* H or H' is applied to C(1:m-k+i+ib-1,1:n) */
mi = m - k + i__ + ib - 1;
}
else {
/* H or H' is applied to C(1:m,1:n-k+i+ib-1) */
ni = n - k + i__ + ib - 1;
}
/* Apply H or H'; First copy T to the GPU */
magma_csetmatrix( ib, ib, T, ib, dwork+i__4*ib, ib );
magma_clarfb_gpu(side, trans, MagmaBackward, MagmaColumnwise,
mi, ni, ib,
dwork, i__4, dwork+i__4*ib, ib,
dc, m,
dwork+i__4*ib + ib*ib, ldwork);
}
magma_cgetmatrix( m, n, dc, m, c, ldc );
}
work[0] = MAGMA_C_MAKE( lwkopt, 0 );
magma_free( dc );
magma_free( dwork );
magma_free_pinned( T);
return *info;
} /* magma_cunmql */
/* ////////////////////////////////////////////////////////////////////////////
-- Testing cherk
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, cublas_perf, cublas_time, cpu_perf, cpu_time;
float cublas_error, Cnorm, work[1];
magma_int_t N, K;
magma_int_t Ak, An;
magma_int_t sizeA, sizeC;
magma_int_t lda, ldc, ldda, lddc;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magmaFloatComplex *h_A, *h_C, *h_Ccublas;
magmaFloatComplex_ptr d_A, d_C;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
float alpha = MAGMA_D_MAKE( 0.29, -0.86 );
float beta = MAGMA_D_MAKE( -0.48, 0.38 );
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
opts.lapack |= opts.check; // check (-c) implies lapack (-l)
float tol = opts.tolerance * lapackf77_slamch("E");
printf("If running lapack (option --lapack), CUBLAS error is computed\n"
"relative to CPU BLAS result.\n\n");
printf("uplo = %s, transA = %s\n",
lapack_uplo_const(opts.uplo), lapack_trans_const(opts.transA) );
printf(" N K CUBLAS Gflop/s (ms) CPU Gflop/s (ms) CUBLAS error\n");
printf("==================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
K = opts.ksize[itest];
gflops = FLOPS_CHERK(K, N) / 1e9;
if ( opts.transA == MagmaNoTrans ) {
lda = An = N;
Ak = K;
} else {
lda = An = K;
Ak = N;
}
ldc = N;
ldda = ((lda+31)/32)*32;
lddc = ((ldc+31)/32)*32;
sizeA = lda*Ak;
sizeC = ldc*N;
TESTING_MALLOC_CPU( h_A, magmaFloatComplex, lda*Ak );
TESTING_MALLOC_CPU( h_C, magmaFloatComplex, ldc*N );
TESTING_MALLOC_CPU( h_Ccublas, magmaFloatComplex, ldc*N );
TESTING_MALLOC_DEV( d_A, magmaFloatComplex, ldda*Ak );
TESTING_MALLOC_DEV( d_C, magmaFloatComplex, lddc*N );
/* Initialize the matrices */
lapackf77_clarnv( &ione, ISEED, &sizeA, h_A );
lapackf77_clarnv( &ione, ISEED, &sizeC, h_C );
/* =====================================================================
Performs operation using CUBLAS
=================================================================== */
magma_csetmatrix( An, Ak, h_A, lda, d_A, ldda );
magma_csetmatrix( N, N, h_C, ldc, d_C, lddc );
cublas_time = magma_sync_wtime( NULL );
cublasCherk( opts.handle, cublas_uplo_const(opts.uplo), cublas_trans_const(opts.transA), N, K,
&alpha, d_A, ldda,
&beta, d_C, lddc );
cublas_time = magma_sync_wtime( NULL ) - cublas_time;
cublas_perf = gflops / cublas_time;
magma_cgetmatrix( N, N, d_C, lddc, h_Ccublas, ldc );
/* =====================================================================
Performs operation using CPU BLAS
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
blasf77_cherk( lapack_uplo_const(opts.uplo), lapack_trans_const(opts.transA), &N, &K,
&alpha, h_A, &lda,
&beta, h_C, &ldc );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
}
/* =====================================================================
Check the result
=================================================================== */
if ( opts.lapack ) {
#ifdef MAGMA_WITH_MKL
// MKL (11.1.2) has bug in multi-threaded clanhe; use single thread to work around
int threads = magma_get_lapack_numthreads();
magma_set_lapack_numthreads( 1 );
#endif
// compute relative error for both magma & cublas, relative to lapack,
// |C_magma - C_lapack| / |C_lapack|
Cnorm = lapackf77_clanhe("fro", lapack_uplo_const(opts.uplo), &N, h_C, &ldc, work);
blasf77_caxpy( &sizeC, &c_neg_one, h_C, &ione, h_Ccublas, &ione );
cublas_error = lapackf77_clanhe( "fro", lapack_uplo_const(opts.uplo), &N, h_Ccublas, &ldc, work ) / Cnorm;
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %s\n",
(int) N, (int) K,
cublas_perf, 1000.*cublas_time,
cpu_perf, 1000.*cpu_time,
cublas_error, (cublas_error < tol ? "ok" : "failed"));
status += ! (cublas_error < tol);
#ifdef MAGMA_WITH_MKL
// end single thread to work around MKL bug
magma_set_lapack_numthreads( threads );
#endif
}
else {
printf("%5d %5d %7.2f (%7.2f) --- ( --- ) --- ---\n",
(int) N, (int) K,
cublas_perf, 1000.*cublas_time);
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_C );
TESTING_FREE_CPU( h_Ccublas );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_C );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing cungqr
*/
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
float error, work[1];
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex *hA, *hR, *tau, *h_work;
magmaFloatComplex *dA, *dT;
magma_int_t m, n, k;
magma_int_t n2, lda, ldda, lwork, min_mn, nb, info;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
float tol = opts.tolerance * lapackf77_slamch("E");
opts.lapack |= opts.check; // check (-c) implies lapack (-l)
printf("Running version %d; available are (specified through --version num):\n",
(int) opts.version);
printf("1 - uses precomputed clarft matrices (default)\n");
printf("2 - recomputes the clarft matrices on the fly\n\n");
printf(" m n k CPU GFlop/s (sec) GPU GFlop/s (sec) ||R|| / ||A||\n");
printf("=========================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
m = opts.msize[itest];
n = opts.nsize[itest];
k = opts.ksize[itest];
if ( m < n || n < k ) {
printf( "%5d %5d %5d skipping because m < n or n < k\n", (int) m, (int) n, (int) k );
continue;
}
lda = m;
ldda = ((m + 31)/32)*32;
n2 = lda*n;
min_mn = min(m, n);
nb = magma_get_cgeqrf_nb( m );
lwork = (m + 2*n+nb)*nb;
gflops = FLOPS_CUNGQR( m, n, k ) / 1e9;
TESTING_MALLOC_PIN( h_work, magmaFloatComplex, lwork );
TESTING_MALLOC_PIN( hR, magmaFloatComplex, lda*n );
TESTING_MALLOC_CPU( hA, magmaFloatComplex, lda*n );
TESTING_MALLOC_CPU( tau, magmaFloatComplex, min_mn );
TESTING_MALLOC_DEV( dA, magmaFloatComplex, ldda*n );
TESTING_MALLOC_DEV( dT, magmaFloatComplex, ( 2*min_mn + ((n + 31)/32)*32 )*nb );
lapackf77_clarnv( &ione, ISEED, &n2, hA );
lapackf77_clacpy( MagmaUpperLowerStr, &m, &n, hA, &lda, hR, &lda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
// first, get QR factors
magma_csetmatrix( m, n, hA, lda, dA, ldda );
magma_cgeqrf_gpu( m, n, dA, ldda, tau, dT, &info );
if (info != 0)
printf("magma_cgeqrf_gpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
magma_cgetmatrix( m, n, dA, ldda, hR, lda );
gpu_time = magma_wtime();
if (opts.version == 1)
magma_cungqr( m, n, k, hR, lda, tau, dT, nb, &info );
else
magma_cungqr2(m, n, k, hR, lda, tau, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_cungqr_gpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
error = lapackf77_clange("f", &m, &n, hA, &lda, work );
lapackf77_cgeqrf( &m, &n, hA, &lda, tau, h_work, &lwork, &info );
if (info != 0)
printf("lapackf77_cgeqrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
cpu_time = magma_wtime();
lapackf77_cungqr( &m, &n, &k, hA, &lda, tau, h_work, &lwork, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_cungqr returned error %d: %s.\n",
(int) info, magma_strerror( info ));
// compute relative error |R|/|A| := |Q_magma - Q_lapack|/|A|
blasf77_caxpy( &n2, &c_neg_one, hA, &ione, hR, &ione );
error = lapackf77_clange("f", &m, &n, hR, &lda, work) / error;
printf("%5d %5d %5d %7.1f (%7.2f) %7.1f (%7.2f) %8.2e %s\n",
(int) m, (int) n, (int) k,
cpu_perf, cpu_time, gpu_perf, gpu_time,
error, (error < tol ? "ok" : "failed"));
status += ! (error < tol);
}
else {
printf("%5d %5d %5d --- ( --- ) %7.1f (%7.2f) --- \n",
(int) m, (int) n, (int) k,
gpu_perf, gpu_time );
}
TESTING_FREE_PIN( h_work );
TESTING_FREE_PIN( hR );
TESTING_FREE_CPU( hA );
TESTING_FREE_CPU( tau );
TESTING_FREE_DEV( dA );
TESTING_FREE_DEV( dT );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing cgemm
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, magma_perf, magma_time, dev_perf, dev_time, cpu_perf, cpu_time;
float magma_error, dev_error, Cnorm, work[1];
magma_int_t M, N, K;
magma_int_t Am, An, Bm, Bn;
magma_int_t sizeA, sizeB, sizeC;
magma_int_t lda, ldb, ldc, ldda, lddb, lddc;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
magmaFloatComplex *h_A, *h_B, *h_C, *h_Cmagma, *h_Cdev;
magmaFloatComplex_ptr d_A, d_B, d_C;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex alpha = MAGMA_C_MAKE( 0.29, -0.86 );
magmaFloatComplex beta = MAGMA_C_MAKE( -0.48, 0.38 );
magma_opts opts;
parse_opts( argc, argv, &opts );
float tol = opts.tolerance * lapackf77_slamch("E");
#ifdef HAVE_CUBLAS
// for CUDA, we can check MAGMA vs. CUBLAS, without running LAPACK
printf("If running lapack (option --lapack), MAGMA and %s error are both computed\n"
"relative to CPU BLAS result. Else, MAGMA error is computed relative to %s result.\n\n",
g_platform_str, g_platform_str );
printf("transA = %s, transB = %s\n",
lapack_trans_const(opts.transA),
lapack_trans_const(opts.transB) );
printf(" M N K MAGMA Gflop/s (ms) %s Gflop/s (ms) CPU Gflop/s (ms) MAGMA error %s error\n",
g_platform_str, g_platform_str );
#else
// for others, we need LAPACK for check
opts.lapack |= opts.check; // check (-c) implies lapack (-l)
printf("transA = %s, transB = %s\n",
lapack_trans_const(opts.transA),
lapack_trans_const(opts.transB) );
printf(" M N K %s Gflop/s (ms) CPU Gflop/s (ms) %s error\n",
g_platform_str, g_platform_str );
#endif
printf("=========================================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[itest];
N = opts.nsize[itest];
K = opts.ksize[itest];
gflops = FLOPS_CGEMM( M, N, K ) / 1e9;
if ( opts.transA == MagmaNoTrans ) {
lda = Am = M;
An = K;
} else {
lda = Am = K;
An = M;
}
if ( opts.transB == MagmaNoTrans ) {
ldb = Bm = K;
Bn = N;
} else {
ldb = Bm = N;
Bn = K;
}
ldc = M;
ldda = ((lda+31)/32)*32;
lddb = ((ldb+31)/32)*32;
lddc = ((ldc+31)/32)*32;
sizeA = lda*An;
sizeB = ldb*Bn;
sizeC = ldc*N;
TESTING_MALLOC_CPU( h_A, magmaFloatComplex, lda*An );
TESTING_MALLOC_CPU( h_B, magmaFloatComplex, ldb*Bn );
TESTING_MALLOC_CPU( h_C, magmaFloatComplex, ldc*N );
TESTING_MALLOC_CPU( h_Cmagma, magmaFloatComplex, ldc*N );
TESTING_MALLOC_CPU( h_Cdev, magmaFloatComplex, ldc*N );
TESTING_MALLOC_DEV( d_A, magmaFloatComplex, ldda*An );
TESTING_MALLOC_DEV( d_B, magmaFloatComplex, lddb*Bn );
TESTING_MALLOC_DEV( d_C, magmaFloatComplex, lddc*N );
/* Initialize the matrices */
lapackf77_clarnv( &ione, ISEED, &sizeA, h_A );
lapackf77_clarnv( &ione, ISEED, &sizeB, h_B );
lapackf77_clarnv( &ione, ISEED, &sizeC, h_C );
magma_csetmatrix( Am, An, h_A, lda, d_A, ldda );
magma_csetmatrix( Bm, Bn, h_B, ldb, d_B, lddb );
/* =====================================================================
Performs operation using MAGMABLAS (currently only with CUDA)
=================================================================== */
#ifdef HAVE_CUBLAS
magma_csetmatrix( M, N, h_C, ldc, d_C, lddc );
magma_time = magma_sync_wtime( NULL );
magmablas_cgemm( opts.transA, opts.transB, M, N, K,
alpha, d_A, ldda,
d_B, lddb,
beta, d_C, lddc );
magma_time = magma_sync_wtime( NULL ) - magma_time;
magma_perf = gflops / magma_time;
magma_cgetmatrix( M, N, d_C, lddc, h_Cmagma, ldc );
#endif
/* =====================================================================
Performs operation using CUBLAS / clBLAS / Xeon Phi MKL
=================================================================== */
magma_csetmatrix( M, N, h_C, ldc, d_C, lddc );
#ifdef HAVE_CUBLAS
dev_time = magma_sync_wtime( NULL );
cublasCgemm( opts.handle, cublas_trans_const(opts.transA), cublas_trans_const(opts.transB), M, N, K,
&alpha, d_A, ldda,
d_B, lddb,
&beta, d_C, lddc );
dev_time = magma_sync_wtime( NULL ) - dev_time;
#else
dev_time = magma_sync_wtime( opts.queue );
magma_cgemm( opts.transA, opts.transB, M, N, K,
alpha, d_A, 0, ldda,
d_B, 0, lddb,
beta, d_C, 0, lddc, opts.queue );
dev_time = magma_sync_wtime( opts.queue ) - dev_time;
#endif
dev_perf = gflops / dev_time;
magma_cgetmatrix( M, N, d_C, lddc, h_Cdev, ldc );
/* =====================================================================
Performs operation using CPU BLAS
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
blasf77_cgemm( lapack_trans_const(opts.transA), lapack_trans_const(opts.transB), &M, &N, &K,
&alpha, h_A, &lda,
h_B, &ldb,
&beta, h_C, &ldc );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
}
/* =====================================================================
Check the result
=================================================================== */
if ( opts.lapack ) {
// compute relative error for both magma & dev, relative to lapack,
// |C_magma - C_lapack| / |C_lapack|
Cnorm = lapackf77_clange( "F", &M, &N, h_C, &ldc, work );
blasf77_caxpy( &sizeC, &c_neg_one, h_C, &ione, h_Cdev, &ione );
dev_error = lapackf77_clange( "F", &M, &N, h_Cdev, &ldc, work ) / Cnorm;
#ifdef HAVE_CUBLAS
blasf77_caxpy( &sizeC, &c_neg_one, h_C, &ione, h_Cmagma, &ione );
magma_error = lapackf77_clange( "F", &M, &N, h_Cmagma, &ldc, work ) / Cnorm;
printf("%5d %5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %8.2e %s\n",
(int) M, (int) N, (int) K,
magma_perf, 1000.*magma_time,
dev_perf, 1000.*dev_time,
cpu_perf, 1000.*cpu_time,
magma_error, dev_error,
(magma_error < tol && dev_error < tol ? "ok" : "failed"));
status += ! (magma_error < tol && dev_error < tol);
#else
printf("%5d %5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %s\n",
(int) M, (int) N, (int) K,
dev_perf, 1000.*dev_time,
cpu_perf, 1000.*cpu_time,
dev_error,
(dev_error < tol ? "ok" : "failed"));
status += ! (dev_error < tol);
#endif
}
else {
#ifdef HAVE_CUBLAS
// compute relative error for magma, relative to dev (currently only with CUDA)
Cnorm = lapackf77_clange( "F", &M, &N, h_Cdev, &ldc, work );
blasf77_caxpy( &sizeC, &c_neg_one, h_Cdev, &ione, h_Cmagma, &ione );
magma_error = lapackf77_clange( "F", &M, &N, h_Cmagma, &ldc, work ) / Cnorm;
printf("%5d %5d %5d %7.2f (%7.2f) %7.2f (%7.2f) --- ( --- ) %8.2e --- %s\n",
(int) M, (int) N, (int) K,
magma_perf, 1000.*magma_time,
dev_perf, 1000.*dev_time,
magma_error,
(magma_error < tol ? "ok" : "failed"));
status += ! (magma_error < tol);
#else
printf("%5d %5d %5d %7.2f (%7.2f) --- ( --- ) ---\n",
(int) M, (int) N, (int) K,
dev_perf, 1000.*dev_time );
#endif
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_B );
TESTING_FREE_CPU( h_C );
TESTING_FREE_CPU( h_Cmagma );
TESTING_FREE_CPU( h_Cdev );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_B );
TESTING_FREE_DEV( d_C );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
extern "C" magma_int_t
magma_ctrtri_gpu(
magma_uplo_t uplo, magma_diag_t diag, magma_int_t n,
magmaFloatComplex_ptr dA, size_t dA_offset, magma_int_t ldda,
magma_queue_t queues[2],
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
=======
CTRTRI computes the inverse of a real upper or lower triangular
matrix dA.
This is the Level 3 BLAS version of the algorithm.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
DIAG (input) CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N (input) INTEGER
The order of the matrix A. N >= 0.
dA (input/output) COMPLEX array ON THE GPU, dimension (LDDA,N)
On entry, the triangular matrix A. If UPLO = 'U', the
leading N-by-N upper triangular part of the array dA contains
the upper triangular matrix, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of the array dA contains
the lower triangular matrix, and the strictly upper
triangular part of A is not referenced. If DIAG = 'U', the
diagonal elements of A are also not referenced and are
assumed to be 1.
On exit, the (triangular) inverse of the original matrix, in
the same storage format.
LDDA (input) INTEGER
The leading dimension of the array dA. LDDA >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, dA(i,i) is exactly zero. The triangular
matrix is singular and its inverse cannot be computed.
(Singularity check is currently disabled.)
===================================================================== */
/* Local variables */
magma_int_t nb, nn, j, jb;
//magmaFloatComplex c_zero = MAGMA_C_ZERO;
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex *work;
int upper = (uplo == MagmaUpper);
int nounit = (diag == MagmaNonUnit);
*info = 0;
if (! upper && uplo != MagmaLower)
*info = -1;
else if (! nounit && diag != MagmaUnit)
*info = -2;
else if (n < 0)
*info = -3;
else if (ldda < max(1,n))
*info = -5;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Check for singularity if non-unit */
/* cannot do here with matrix dA on GPU -- need kernel */
/*
if (nounit) {
for (j=0; j < n; ++j) {
if ( MAGMA_C_EQUAL( *dA(j,j), c_zero )) {
*info = j+1; // Fortran index
return *info;
}
}
}
*/
/* Determine the block size for this environment */
nb = magma_get_cpotrf_nb(n);
/* Create Queues */
//magma_queue_t queues[2];
//magma_device_t device[MagmaMaxGPUs];
//magma_int_t num = 0;
//magma_int_t err;
//
//err = magma_getdevices( device, MagmaMaxGPUs, &num );
//if ( err != 0 || num < 1 ) {
// fprintf( stderr, "magma_getdevices failed: %d\n", err );
// exit(-1);
//}
//err = magma_queue_create( device[0], &queues[0] );
//if ( err != 0 ) {
// fprintf( stderr, "magma_queue_create 0 failed: %d\n", err );
// exit(-1);
//}
//err = magma_queue_create( device[0], &queues[1] );
//if ( err != 0 ) {
// fprintf( stderr, "magma_queue_create 1 failed: %d\n", err );
// exit(-1);
//}
if (MAGMA_SUCCESS != magma_cmalloc_cpu( &work, nb*nb )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
if (nb <= 1 || nb >= n) {
magma_cgetmatrix( n, n, dA, dA_offset, ldda, work, n, queues[0] );
lapackf77_ctrtri( lapack_const(uplo), lapack_const(diag), &n, work, &n, info );
magma_csetmatrix( n, n, work, n, dA, dA_offset, ldda, queues[0] );
}
else {
if (upper) {
/* Compute inverse of upper triangular matrix */
for (j=0; j < n; j += nb) {
jb = min(nb, (n-j));
/* Compute rows 1:j-1 of current block column */
magma_ctrmm( MagmaLeft, MagmaUpper,
MagmaNoTrans, MagmaNonUnit, j, jb,
c_one, dA(0,0), ldda, dA(0, j), ldda,
queues[0] );
magma_ctrsm( MagmaRight, MagmaUpper,
MagmaNoTrans, MagmaNonUnit, j, jb,
c_neg_one, dA(j,j), ldda, dA(0, j), ldda,
queues[0] );
magma_cgetmatrix_async( jb, jb,
dA(j, j), ldda,
work, jb, queues[1], NULL );
magma_queue_sync( queues[1] );
/* Compute inverse of current diagonal block */
lapackf77_ctrtri( MagmaUpperStr, lapack_const(diag), &jb, work, &jb, info );
/*
magma_csetmatrix_async( jb, jb,
work, 0, jb,
dA(j, j), ldda, queues[0], NULL );
*/
magma_csetmatrix( jb, jb,
work, jb,
dA(j, j), ldda, queues[0] );
}
}
else {
/* Compute inverse of lower triangular matrix */
nn = ((n-1)/nb)*nb+1;
for(j=nn-1; j >= 0; j -= nb) {
jb = min(nb,(n-j));
if((j+jb) < n) {
/* Compute rows j+jb:n of current block column */
magma_ctrmm( MagmaLeft, MagmaLower,
MagmaNoTrans, MagmaNonUnit, (n-j-jb), jb,
c_one, dA(j+jb,j+jb), ldda, dA(j+jb, j), ldda,
queues[0] );
magma_ctrsm( MagmaRight, MagmaLower,
MagmaNoTrans, MagmaNonUnit, (n-j-jb), jb,
c_neg_one, dA(j,j), ldda, dA(j+jb, j), ldda,
queues[0] );
}
magma_cgetmatrix_async( jb, jb,
dA(j, j), ldda,
work, jb, queues[1], NULL );
magma_queue_sync( queues[1] );
/* Compute inverse of current diagonal block */
lapackf77_ctrtri( MagmaLowerStr, lapack_const(diag), &jb, work, &jb, info );
/*
magma_csetmatrix_async( jb, jb,
work, 0, jb,
dA(j, j), ldda, queues[0], NULL );
*/
magma_csetmatrix( jb, jb,
work, jb,
dA(j, j), ldda, queues[0] );
}
}
}
//magma_queue_destroy( queues[0] );
//magma_queue_destroy( queues[1] );
magma_free_cpu( work );
return *info;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing cgemm_batched
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, magma_perf, magma_time, cublas_perf, cublas_time, cpu_perf, cpu_time;
float magma_error, cublas_error, magma_err, cublas_err, Cnorm, work[1];
magma_int_t M, N, K;
magma_int_t Am, An, Bm, Bn;
magma_int_t sizeA, sizeB, sizeC;
magma_int_t lda, ldb, ldc, ldda, lddb, lddc;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
magma_int_t NN;
magma_int_t batchCount;
magmaFloatComplex *h_A, *h_B, *h_C, *h_Cmagma, *h_Ccublas;
magmaFloatComplex *d_A, *d_B, *d_C;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex alpha = MAGMA_C_MAKE( 0.29, -0.86 );
magmaFloatComplex beta = MAGMA_C_MAKE( -0.48, 0.38 );
magmaFloatComplex **A_array = NULL;
magmaFloatComplex **B_array = NULL;
magmaFloatComplex **C_array = NULL;
magma_queue_t queue = magma_stream;
magma_opts opts;
parse_opts( argc, argv, &opts );
batchCount = opts.batchcount;
cublasHandle_t handle = opts.handle;
//float tol = opts.tolerance * lapackf77_slamch("E");
printf("If running lapack (option --lapack), MAGMA and CUBLAS error are both computed\n"
"relative to CPU BLAS result. Else, MAGMA error is computed relative to CUBLAS result.\n\n"
"transA = %s, transB = %s\n",
lapack_trans_const(opts.transA),
lapack_trans_const(opts.transB));
printf("BatchCount M N K MAGMA Gflop/s (ms) CUBLAS Gflop/s (ms) CPU Gflop/s (ms) MAGMA error CUBLAS error\n");
printf("=========================================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[itest];
N = opts.nsize[itest];
K = opts.ksize[itest];
gflops = FLOPS_CGEMM( M, N, K ) / 1e9 * batchCount;
if ( opts.transA == MagmaNoTrans ) {
lda = Am = M;
An = K;
} else {
lda = Am = K;
An = M;
}
if ( opts.transB == MagmaNoTrans ) {
ldb = Bm = K;
Bn = N;
} else {
ldb = Bm = N;
Bn = K;
}
ldc = M;
NN = N * batchCount;
ldda = ((lda+31)/32)*32;
lddb = ((ldb+31)/32)*32;
lddc = ((ldc+31)/32)*32;
sizeA = lda*An*batchCount;
sizeB = ldb*Bn*batchCount;
sizeC = ldc*N*batchCount;
TESTING_MALLOC_CPU( h_A, magmaFloatComplex, sizeA );
TESTING_MALLOC_CPU( h_B, magmaFloatComplex, sizeB );
TESTING_MALLOC_CPU( h_C, magmaFloatComplex, sizeC );
TESTING_MALLOC_CPU( h_Cmagma, magmaFloatComplex, sizeC );
TESTING_MALLOC_CPU( h_Ccublas, magmaFloatComplex, sizeC );
TESTING_MALLOC_DEV( d_A, magmaFloatComplex, ldda*An*batchCount );
TESTING_MALLOC_DEV( d_B, magmaFloatComplex, lddb*Bn*batchCount );
TESTING_MALLOC_DEV( d_C, magmaFloatComplex, lddc*N*batchCount );
magma_malloc((void**)&A_array, batchCount * sizeof(*A_array));
magma_malloc((void**)&B_array, batchCount * sizeof(*B_array));
magma_malloc((void**)&C_array, batchCount * sizeof(*C_array));
/* Initialize the matrices */
lapackf77_clarnv( &ione, ISEED, &sizeA, h_A );
lapackf77_clarnv( &ione, ISEED, &sizeB, h_B );
lapackf77_clarnv( &ione, ISEED, &sizeC, h_C );
/* =====================================================================
Performs operation using MAGMABLAS
=================================================================== */
magma_csetmatrix( Am, An*batchCount, h_A, lda, d_A, ldda );
magma_csetmatrix( Bm, Bn*batchCount, h_B, ldb, d_B, lddb );
magma_csetmatrix( M, N*batchCount, h_C, ldc, d_C, lddc );
cset_pointer(A_array, d_A, ldda, 0, 0, ldda*An, batchCount, queue);
cset_pointer(B_array, d_B, lddb, 0, 0, lddb*Bn, batchCount, queue);
cset_pointer(C_array, d_C, lddc, 0, 0, lddc*N, batchCount, queue);
magma_time = magma_sync_wtime( NULL );
magmablas_cgemm_batched(opts.transA, opts.transB, M, N, K,
alpha, A_array, ldda,
B_array, lddb,
beta, C_array, lddc, batchCount, queue);
magma_time = magma_sync_wtime( NULL ) - magma_time;
magma_perf = gflops / magma_time;
magma_cgetmatrix( M, N*batchCount, d_C, lddc, h_Cmagma, ldc );
/* =====================================================================
Performs operation using CUBLAS
=================================================================== */
magma_csetmatrix( M, N*batchCount, h_C, ldc, d_C, lddc );
cublas_time = magma_sync_wtime( NULL );
cublasCgemmBatched(handle, cublas_trans_const(opts.transA), cublas_trans_const(opts.transB), M, N, K,
&alpha, (const magmaFloatComplex**) A_array, ldda,
(const magmaFloatComplex**) B_array, lddb,
&beta, C_array, lddc, batchCount );
cublas_time = magma_sync_wtime( NULL ) - cublas_time;
cublas_perf = gflops / cublas_time;
magma_cgetmatrix( M, N*batchCount, d_C, lddc, h_Ccublas, ldc );
/* =====================================================================
Performs operation using CPU BLAS
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
for(int i=0; i<batchCount; i++)
{
blasf77_cgemm(
lapack_trans_const(opts.transA), lapack_trans_const(opts.transB),
&M, &N, &K,
&alpha, h_A + i*lda*An, &lda,
h_B + i*ldb*Bn, &ldb,
&beta, h_C + i*ldc*N, &ldc );
}
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
}
/* =====================================================================
Check the result
=================================================================== */
if ( opts.lapack ) {
// compute relative error for both magma & cublas, relative to lapack,
// |C_magma - C_lapack| / |C_lapack|
magma_error = 0.0;
cublas_error = 0.0;
for(int s=0; s<batchCount; s++)
{
magma_int_t C_batchSize = ldc * N;
Cnorm = lapackf77_clange( "M", &M, &N, h_C + s*C_batchSize, &ldc, work );
blasf77_caxpy( &C_batchSize, &c_neg_one, h_C + s*C_batchSize, &ione, h_Cmagma + s*C_batchSize, &ione );
magma_err = lapackf77_clange( "M", &M, &N, h_Cmagma + s*C_batchSize, &ldc, work ) / Cnorm;
if ( isnan(magma_err) || isinf(magma_err) ) {
magma_error = magma_err;
break;
}
magma_error = max(fabs(magma_err), magma_error);
blasf77_caxpy( &C_batchSize, &c_neg_one, h_C + s*C_batchSize, &ione, h_Ccublas + s*C_batchSize, &ione );
cublas_err = lapackf77_clange( "M", &M, &N, h_Ccublas + s*C_batchSize, &ldc, work ) / Cnorm;
if ( isnan(cublas_err) || isinf(cublas_err) ) {
cublas_error = cublas_err;
break;
}
cublas_error = max(fabs(cublas_err), cublas_error);
}
printf("%10d %5d %5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %8.2e \n",
(int) batchCount, (int) M, (int) N, (int) K,
magma_perf, 1000.*magma_time,
cublas_perf, 1000.*cublas_time,
cpu_perf, 1000.*cpu_time,
magma_error, cublas_error);
}
else {
// compute relative error for magma, relative to cublas
Cnorm = lapackf77_clange( "M", &M, &NN, h_Ccublas, &ldc, work );
blasf77_caxpy( &sizeC, &c_neg_one, h_Ccublas, &ione, h_Cmagma, &ione );
magma_error = lapackf77_clange( "M", &M, &NN, h_Cmagma, &ldc, work ) / Cnorm;
printf("%10d %5d %5d %5d %7.2f (%7.2f) %7.2f (%7.2f) --- ( --- ) %8.2e ---\n",
(int) batchCount, (int) M, (int) N, (int) K,
magma_perf, 1000.*magma_time,
cublas_perf, 1000.*cublas_time,
magma_error );
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_B );
TESTING_FREE_CPU( h_C );
TESTING_FREE_CPU( h_Cmagma );
TESTING_FREE_CPU( h_Ccublas );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_B );
TESTING_FREE_DEV( d_C );
TESTING_FREE_DEV( A_array );
TESTING_FREE_DEV( B_array );
TESTING_FREE_DEV( C_array );
fflush( stdout);
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
extern "C" magma_int_t
magma_chetrd_gpu(char uplo, magma_int_t n,
magmaFloatComplex *da, magma_int_t ldda,
float *d, float *e, magmaFloatComplex *tau,
magmaFloatComplex *wa, magma_int_t ldwa,
magmaFloatComplex *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
=======
CHETRD_GPU reduces a complex Hermitian matrix A to real symmetric
tridiagonal form T by an orthogonal similarity transformation:
Q**H * A * Q = T.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
DA (device input/output) COMPLEX array on the GPU, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if UPLO = 'U', the diagonal and first superdiagonal
of A are overwritten by the corresponding elements of the
tridiagonal matrix T, and the elements above the first
superdiagonal, with the array TAU, represent the orthogonal
matrix Q as a product of elementary reflectors; if UPLO
= 'L', the diagonal and first subdiagonal of A are over-
written by the corresponding elements of the tridiagonal
matrix T, and the elements below the first subdiagonal, with
the array TAU, represent the orthogonal matrix Q as a product
of elementary reflectors. See Further Details.
LDDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
D (output) COMPLEX array, dimension (N)
The diagonal elements of the tridiagonal matrix T:
D(i) = A(i,i).
E (output) COMPLEX array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix T:
E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.
TAU (output) COMPLEX array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).
WA (workspace/output) COMPLEX array, dimension (LDA,N)
On exit the diagonal, the upper part (UPLO='U')
or the lower part (UPLO='L') are copies of DA
LDWA (input) INTEGER
The leading dimension of the array WA. LDWA >= max(1,N).
WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= N*NB, where NB is the
optimal blocksize given by magma_get_chetrd_nb().
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
Further Details
===============
If UPLO = 'U', the matrix Q is represented as a product of elementary
reflectors
Q = H(n-1) . . . H(2) H(1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
A(1:i-1,i+1), and tau in TAU(i).
If UPLO = 'L', the matrix Q is represented as a product of elementary
reflectors
Q = H(1) H(2) . . . H(n-1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
and tau in TAU(i).
The contents of A on exit are illustrated by the following examples
with n = 5:
if UPLO = 'U': if UPLO = 'L':
( d e v2 v3 v4 ) ( d )
( d e v3 v4 ) ( e d )
( d e v4 ) ( v1 e d )
( d e ) ( v1 v2 e d )
( d ) ( v1 v2 v3 e d )
where d and e denote diagonal and off-diagonal elements of T, and vi
denotes an element of the vector defining H(i).
===================================================================== */
char uplo_[2] = {uplo, 0};
magma_int_t nb = magma_get_chetrd_nb(n);
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex c_one = MAGMA_C_ONE;
float d_one = MAGMA_D_ONE;
magma_int_t kk, nx;
magma_int_t i, j, i_n;
magma_int_t iinfo;
magma_int_t ldw, lddw, lwkopt;
magma_int_t lquery;
*info = 0;
int upper = lapackf77_lsame(uplo_, "U");
lquery = lwork == -1;
if (! upper && ! lapackf77_lsame(uplo_, "L")) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,n)) {
*info = -4;
} else if (ldwa < max(1,n)) {
*info = -9;
} else if (lwork < nb*n && ! lquery) {
*info = -11;
}
/* Determine the block size. */
ldw = lddw = n;
lwkopt = n * nb;
if (*info == 0) {
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 (n == 0) {
work[0] = c_one;
return *info;
}
magmaFloatComplex *dwork;
if (n < 2048)
nx = n;
else
nx = 512;
if (MAGMA_SUCCESS != magma_cmalloc( &dwork, (ldw*nb) )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
if (upper) {
/* Reduce the upper triangle of A.
Columns 1:kk are handled by the unblocked method. */
kk = n - (n - nx + nb - 1) / nb * nb;
for (i = n - nb; i >= kk; i -= nb)
{
/* Reduce columns i:i+nb-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel */
magma_cgetmatrix( i+nb, nb, dA(0, i), ldda, A(0, i), ldwa );
magma_clatrd(uplo, i+nb, nb, A(0, 0), ldwa, e, tau,
work, ldw, dA(0, 0), ldda, dwork, lddw);
/* Update the unreduced submatrix A(0:i-2,0:i-2), using an
update of the form: A := A - V*W' - W*V' */
magma_csetmatrix( i + nb, nb, work, ldw, dwork, lddw );
magma_cher2k(uplo, MagmaNoTrans, i, nb, c_neg_one,
dA(0, i), ldda, dwork,
lddw, d_one, dA(0, 0), ldda);
/* Copy superdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+nb; ++j) {
*A(j-1,j) = MAGMA_C_MAKE( e[j - 1], 0 );
d[j] = MAGMA_C_REAL( *A(j, j) );
}
}
magma_cgetmatrix( kk, kk, dA(0, 0), ldda, A(0, 0), ldwa );
/* Use CPU code to reduce the last or only block */
lapackf77_chetrd(uplo_, &kk, A(0, 0), &ldwa, d, e, tau, work, &lwork, &iinfo);
magma_csetmatrix( kk, kk, A(0, 0), ldwa, dA(0, 0), ldda );
}
else
{
/* Reduce the lower triangle of A */
for (i = 0; i < n-nx; i += nb)
{
/* Reduce columns i:i+nb-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel */
magma_cgetmatrix( n-i, nb, dA(i, i), ldda, A(i, i), ldwa );
magma_clatrd(uplo, n-i, nb, A(i, i), ldwa, &e[i],
&tau[i], work, ldw,
dA(i, i), ldda,
dwork, lddw);
/* Update the unreduced submatrix A(i+ib:n,i+ib:n), using
an update of the form: A := A - V*W' - W*V' */
magma_csetmatrix( n-i, nb, work, ldw, dwork, lddw );
magma_cher2k(MagmaLower, MagmaNoTrans, n-i-nb, nb, c_neg_one,
dA(i+nb, i), ldda,
&dwork[nb], lddw, d_one,
dA(i+nb, i+nb), ldda);
/* Copy subdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+nb; ++j) {
*A(j+1,j) = MAGMA_C_MAKE( e[j], 0 );
d[j] = MAGMA_C_REAL( *A(j, j) );
}
}
/* Use unblocked code to reduce the last or only block */
magma_cgetmatrix( n-i, n-i, dA(i, i), ldda, A(i, i), ldwa );
i_n = n-i;
lapackf77_chetrd(uplo_, &i_n, A(i, i), &ldwa, &d[i], &e[i],
&tau[i], work, &lwork, &iinfo);
magma_csetmatrix( n-i, n-i, A(i, i), ldwa, dA(i, i), ldda );
}
magma_free( dwork );
work[0] = MAGMA_C_MAKE( lwkopt, 0 );
return *info;
} /* chetrd_gpu */
extern "C" magma_int_t
magma_cunmqr(const char side, const char trans,
magma_int_t m, magma_int_t n, magma_int_t k,
cuFloatComplex *A, magma_int_t lda,
cuFloatComplex *tau,
cuFloatComplex *C, magma_int_t ldc,
cuFloatComplex *work, magma_int_t lwork,
magma_int_t *info)
{
/* -- MAGMA (version 1.3.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
November 2012
Purpose
=======
CUNMQR overwrites the general complex M-by-N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'T': Q**H * C C * Q**H
where Q is a complex orthogonal matrix defined as the product of k
elementary reflectors
Q = H(1) H(2) . . . H(k)
as returned by CGEQRF. 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**H from the Left;
= 'R': apply Q or Q**H from the Right.
TRANS (input) CHARACTER*1
= 'N': No transpose, apply Q;
= 'T': Transpose, apply Q**H.
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) COMPLEX array, dimension (LDA,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
CGEQRF 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) COMPLEX array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by CGEQRF.
C (input/output) 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.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace/output) COMPLEX 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_cgeqrf_nb( min( m, n ));
cuFloatComplex c_one = MAGMA_C_ONE;
char side_[2] = {side, 0};
char trans_[2] = {trans, 0};
magma_int_t nq_i, lddwork;
magma_int_t i;
cuFloatComplex T[ 2*nb*nb ];
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_C_MAKE( lwkopt, 0 );
if (! left && ! lapackf77_lsame(side_, "R")) {
*info = -1;
} else if (! notran && ! lapackf77_lsame(trans_, MagmaConjTransStr)) {
*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;
cuFloatComplex *dwork, *dC;
magma_cmalloc( &dC, lddc*n );
magma_cmalloc( &dwork, (m + n + nb)*nb );
/* Copy matrix C from the CPU to the GPU */
magma_csetmatrix( m, n, C, ldc, dC, lddc );
if (nb >= k) {
/* Use CPU code */
lapackf77_cunmqr(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;
}
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_clarft("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 */
cpanel_to_q('U', ib, A(i,i), lda, T+ib*ib);
magma_csetmatrix( nq_i, ib, A(i,i), lda, dwork, nq_i );
cq_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_csetmatrix( ib, ib, T, ib, dwork+nq_i*ib, ib );
magma_clarfb_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_cgetmatrix( m, n, dC, lddc, C, ldc );
}
work[0] = MAGMA_C_MAKE( lwkopt, 0 );
magma_free( dC );
magma_free( dwork );
return *info;
} /* magma_cunmqr */
/**
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 */
/* ////////////////////////////////////////////////////////////////////////////
-- Testing ctranspose
Code is very similar to testing_csymmetrize.cpp
*/
int main( int argc, char** argv)
{
TESTING_INIT();
// OpenCL use: cl_mem , offset (two arguments);
// else use: pointer + offset (one argument).
#ifdef HAVE_clBLAS
#define d_A(i_, j_) d_A, ((i_) + (j_)*ldda)
#define d_B(i_, j_) d_B, ((i_) + (j_)*lddb)
#else
#define d_A(i_, j_) (d_A + (i_) + (j_)*ldda)
#define d_B(i_, j_) (d_B + (i_) + (j_)*lddb)
#endif
real_Double_t gbytes, gpu_perf, gpu_time, gpu_perf2=0, gpu_time2=0, cpu_perf, cpu_time;
float error, error2, work[1];
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex *h_A, *h_B, *h_R;
magmaFloatComplex_ptr d_A, d_B;
magma_int_t M, N, size, lda, ldda, ldb, lddb;
magma_int_t ione = 1;
magma_int_t status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
#ifdef COMPLEX
magma_int_t ntrans = 2;
magma_trans_t trans[] = { Magma_ConjTrans, MagmaTrans };
#else
magma_int_t ntrans = 1;
magma_trans_t trans[] = { MagmaTrans };
#endif
printf("%% Inplace transpose requires M == N.\n");
printf("%% Trans M N CPU GByte/s (ms) GPU GByte/s (ms) check Inplace GB/s (ms) check\n");
printf("%%=========================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int itran = 0; itran < ntrans; ++itran ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[itest];
N = opts.nsize[itest];
lda = M;
ldda = magma_roundup( M, opts.align ); // multiple of 32 by default
ldb = N;
lddb = magma_roundup( N, opts.align ); // multiple of 32 by default
// load entire matrix, save entire matrix
gbytes = sizeof(magmaFloatComplex) * 2.*M*N / 1e9;
TESTING_MALLOC_CPU( h_A, magmaFloatComplex, lda*N ); // input: M x N
TESTING_MALLOC_CPU( h_B, magmaFloatComplex, ldb*M ); // output: N x M
TESTING_MALLOC_CPU( h_R, magmaFloatComplex, ldb*M ); // output: N x M
TESTING_MALLOC_DEV( d_A, magmaFloatComplex, ldda*N ); // input: M x N
TESTING_MALLOC_DEV( d_B, magmaFloatComplex, lddb*M ); // output: N x M
/* Initialize the matrix */
for( int j = 0; j < N; ++j ) {
for( int i = 0; i < M; ++i ) {
h_A[i + j*lda] = MAGMA_C_MAKE( i + j/10000., j );
}
}
for( int j = 0; j < M; ++j ) {
for( int i = 0; i < N; ++i ) {
h_B[i + j*ldb] = MAGMA_C_MAKE( i + j/10000., j );
}
}
magma_csetmatrix( N, M, h_B, ldb, d_B(0,0), lddb, opts.queue );
/* =====================================================================
Performs operation using naive out-of-place algorithm
(LAPACK doesn't implement transpose)
=================================================================== */
cpu_time = magma_wtime();
//for( int j = 1; j < N-1; ++j ) { // inset by 1 row & col
// for( int i = 1; i < M-1; ++i ) { // inset by 1 row & col
if ( trans[itran] == MagmaTrans ) {
for( int j = 0; j < N; ++j ) {
for( int i = 0; i < M; ++i ) {
h_B[j + i*ldb] = h_A[i + j*lda];
}
}
}
else {
for( int j = 0; j < N; ++j ) {
for( int i = 0; i < M; ++i ) {
h_B[j + i*ldb] = conj( h_A[i + j*lda] );
}
}
}
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gbytes / cpu_time;
/* ====================================================================
Performs operation using MAGMA, out-of-place
=================================================================== */
magma_csetmatrix( M, N, h_A, lda, d_A(0,0), ldda, opts.queue );
magma_csetmatrix( N, M, h_B, ldb, d_B(0,0), lddb, opts.queue );
gpu_time = magma_sync_wtime( opts.queue );
if ( trans[itran] == MagmaTrans ) {
//magmablas_ctranspose( M-2, N-2, d_A(1,1), ldda, d_B(1,1), lddb, opts.queue ); // inset by 1 row & col
magmablas_ctranspose( M, N, d_A(0,0), ldda, d_B(0,0), lddb, opts.queue );
}
#ifdef HAVE_CUBLAS
else {
//magmablas_ctranspose_conj( M-2, N-2, d_A(1,1), ldda, d_B(1,1), lddb, opts.queue ); // inset by 1 row & col
magmablas_ctranspose_conj( M, N, d_A(0,0), ldda, d_B(0,0), lddb, opts.queue );
}
#endif
gpu_time = magma_sync_wtime( opts.queue ) - gpu_time;
gpu_perf = gbytes / gpu_time;
/* ====================================================================
Performs operation using MAGMA, in-place
=================================================================== */
if ( M == N ) {
magma_csetmatrix( M, N, h_A, lda, d_A(0,0), ldda, opts.queue );
gpu_time2 = magma_sync_wtime( opts.queue );
if ( trans[itran] == MagmaTrans ) {
//magmablas_ctranspose_inplace( N-2, d_A(1,1), ldda, opts.queue ); // inset by 1 row & col
magmablas_ctranspose_inplace( N, d_A(0,0), ldda, opts.queue );
}
#ifdef HAVE_CUBLAS
else {
//magmablas_ctranspose_conj_inplace( N-2, d_A(1,1), ldda, opts.queue ); // inset by 1 row & col
magmablas_ctranspose_conj_inplace( N, d_A(0,0), ldda, opts.queue );
}
#endif
gpu_time2 = magma_sync_wtime( opts.queue ) - gpu_time2;
gpu_perf2 = gbytes / gpu_time2;
}
/* =====================================================================
Check the result
=================================================================== */
// check out-of-place transpose (d_B)
size = ldb*M;
magma_cgetmatrix( N, M, d_B(0,0), lddb, h_R, ldb, opts.queue );
blasf77_caxpy( &size, &c_neg_one, h_B, &ione, h_R, &ione );
error = lapackf77_clange("f", &N, &M, h_R, &ldb, work );
if ( M == N ) {
// also check in-place tranpose (d_A)
magma_cgetmatrix( N, M, d_A(0,0), ldda, h_R, ldb, opts.queue );
blasf77_caxpy( &size, &c_neg_one, h_B, &ione, h_R, &ione );
error2 = lapackf77_clange("f", &N, &M, h_R, &ldb, work );
printf("%5c %5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %6s %7.2f (%7.2f) %s\n",
lapacke_trans_const( trans[itran] ),
(int) M, (int) N,
cpu_perf, cpu_time*1000., gpu_perf, gpu_time*1000.,
(error == 0. ? "ok" : "failed"),
gpu_perf2, gpu_time2,
(error2 == 0. ? "ok" : "failed") );
status += ! (error == 0. && error2 == 0.);
}
else {
printf("%5c %5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %6s --- ( --- )\n",
lapacke_trans_const( trans[itran] ),
(int) M, (int) N,
cpu_perf, cpu_time*1000., gpu_perf, gpu_time*1000.,
(error == 0. ? "ok" : "failed") );
status += ! (error == 0.);
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_B );
TESTING_FREE_CPU( h_R );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_B );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
/**
Purpose
-------
Solves a system of linear equations
A * X = B
where A is a general N-by-N matrix and X and B are N-by-NRHS matrices.
The LU decomposition with partial pivoting and row interchanges is
used to factor A as
A = P * L * U,
where P is a permutation matrix, L is unit lower triangular, and U is
upper triangular. The factored form of A is then used to solve the
system of equations A * X = B.
Arguments
---------
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in]
nrhs INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
@param[in,out]
A COMPLEX array, dimension (LDA,N).
On entry, the M-by-N matrix to be factored.
On exit, the factors L and U from the factorization
A = P*L*U; the unit diagonal elements of L are not stored.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[out]
ipiv INTEGER array, dimension (min(M,N))
The pivot indices; for 1 <= i <= min(M,N), row i of the
matrix was interchanged with row IPIV(i).
@param[in,out]
B COMPLEX array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
@param[in]
ldb INTEGER
The leading dimension of the array B. LDB >= max(1,N).
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_cgesv_driver
********************************************************************/
extern "C" magma_int_t
magma_cgesv(
magma_int_t n, magma_int_t nrhs,
magmaFloatComplex *A, magma_int_t lda,
magma_int_t *ipiv,
magmaFloatComplex *B, magma_int_t ldb,
magma_int_t *info)
{
magma_int_t ngpu, ldda, lddb;
*info = 0;
if (n < 0) {
*info = -1;
} else if (nrhs < 0) {
*info = -2;
} else if (lda < max(1,n)) {
*info = -4;
} else if (ldb < max(1,n)) {
*info = -7;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (n == 0 || nrhs == 0) {
return *info;
}
/* If single-GPU and allocation suceeds, use GPU interface. */
ngpu = magma_num_gpus();
magmaFloatComplex *dA, *dB;
if ( ngpu > 1 ) {
goto CPU_INTERFACE;
}
ldda = ((n+31)/32)*32;
lddb = ldda;
if ( MAGMA_SUCCESS != magma_cmalloc( &dA, ldda*n )) {
goto CPU_INTERFACE;
}
if ( MAGMA_SUCCESS != magma_cmalloc( &dB, lddb*nrhs )) {
magma_free( dA );
goto CPU_INTERFACE;
}
magma_csetmatrix( n, n, A, lda, dA, ldda );
magma_cgetrf_gpu( n, n, dA, ldda, ipiv, info );
if ( *info == MAGMA_ERR_DEVICE_ALLOC ) {
magma_free( dA );
magma_free( dB );
goto CPU_INTERFACE;
}
magma_cgetmatrix( n, n, dA, ldda, A, lda );
if ( *info == 0 ) {
magma_csetmatrix( n, nrhs, B, ldb, dB, lddb );
magma_cgetrs_gpu( MagmaNoTrans, n, nrhs, dA, ldda, ipiv, dB, lddb, info );
magma_cgetmatrix( n, nrhs, dB, lddb, B, ldb );
}
magma_free( dA );
magma_free( dB );
return *info;
CPU_INTERFACE:
/* If multi-GPU or allocation failed, use CPU interface and LAPACK.
* Faster to use LAPACK for getrs than to copy A to GPU. */
magma_cgetrf( n, n, A, lda, ipiv, info );
if ( *info == 0 ) {
lapackf77_cgetrs( MagmaNoTransStr, &n, &nrhs, A, &lda, ipiv, B, &ldb, info );
}
return *info;
}
/**
Purpose
-------
CGEQLF computes a QL factorization of a COMPLEX 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 COMPLEX 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 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,N,2*NB^2).
For optimum performance LWORK >= max(N*NB, 2*NB^2) where NB can be obtained
through magma_get_cgeqlf_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 complex scalar, and v is a complex 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_cgeqlf_comp
********************************************************************/
extern "C" magma_int_t
magma_cgeqlf(
magma_int_t m, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork,
magma_int_t *info)
{
#define A(i_,j_) ( A + (i_) + (j_)*lda)
#define dA(i_,j_) (dA + (i_) + (j_)*ldda)
#define dwork(i_) (dwork + (i_))
magmaFloatComplex_ptr dA, dwork;
magmaFloatComplex c_one = MAGMA_C_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_cgeqlf_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_C_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_cmalloc( &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_csetmatrix_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_cgetmatrix_async( rows, ib,
dA(0, n-k+i), ldda,
A(0, n-k+i), lda, queues[1] );
magma_cgetmatrix_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_clarfb_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_cgeqlf( &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_clarft( MagmaBackwardStr, MagmaColumnwiseStr,
&rows, &ib,
A(0, cols), &lda, tau + i, work, &ib);
cpanel_to_q( MagmaLower, ib, A(rows-ib,cols), lda, work+ib*ib);
magma_csetmatrix( rows, ib,
A(0,cols), lda,
dA(0,cols), ldda );
cq_to_panel( MagmaLower, ib, A(rows-ib,cols), lda, work+ib*ib);
// Send the triangular part on the GPU
magma_csetmatrix( 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_clarfb_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_clarfb_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_cgetmatrix( 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_cgeqlf(&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_cgeqlf */
/* ////////////////////////////////////////////////////////////////////////////
-- Testing cunmqr_gpu
*/
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
float error, work[1];
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magma_int_t ione = 1;
magma_int_t m, n, k, size, info;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t nb, ldc, lda, lwork, lwork_max, dt_size;
magmaFloatComplex *C, *R, *A, *W, *tau;
magmaFloatComplex *dC, *dA, *dT;
magma_opts opts;
parse_opts( argc, argv, &opts );
// test all combinations of input parameters
const char* side[] = { MagmaLeftStr, MagmaRightStr };
const char* trans[] = { MagmaConjTransStr, MagmaNoTransStr };
printf(" M N K side trans CPU GFlop/s (sec) GPU GFlop/s (sec) ||R||_F / ||QC||_F\n");
printf("===============================================================================================\n");
for( int i = 0; i < opts.ntest; ++i ) {
for( int iside = 0; iside < 2; ++iside ) {
for( int itran = 0; itran < 2; ++itran ) {
m = opts.msize[i];
n = opts.nsize[i];
k = opts.ksize[i];
nb = magma_get_cgeqrf_nb( m );
ldc = ((m + 31)/32)*32;
lda = ((max(m,n) + 31)/32)*32;
gflops = FLOPS_CUNMQR( m, n, k, *side[iside] ) / 1e9;
if ( *side[iside] == 'L' && m < k ) {
printf( "%5d %5d %5d %-5s %-9s skipping because side=left and m < k\n",
(int) m, (int) n, (int) k, side[iside], trans[itran] );
continue;
}
if ( *side[iside] == 'R' && n < k ) {
printf( "%5d %5d %5d %-5s %-9s skipping because side=right and n < k\n",
(int) m, (int) n, (int) k, side[iside], trans[itran] );
continue;
}
if ( *side[iside] == 'L' ) {
// side = left
lwork_max = (m - k + nb)*(n + nb) + n*nb;
dt_size = ( 2*min(m,k) + ((k + 31)/32)*32 )*nb;
}
else {
// side = right
lwork_max = (n - k + nb)*(m + nb) + m*nb;
dt_size = ( 2*min(n,k) + ((k + 31)/32)*32 )*nb;
}
TESTING_MALLOC( C, magmaFloatComplex, ldc*n );
TESTING_MALLOC( R, magmaFloatComplex, ldc*n );
TESTING_MALLOC( A, magmaFloatComplex, lda*k );
TESTING_MALLOC( W, magmaFloatComplex, lwork_max );
TESTING_MALLOC( tau, magmaFloatComplex, k );
TESTING_DEVALLOC( dC, magmaFloatComplex, ldc*n );
TESTING_DEVALLOC( dA, magmaFloatComplex, lda*k );
TESTING_DEVALLOC( dT, magmaFloatComplex, dt_size );
// C is full, m x n
size = ldc*n;
lapackf77_clarnv( &ione, ISEED, &size, C );
magma_csetmatrix( m, n, C, ldc, dC, ldc );
// A is m x k (left) or n x k (right)
lda = (*side[iside] == 'L' ? m : n);
size = lda*k;
lapackf77_clarnv( &ione, ISEED, &size, A );
// compute QR factorization to get Householder vectors in dA, tau, dT
magma_csetmatrix( lda, k, A, lda, dA, lda );
magma_cgeqrf_gpu( lda, k, dA, lda, tau, dT, &info );
magma_cgetmatrix( lda, k, dA, lda, A, lda );
if (info != 0)
printf("magma_cgeqrf_gpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
lapackf77_cunmqr( side[iside], 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_cunmqr returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
// query for work size
lwork = -1;
magma_cunmqr_gpu( *side[iside], *trans[itran],
m, n, k,
dA, lda, tau, dC, ldc, W, lwork, dT, nb, &info );
if (info != 0)
printf("magma_cunmqr_gpu (lwork query) returned error %d: %s.\n",
(int) info, magma_strerror( info ));
lwork = (magma_int_t) MAGMA_C_REAL( W[0] );
if ( lwork < 0 || lwork > lwork_max )
printf("invalid lwork %d, lwork_max %d\n", (int) lwork, (int) lwork_max );
gpu_time = magma_sync_wtime( 0 ); // sync needed for L,N and R,T cases
magma_cunmqr_gpu( *side[iside], *trans[itran],
m, n, k,
dA, lda, tau, dC, ldc, W, lwork, dT, nb, &info );
gpu_time = magma_sync_wtime( 0 ) - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_cunmqr_gpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
magma_cgetmatrix( m, n, dC, ldc, R, ldc );
/* =====================================================================
compute relative error |QC_magma - QC_lapack| / |QC_lapack|
=================================================================== */
error = lapackf77_clange( "Fro", &m, &n, C, &ldc, work );
size = ldc*n;
blasf77_caxpy( &size, &c_neg_one, C, &ione, R, &ione );
error = lapackf77_clange( "Fro", &m, &n, R, &ldc, work ) / error;
printf( "%5d %5d %5d %-5s %-9s %7.2f (%7.2f) %7.2f (%7.2f) %8.2e\n",
(int) m, (int) n, (int) k, side[iside], trans[itran],
cpu_perf, cpu_time, gpu_perf, gpu_time, error );
TESTING_FREE( C );
TESTING_FREE( R );
TESTING_FREE( A );
TESTING_FREE( W );
TESTING_FREE( tau );
TESTING_DEVFREE( dC );
TESTING_DEVFREE( dA );
TESTING_DEVFREE( dT );
}} // end iside, itran
printf( "\n" );
}
TESTING_FINALIZE();
return 0;
}
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, t1, t2;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magma_int_t ione = 1;
magma_trans_t trans[] = { MagmaNoTrans, MagmaConjTrans, MagmaTrans };
magma_uplo_t uplo [] = { MagmaLower, MagmaUpper };
magma_diag_t diag [] = { MagmaUnit, MagmaNonUnit };
magma_side_t side [] = { MagmaLeft, MagmaRight };
magmaFloatComplex *A, *B, *C, *C2, *LU;
magmaFloatComplex *dA, *dB, *dC1, *dC2;
magmaFloatComplex alpha = MAGMA_C_MAKE( 0.5, 0.1 );
magmaFloatComplex beta = MAGMA_C_MAKE( 0.7, 0.2 );
float dalpha = 0.6;
float dbeta = 0.8;
float work[1], error, total_error;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t m, n, k, size, maxn, ld, info;
magma_int_t *piv;
magma_int_t err;
magma_opts opts;
parse_opts( argc, argv, &opts );
printf( "Compares magma wrapper function to cublas function; all diffs should be exactly 0.\n\n" );
total_error = 0.;
for( int itest = 0; itest < opts.ntest; ++itest ) {
m = opts.msize[itest];
n = opts.nsize[itest];
k = opts.ksize[itest];
printf("=========================================================================\n");
printf( "m=%d, n=%d, k=%d\n", (int) m, (int) n, (int) k );
// allocate matrices
// over-allocate so they can be any combination of {m,n,k} x {m,n,k}.
maxn = max( max( m, n ), k );
ld = max( 1, maxn );
size = ld*maxn;
err = magma_malloc_cpu( (void**) &piv, maxn*sizeof(magma_int_t) ); assert( err == 0 );
err = magma_cmalloc_pinned( &A, size ); assert( err == 0 );
err = magma_cmalloc_pinned( &B, size ); assert( err == 0 );
err = magma_cmalloc_pinned( &C, size ); assert( err == 0 );
err = magma_cmalloc_pinned( &C2, size ); assert( err == 0 );
err = magma_cmalloc_pinned( &LU, size ); assert( err == 0 );
err = magma_cmalloc( &dA, size ); assert( err == 0 );
err = magma_cmalloc( &dB, size ); assert( err == 0 );
err = magma_cmalloc( &dC1, size ); assert( err == 0 );
err = magma_cmalloc( &dC2, size ); assert( err == 0 );
// initialize matrices
size = maxn*maxn;
lapackf77_clarnv( &ione, ISEED, &size, A );
lapackf77_clarnv( &ione, ISEED, &size, B );
lapackf77_clarnv( &ione, ISEED, &size, C );
printf( "========== Level 1 BLAS ==========\n" );
// ----- test CSWAP
// swap columns 2 and 3 of dA, then copy to C2 and compare with A
if ( n >= 3 ) {
magma_csetmatrix( m, n, A, ld, dA, ld );
magma_csetmatrix( m, n, A, ld, dB, ld );
magma_cswap( m, dA(0,1), 1, dA(0,2), 1 );
magma_cswap( m, dB(0,1), 1, dB(0,2), 1 );
// check results, storing diff between magma and cuda calls in C2
cublasCaxpy( handle, ld*n, &c_neg_one, dA, 1, dB, 1 );
magma_cgetmatrix( m, n, dB, ld, C2, ld );
error = lapackf77_clange( "F", &m, &k, C2, &ld, work );
total_error += error;
printf( "cswap diff %.2g\n", error );
}
else {
printf( "cswap skipped for n < 3\n" );
}
// ----- test ICAMAX
// get argmax of column of A
magma_csetmatrix( m, k, A, ld, dA, ld );
error = 0;
for( int j = 0; j < k; ++j ) {
magma_int_t i1 = magma_icamax( m, dA(0,j), 1 );
int i2; // NOT magma_int_t, for cublas
cublasIcamax( handle, m, dA(0,j), 1, &i2 );
// todo need sync here?
assert( i1 == i2 );
error += abs( i1 - i2 );
}
total_error += error;
gflops = (float)m * k / 1e9;
printf( "icamax diff %.2g\n", error );
printf( "\n" );
printf( "========== Level 2 BLAS ==========\n" );
// ----- test CGEMV
// c = alpha*A*b + beta*c, with A m*n; b,c m or n-vectors
// try no-trans/trans
for( int ia = 0; ia < 3; ++ia ) {
magma_csetmatrix( m, n, A, ld, dA, ld );
magma_csetvector( maxn, B, 1, dB, 1 );
magma_csetvector( maxn, C, 1, dC1, 1 );
magma_csetvector( maxn, C, 1, dC2, 1 );
t1 = magma_sync_wtime( 0 );
magma_cgemv( trans[ia], m, n, alpha, dA, ld, dB, 1, beta, dC1, 1 );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasCgemv( handle, cublas_trans_const(trans[ia]),
m, n, &alpha, dA, ld, dB, 1, &beta, dC2, 1 );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
size = (trans[ia] == MagmaNoTrans ? m : n);
cublasCaxpy( handle, size, &c_neg_one, dC1, 1, dC2, 1 );
magma_cgetvector( size, dC2, 1, C2, 1 );
error = lapackf77_clange( "F", &size, &ione, C2, &ld, work );
total_error += error;
gflops = FLOPS_CGEMV( m, n ) / 1e9;
printf( "cgemv( %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_trans_const(trans[ia]), error, gflops/t1, gflops/t2 );
}
printf( "\n" );
// ----- test CHEMV
// c = alpha*A*b + beta*c, with A m*m symmetric; b,c m-vectors
// try upper/lower
for( int iu = 0; iu < 2; ++iu ) {
magma_csetmatrix( m, m, A, ld, dA, ld );
magma_csetvector( m, B, 1, dB, 1 );
magma_csetvector( m, C, 1, dC1, 1 );
magma_csetvector( m, C, 1, dC2, 1 );
t1 = magma_sync_wtime( 0 );
magma_chemv( uplo[iu], m, alpha, dA, ld, dB, 1, beta, dC1, 1 );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasChemv( handle, cublas_uplo_const(uplo[iu]),
m, &alpha, dA, ld, dB, 1, &beta, dC2, 1 );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasCaxpy( handle, m, &c_neg_one, dC1, 1, dC2, 1 );
magma_cgetvector( m, dC2, 1, C2, 1 );
error = lapackf77_clange( "F", &m, &ione, C2, &ld, work );
total_error += error;
gflops = FLOPS_CHEMV( m ) / 1e9;
printf( "chemv( %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), error, gflops/t1, gflops/t2 );
}
printf( "\n" );
// ----- test CTRSV
// solve A*c = c, with A m*m triangular; c m-vector
// try upper/lower, no-trans/trans, unit/non-unit diag
// Factor A into LU to get well-conditioned triangles, else solve yields garbage.
// Still can give garbage if solves aren't consistent with LU factors,
// e.g., using unit diag for U, so copy lower triangle to upper triangle.
// Also used for trsm later.
lapackf77_clacpy( "Full", &maxn, &maxn, A, &ld, LU, &ld );
lapackf77_cgetrf( &maxn, &maxn, LU, &ld, piv, &info );
for( int j = 0; j < maxn; ++j ) {
for( int i = 0; i < j; ++i ) {
*LU(i,j) = *LU(j,i);
}
}
for( int iu = 0; iu < 2; ++iu ) {
for( int it = 0; it < 3; ++it ) {
for( int id = 0; id < 2; ++id ) {
magma_csetmatrix( m, m, LU, ld, dA, ld );
magma_csetvector( m, C, 1, dC1, 1 );
magma_csetvector( m, C, 1, dC2, 1 );
t1 = magma_sync_wtime( 0 );
magma_ctrsv( uplo[iu], trans[it], diag[id], m, dA, ld, dC1, 1 );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasCtrsv( handle, cublas_uplo_const(uplo[iu]), cublas_trans_const(trans[it]),
cublas_diag_const(diag[id]), m, dA, ld, dC2, 1 );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasCaxpy( handle, m, &c_neg_one, dC1, 1, dC2, 1 );
magma_cgetvector( m, dC2, 1, C2, 1 );
error = lapackf77_clange( "F", &m, &ione, C2, &ld, work );
total_error += error;
gflops = FLOPS_CTRSM( MagmaLeft, m, 1 ) / 1e9;
printf( "ctrsv( %c, %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), lapacke_trans_const(trans[it]), lapacke_diag_const(diag[id]),
error, gflops/t1, gflops/t2 );
}}}
printf( "\n" );
printf( "========== Level 3 BLAS ==========\n" );
// ----- test CGEMM
// C = alpha*A*B + beta*C, with A m*k or k*m; B k*n or n*k; C m*n
// try combinations of no-trans/trans
for( int ia = 0; ia < 3; ++ia ) {
for( int ib = 0; ib < 3; ++ib ) {
bool nta = (trans[ia] == MagmaNoTrans);
bool ntb = (trans[ib] == MagmaNoTrans);
magma_csetmatrix( (nta ? m : k), (nta ? m : k), A, ld, dA, ld );
magma_csetmatrix( (ntb ? k : n), (ntb ? n : k), B, ld, dB, ld );
magma_csetmatrix( m, n, C, ld, dC1, ld );
magma_csetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_cgemm( trans[ia], trans[ib], m, n, k, alpha, dA, ld, dB, ld, beta, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasCgemm( handle, cublas_trans_const(trans[ia]), cublas_trans_const(trans[ib]),
m, n, k, &alpha, dA, ld, dB, ld, &beta, dC2, ld );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasCaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_cgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_clange( "F", &m, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_CGEMM( m, n, k ) / 1e9;
printf( "cgemm( %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_trans_const(trans[ia]), lapacke_trans_const(trans[ib]),
error, gflops/t1, gflops/t2 );
}}
printf( "\n" );
// ----- test CHEMM
// C = alpha*A*B + beta*C (left) with A m*m symmetric; B,C m*n; or
// C = alpha*B*A + beta*C (right) with A n*n symmetric; B,C m*n
// try left/right, upper/lower
for( int is = 0; is < 2; ++is ) {
for( int iu = 0; iu < 2; ++iu ) {
magma_csetmatrix( m, m, A, ld, dA, ld );
magma_csetmatrix( m, n, B, ld, dB, ld );
magma_csetmatrix( m, n, C, ld, dC1, ld );
magma_csetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_chemm( side[is], uplo[iu], m, n, alpha, dA, ld, dB, ld, beta, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasChemm( handle, cublas_side_const(side[is]), cublas_uplo_const(uplo[iu]),
m, n, &alpha, dA, ld, dB, ld, &beta, dC2, ld );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasCaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_cgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_clange( "F", &m, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_CHEMM( side[is], m, n ) / 1e9;
printf( "chemm( %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_side_const(side[is]), lapacke_uplo_const(uplo[iu]),
error, gflops/t1, gflops/t2 );
}}
printf( "\n" );
// ----- test CHERK
// C = alpha*A*A^H + beta*C (no-trans) with A m*k and C m*m symmetric; or
// C = alpha*A^H*A + beta*C (trans) with A k*m and C m*m symmetric
// try upper/lower, no-trans/trans
for( int iu = 0; iu < 2; ++iu ) {
for( int it = 0; it < 3; ++it ) {
magma_csetmatrix( n, k, A, ld, dA, ld );
magma_csetmatrix( n, n, C, ld, dC1, ld );
magma_csetmatrix( n, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_cherk( uplo[iu], trans[it], n, k, dalpha, dA, ld, dbeta, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasCherk( handle, cublas_uplo_const(uplo[iu]), cublas_trans_const(trans[it]),
n, k, &dalpha, dA, ld, &dbeta, dC2, ld );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasCaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_cgetmatrix( n, n, dC2, ld, C2, ld );
error = lapackf77_clange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_CHERK( k, n ) / 1e9;
printf( "cherk( %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), lapacke_trans_const(trans[it]),
error, gflops/t1, gflops/t2 );
}}
printf( "\n" );
// ----- test CHER2K
// C = alpha*A*B^H + ^alpha*B*A^H + beta*C (no-trans) with A,B n*k; C n*n symmetric; or
// C = alpha*A^H*B + ^alpha*B^H*A + beta*C (trans) with A,B k*n; C n*n symmetric
// try upper/lower, no-trans/trans
for( int iu = 0; iu < 2; ++iu ) {
for( int it = 0; it < 3; ++it ) {
bool nt = (trans[it] == MagmaNoTrans);
magma_csetmatrix( (nt ? n : k), (nt ? n : k), A, ld, dA, ld );
magma_csetmatrix( n, n, C, ld, dC1, ld );
magma_csetmatrix( n, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_cher2k( uplo[iu], trans[it], n, k, alpha, dA, ld, dB, ld, dbeta, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasCher2k( handle, cublas_uplo_const(uplo[iu]), cublas_trans_const(trans[it]),
n, k, &alpha, dA, ld, dB, ld, &dbeta, dC2, ld );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasCaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_cgetmatrix( n, n, dC2, ld, C2, ld );
error = lapackf77_clange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_CHER2K( k, n ) / 1e9;
printf( "cher2k( %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), lapacke_trans_const(trans[it]),
error, gflops/t1, gflops/t2 );
}}
printf( "\n" );
// ----- test CTRMM
// C = alpha*A*C (left) with A m*m triangular; C m*n; or
// C = alpha*C*A (right) with A n*n triangular; C m*n
// try left/right, upper/lower, no-trans/trans, unit/non-unit
for( int is = 0; is < 2; ++is ) {
for( int iu = 0; iu < 2; ++iu ) {
for( int it = 0; it < 3; ++it ) {
for( int id = 0; id < 2; ++id ) {
bool left = (side[is] == MagmaLeft);
magma_csetmatrix( (left ? m : n), (left ? m : n), A, ld, dA, ld );
magma_csetmatrix( m, n, C, ld, dC1, ld );
magma_csetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_ctrmm( side[is], uplo[iu], trans[it], diag[id], m, n, alpha, dA, ld, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
// note cublas does trmm out-of-place (i.e., adds output matrix C),
// but allows C=B to do in-place.
t2 = magma_sync_wtime( 0 );
cublasCtrmm( handle, cublas_side_const(side[is]), cublas_uplo_const(uplo[iu]),
cublas_trans_const(trans[it]), cublas_diag_const(diag[id]),
m, n, &alpha, dA, ld, dC2, ld, dC2, ld );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasCaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_cgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_clange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_CTRMM( side[is], m, n ) / 1e9;
printf( "ctrmm( %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), lapacke_trans_const(trans[it]),
error, gflops/t1, gflops/t2 );
}}}}
printf( "\n" );
// ----- test CTRSM
// solve A*X = alpha*B (left) with A m*m triangular; B m*n; or
// solve X*A = alpha*B (right) with A n*n triangular; B m*n
// try left/right, upper/lower, no-trans/trans, unit/non-unit
for( int is = 0; is < 2; ++is ) {
for( int iu = 0; iu < 2; ++iu ) {
for( int it = 0; it < 3; ++it ) {
for( int id = 0; id < 2; ++id ) {
bool left = (side[is] == MagmaLeft);
magma_csetmatrix( (left ? m : n), (left ? m : n), LU, ld, dA, ld );
magma_csetmatrix( m, n, C, ld, dC1, ld );
magma_csetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_ctrsm( side[is], uplo[iu], trans[it], diag[id], m, n, alpha, dA, ld, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasCtrsm( handle, cublas_side_const(side[is]), cublas_uplo_const(uplo[iu]),
cublas_trans_const(trans[it]), cublas_diag_const(diag[id]),
m, n, &alpha, dA, ld, dC2, ld );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasCaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_cgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_clange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_CTRSM( side[is], m, n ) / 1e9;
printf( "ctrsm( %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), lapacke_trans_const(trans[it]),
error, gflops/t1, gflops/t2 );
}}}}
printf( "\n" );
// cleanup
magma_free_cpu( piv );
magma_free_pinned( A );
magma_free_pinned( B );
magma_free_pinned( C );
magma_free_pinned( C2 );
magma_free_pinned( LU );
magma_free( dA );
magma_free( dB );
magma_free( dC1 );
magma_free( dC2 );
}
if ( total_error != 0. ) {
printf( "total error %.2g -- ought to be 0 -- some test failed (see above).\n",
total_error );
}
else {
printf( "all tests passed\n" );
}
TESTING_FINALIZE();
int status = (total_error != 0.);
return status;
}
