// Solve dA * dX = dB, where dA and dX are stored in GPU device memory.
// Internally, MAGMA uses a hybrid CPU + GPU algorithm.
void GpuSolver::solve( magmaDouble_ptr X )
{
real_Double_t gpu_time;
magmaDouble_ptr dX=NULL, dWORKD=NULL, Z=NULL;
float *dWORKS=NULL;
magma_int_t qrsv_iters;
magma_int_t info = 0;
magma_dmalloc( &dX, n*nrhs );
magma_dmalloc( &dWORKD, n*nrhs );
magma_smalloc( &dWORKS, n*(n+nrhs) );
if ( dX == NULL || dWORKD == NULL || dWORKS == NULL ) {
fprintf( stderr, "malloc failed - not enough GPU memory?\n" );
goto cleanup;
}
gpu_time = magma_wtime();
magma_dsposv_gpu( MagmaUpper, n, nrhs,
dA, n, dB, n, dX, n,
dWORKD, dWORKS, &qrsv_iters, &info );
gpu_time = magma_wtime() - gpu_time;
fprintf( stdout, "DSPOSV GPU solution time = %fs\n", gpu_time);
if ( qrsv_iters == -3 ) {fprintf( stderr, "cannot factor input matrix in single precision, bad initialization?\n"); }
if ( info != 0 ) { fprintf( stderr, "magma_dsposv_gpu failed with info=%d\n", info ); }
magma_dgetmatrix( n, nrhs, dX, n, X, n );
cleanup:
magma_free( dX );
}
// init a zero matrix on GPU to store X'*X
GpuSolver::GpuSolver ( int nn, int outs ) {
magma_init();
n = nn;
nrhs = outs;
magma_int_t i, j;
magmaDouble_ptr A=NULL, B=NULL;
magma_dmalloc_cpu( &A, n*n );
magma_dmalloc_cpu( &B, n*nrhs );
magma_dmalloc( &dA, n*n );
magma_dmalloc( &dB, n*nrhs );
if ( dA == NULL || dB == NULL || A == NULL || B == NULL ) {
fprintf( stderr, "malloc failed - not enough GPU or system memory?\n" );
goto cleanup;
}
for( j=0; j < n; ++j ) {
for( i=0; i < n; ++i ) { A[i + j*n] = 0; }
}
for( j=0; j < nrhs; ++j ) {
for( i=0; i < n; ++i ) { B[i + j*n] = 0; }
}
magma_dsetmatrix( n, n, A, n, dA, n );
magma_dsetmatrix( n, nrhs, B, n, dB, n );
cleanup:
magma_free_cpu( A );
magma_free_cpu( B );
};
// init a zero matrix on GPU to store X'*X
void GpuSolver::add_data ( magma_int_t m, magmaDouble_ptr X, magmaDouble_ptr T ) {
real_Double_t time;
magmaDouble_ptr dX=NULL, dT=NULL;
magma_dmalloc( &dX, m*n );
magma_dmalloc( &dT, m*nrhs );
if ( dX == NULL || dT == NULL ) {
fprintf( stderr, "malloc failed - not enough GPU or system memory?\n" );
goto cleanup;
}
magma_dsetmatrix( m, n, X, m, dX, m );
magma_dsetmatrix( m, nrhs, T, m, dT, m );
time = magma_sync_wtime( NULL );
magma_dgemm( MagmaTrans, MagmaNoTrans, n, nrhs, m,
1, dX, m,
dT, m,
1, dB, n );
magma_dgemm( MagmaTrans, MagmaNoTrans, n, n, m,
1, dX, m,
dX, m,
1, dA, n );
time = magma_sync_wtime( NULL ) - time;
fprintf( stdout, "added data in %f sec\n", time );
cleanup:
magma_free( dX );
magma_free( dT );
};
// init a zero matrix on GPU to store X'*X, add normalization
GpuSolver::GpuSolver ( int nn, int outs, magmaDouble_ptr A, magmaDouble_ptr B ) {
magma_int_t err;
magma_int_t num = 0;
magma_device_t device;
magma_init();
err = magma_get_devices( &device, 1, &num );
if ( err != MAGMA_SUCCESS or num < 1 ) {
fprintf( stderr, "magma_get_devices failed: %d\n", (int) err );
exit(-1);
}
err = magma_queue_create( device, &queue );
if ( err != MAGMA_SUCCESS ) {
fprintf( stderr, "magma_queue_create failed: %d\n", (int) err );
exit(-1);
}
n = nn;
nrhs = outs;
magma_dmalloc( &dA, n*n );
magma_dmalloc( &dB, n*nrhs );
if ( dA == NULL || dB == NULL ) { fprintf( stderr, "malloc failed - not enough GPU memory?\n" ); }
magma_dsetmatrix( n, n, A, 0, n, dA, 0, n, queue );
magma_dsetmatrix( n, nrhs, B, 0, n, dB, 0, n, queue );
};
extern "C" magma_int_t
magma_dvinit(
magma_d_matrix *x,
magma_location_t mem_loc,
magma_int_t num_rows,
magma_int_t num_cols,
double values,
magma_queue_t queue )
{
magma_int_t info = 0;
x->val = NULL;
x->diag = NULL;
x->row = NULL;
x->rowidx = NULL;
x->col = NULL;
x->list = NULL;
x->blockinfo = NULL;
x->dval = NULL;
x->ddiag = NULL;
x->drow = NULL;
x->drowidx = NULL;
x->dcol = NULL;
x->dlist = NULL;
x->storage_type = Magma_DENSE;
x->memory_location = mem_loc;
x->sym = Magma_GENERAL;
x->diagorder_type = Magma_VALUE;
x->fill_mode = MagmaFull;
x->num_rows = num_rows;
x->num_cols = num_cols;
x->nnz = num_rows*num_cols;
x->max_nnz_row = num_cols;
x->diameter = 0;
x->blocksize = 1;
x->numblocks = 1;
x->alignment = 1;
x->major = MagmaColMajor;
x->ld = num_rows;
if ( mem_loc == Magma_CPU ) {
CHECK( magma_dmalloc_cpu( &x->val, x->nnz ));
for( magma_int_t i=0; i<x->nnz; i++) {
x->val[i] = values;
}
}
else if ( mem_loc == Magma_DEV ) {
CHECK( magma_dmalloc( &x->val, x->nnz ));
magmablas_dlaset( MagmaFull, x->num_rows, x->num_cols, values, values, x->val, x->num_rows, queue );
}
cleanup:
return info;
}
//////////////////////////////////////////////////////////////
// ZSTEDC Divide and Conquer for tridiag
//////////////////////////////////////////////////////////////
extern "C" void magma_zstedx_withZ(magma_int_t N, magma_int_t NE, double *D, double * E, magmaDoubleComplex *Z, magma_int_t LDZ) {
double *RWORK;
double *dwork;
magma_int_t *IWORK;
magma_int_t LWORK, LIWORK, LRWORK;
magma_int_t INFO;
LWORK = N;
LRWORK = 2*N*N+4*N+1+256*N;
LIWORK = 256*N;
RWORK = (double*) malloc( LRWORK*sizeof( double) );
IWORK = (magma_int_t*) malloc( LIWORK*sizeof( magma_int_t) );
if (MAGMA_SUCCESS != magma_dmalloc( &dwork, 3*N*(N/2 + 1) )) {
printf("=================================================\n");
printf("ZSTEDC ERROR OCCURED IN CUDAMALLOC\n");
printf("=================================================\n");
return;
}
printf("using magma_zstedx\n");
#ifdef ENABLE_TIMER
magma_timestr_t start, end;
start = get_current_time();
#endif
char job = 'I';
if(NE==N)
job = 'A';
magma_zstedx(job, N, 0.,0., 1, NE, D, E, Z, LDZ, RWORK, LRWORK, IWORK, LIWORK, dwork, &INFO);
if(INFO!=0){
printf("=================================================\n");
printf("ZSTEDC ERROR OCCURED. HERE IS INFO %d \n ", (int) INFO);
printf("=================================================\n");
//assert(INFO==0);
}
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time zstevx = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
magma_free( dwork );
magma_free_cpu( IWORK );
magma_free_cpu( RWORK );
}
void gmm_magma(const Tensor_core<double,2>& A, const Tensor_core<double,2>& B, Tensor_core<double,2>& C,
char TRANSA, char TRANSB, double alpha, double beta)
{
int AL0 = A.rank(0); int AL1 = A.rank(1);
int BL0 = B.rank(0); int BL1 = B.rank(1);
int CL0 = C.rank(0); int CL1 = C.rank(1);
magma_int_t M, N, K, LDA, LDB, LDC;
magma_trans_t transA=magma_trans_const(TRANSA), transB=magma_trans_const(TRANSB);
magmaDouble_ptr d_A, d_B, d_C;
//Set LDA, LDB, and LDC, round up to multiple of 32 for best GPU performance
LDA = ((AL0+31)/32)*32; LDB = ((BL0+31)/32)*32; LDC = ((CL0+31)/32)*32;
// Allocate memory for the matrices on GPU
magma_dmalloc(&d_A, LDA*AL1 );
magma_dmalloc(&d_B, LDB*BL1 );
magma_dmalloc(&d_C, LDC*CL1 );
// Copy data from host (CPU) to device (GPU)
magma_dsetmatrix( AL0, AL1, A.data(), AL0, d_A, LDA );
magma_dsetmatrix( BL0, BL1, B.data(), BL0, d_B, LDB );
if( abs(beta)>1e-32 ) magma_dsetmatrix( CL0, CL1, C.data(), CL0, d_C, LDC );
//Call magma_sgemm
M=( TRANSA=='N' || TRANSA=='n' ) ? AL0:AL1;
K=( TRANSA=='N' || TRANSA=='n' ) ? AL1:AL0;
N=( TRANSB=='N' || TRANSB=='n' ) ? BL1:BL0;
magma_dgemm(transA, transB, M, N, K, alpha, d_A, LDA, d_B, LDB, beta,d_C, LDC);
// Copy solution from device (GPU) to host (CPU)
magma_dgetmatrix(CL0, CL1, d_C, LDC, C.data(), CL0);
// Free memory on GPU
magma_free(d_A); magma_free(d_B); magma_free(d_C);
}
double *cholesky_gpu(double *ml, int m) {
magma_int_t mm = m*m;
magma_int_t info;
double *a;
double *d_a ;
magma_err_t err;
err = magma_dmalloc_cpu ( &a , mm );
err = magma_dmalloc ( &d_a , mm );
magma_dsetmatrix ( m, m, ml, m, d_a , m );
magma_dpotrf_gpu('L',m,d_a,m,&info);
magma_dpotri_gpu('L',m,d_a,m,&info);
magma_dgetmatrix ( m, m, d_a , m, a, m );
magma_free (d_a );
return a;
}
extern "C" magma_int_t
magma_deigensolverinfo_init(
magma_d_solver_par *solver_par,
magma_queue_t queue )
{
magma_int_t info = 0;
double *initial_guess=NULL;
solver_par->eigenvectors = NULL;
solver_par->eigenvalues = NULL;
if ( solver_par->solver == Magma_LOBPCG ) {
CHECK( magma_dmalloc_cpu( &solver_par->eigenvalues ,
3*solver_par->num_eigenvalues ));
// setup initial guess EV using lapack
// then copy to GPU
magma_int_t ev = solver_par->num_eigenvalues * solver_par->ev_length;
CHECK( magma_dmalloc_cpu( &initial_guess, ev ));
CHECK( magma_dmalloc( &solver_par->eigenvectors, ev ));
magma_int_t ISEED[4] = {0,0,0,1}, ione = 1;
lapackf77_dlarnv( &ione, ISEED, &ev, initial_guess );
magma_dsetmatrix( solver_par->ev_length, solver_par->num_eigenvalues,
initial_guess, solver_par->ev_length, solver_par->eigenvectors,
solver_par->ev_length );
} else {
solver_par->eigenvectors = NULL;
solver_par->eigenvalues = NULL;
}
cleanup:
if( info != 0 ){
magma_free( solver_par->eigenvectors );
magma_free( solver_par->eigenvalues );
}
magma_free_cpu( initial_guess );
return info;
}
int main( int argc, char** argv )
{
magma_init();
cublasHandle_t handle;
cudaSetDevice( 0 );
cublasCreate( &handle );
double *A, *B, *C;
double *dA, *dB, *dC;
double error, work[1];
double c_one = MAGMA_D_ONE;
double c_neg_one = MAGMA_D_NEG_ONE;
magma_int_t ione = 1;
magma_int_t ISEED[4] = { 1, 2, 3, 4 };
magma_int_t n = 10;
magma_int_t lda = n;
magma_int_t ldda = ((n+31)/32)*32;
magma_int_t size = lda*n;
magma_int_t info;
magma_dmalloc_cpu( &A, lda*n );
magma_dmalloc_cpu( &B, lda*n );
magma_dmalloc_cpu( &C, lda*n );
magma_dmalloc( &dA, ldda*n );
magma_dmalloc( &dB, ldda*n );
magma_dmalloc( &dC, ldda*n );
// initialize matrices
lapackf77_dlarnv( &ione, ISEED, &size, A );
lapackf77_dlarnv( &ione, ISEED, &size, B );
lapackf77_dlarnv( &ione, ISEED, &size, C );
// increase diagonal to be SPD
for( int i=0; i < n; ++i ) {
C[i+i*lda] = MAGMA_D_ADD( C[i+i*lda], MAGMA_D_MAKE( n*n, 0 ));
}
magma_dsetmatrix( n, n, A, lda, dA, ldda );
magma_dsetmatrix( n, n, B, lda, dB, ldda );
magma_dsetmatrix( n, n, C, lda, dC, ldda );
// compute with cublas
cublasDgemm( handle, CUBLAS_OP_N, CUBLAS_OP_N, n, n, n,
&c_neg_one, dA, ldda, dB, ldda, &c_one, dC, ldda );
magma_dpotrf_gpu( MagmaLower, n, dC, ldda, &info );
if (info != 0)
printf("magma_dpotrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
// compute with LAPACK
blasf77_dgemm( MagmaNoTransStr, MagmaNoTransStr, &n, &n, &n,
&c_neg_one, A, &lda, B, &lda, &c_one, C, &lda );
lapackf77_dpotrf( MagmaLowerStr, &n, C, &lda, &info );
if (info != 0)
printf("lapackf77_dpotrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
// compute difference
magma_dgetmatrix( n, n, dC, ldda, A, lda );
blasf77_daxpy( &size, &c_neg_one, C, &ione, A, &ione );
error = lapackf77_dlange( "F", &n, &n, A, &lda, work );
printf( "n %d, error %8.2e\n", n, error );
magma_free( dA );
magma_free( dB );
magma_free( dC );
magma_free_cpu( A );
magma_free_cpu( B );
magma_free_cpu( C );
cublasDestroy( handle );
magma_finalize();
return 0;
}
/**
Purpose
-------
DORMQR overwrites the general real M-by-N matrix C with
@verbatim
SIDE = MagmaLeft SIDE = MagmaRight
TRANS = MagmaNoTrans: Q * C C * Q
TRANS = MagmaTrans: Q**H * C C * Q**H
@endverbatim
where Q is a real unitary matrix defined as the product of k
elementary reflectors
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF. Q is of order M if SIDE = MagmaLeft and of order N
if SIDE = MagmaRight.
Arguments
---------
@param[in]
ngpu INTEGER
Number of GPUs to use. ngpu > 0.
@param[in]
side magma_side_t
- = MagmaLeft: apply Q or Q**H from the Left;
- = MagmaRight: apply Q or Q**H from the Right.
@param[in]
trans magma_trans_t
- = MagmaNoTrans: No transpose, apply Q;
- = MagmaTrans: Conjugate transpose, apply Q**H.
@param[in]
m INTEGER
The number of rows of the matrix C. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix C. N >= 0.
@param[in]
k INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = MagmaLeft, M >= K >= 0;
if SIDE = MagmaRight, N >= K >= 0.
@param[in]
A DOUBLE_PRECISION array, dimension (LDA,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
DGEQRF in the first k columns of its array argument A.
@param[in]
lda INTEGER
The leading dimension of the array A.
If SIDE = MagmaLeft, LDA >= max(1,M);
if SIDE = MagmaRight, LDA >= max(1,N).
@param[in]
tau DOUBLE_PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQRF.
@param[in,out]
C DOUBLE_PRECISION array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
@param[in]
ldc INTEGER
The leading dimension of the array C. LDC >= max(1,M).
@param[out]
work (workspace) DOUBLE_PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The dimension of the array WORK.
If SIDE = MagmaLeft, LWORK >= max(1,N);
if SIDE = MagmaRight, LWORK >= max(1,M).
For optimum performance LWORK >= N*NB if SIDE = MagmaLeft, and
LWORK >= M*NB if SIDE = MagmaRight, where NB is the optimal
blocksize.
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_dgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_dormqr_m(
magma_int_t ngpu,
magma_side_t side, magma_trans_t trans,
magma_int_t m, magma_int_t n, magma_int_t k,
double *A, magma_int_t lda,
double *tau,
double *C, magma_int_t ldc,
double *work, magma_int_t lwork,
magma_int_t *info)
{
#define A(i, j) (A + (j)*lda + (i))
#define C(i, j) (C + (j)*ldc + (i))
#define dC(gpui, i, j) (dw[gpui] + (j)*lddc + (i))
#define dA_c(gpui, ind, i, j) (dw[gpui] + maxnlocal*lddc + (ind)*lddar*lddac + (i) + (j)*lddac)
#define dA_r(gpui, ind, i, j) (dw[gpui] + maxnlocal*lddc + (ind)*lddar*lddac + (i) + (j)*lddar)
#define dT(gpui, ind) (dw[gpui] + maxnlocal*lddc + 2*lddac*lddar + (ind)*((nb+1)*nb))
#define dwork(gpui, ind) (dw[gpui] + maxnlocal*lddc + 2*lddac*lddar + 2*((nb+1)*nb) + (ind)*(lddwork*nb))
double c_zero = MAGMA_D_ZERO;
double c_one = MAGMA_D_ONE;
const char* side_ = lapack_side_const( side );
const char* trans_ = lapack_trans_const( trans );
// TODO fix memory leak (alloc after argument checks)
magma_int_t nb = 128;
double *T;
magma_dmalloc_pinned(&T, nb*nb);
//printf("calling dormqr_m with nb=%d\n", (int) nb);
double* dw[MagmaMaxGPUs];
magma_queue_t stream [MagmaMaxGPUs][2];
magma_event_t event [MagmaMaxGPUs][2];
magma_int_t ind_c;
magma_device_t igpu;
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
magma_queue_t orig_stream;
magmablasGetKernelStream( &orig_stream );
*info = 0;
magma_int_t left = (side == MagmaLeft);
magma_int_t notran = (trans == MagmaNoTrans);
magma_int_t lquery = (lwork == -1);
/* NQ is the order of Q and NW is the minimum dimension of WORK */
magma_int_t nq, nw;
if (left) {
nq = m;
nw = n;
} else {
nq = n;
nw = m;
}
if (! left && side != MagmaRight) {
*info = -1;
} else if (! notran && trans != MagmaTrans) {
*info = -2;
} else if (m < 0) {
*info = -3;
} else if (n < 0) {
*info = -4;
} else if (k < 0 || k > nq) {
*info = -5;
} else if (lda < max(1,nq)) {
*info = -7;
} else if (ldc < max(1,m)) {
*info = -10;
} else if (lwork < max(1,nw) && ! lquery) {
*info = -12;
}
magma_int_t lwkopt = max(1,nw) * nb;
if (*info == 0) {
work[0] = MAGMA_D_MAKE( lwkopt, 0 );
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0 || k == 0) {
work[0] = c_one;
return *info;
}
if (nb >= k) {
/* Use CPU code */
lapackf77_dormqr(side_, trans_, &m, &n, &k, A, &lda, tau,
C, &ldc, work, &lwork, info);
return *info;
}
magma_int_t lddc = (m+63)/64*64;
magma_int_t lddac = nq;
magma_int_t lddar = nb;
magma_int_t lddwork = nw;
magma_int_t nlocal[ MagmaMaxGPUs ] = { 0 };
magma_int_t nb_l=256;
magma_int_t nbl = (n-1)/nb_l+1; // number of blocks
magma_int_t maxnlocal = (nbl+ngpu-1)/ngpu*nb_l;
ngpu = min(ngpu, (n+nb_l-1)/nb_l); // Don't use GPU that will not have data.
magma_int_t ldw = maxnlocal*lddc // dC
+ 2*lddac*lddar // 2*dA
+ 2*(nb + 1 + lddwork)*nb; // 2*(dT and dwork)
for (igpu = 0; igpu < ngpu; ++igpu) {
magma_setdevice(igpu);
if (MAGMA_SUCCESS != magma_dmalloc( &dw[igpu], ldw )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
magma_xerbla( __func__, -(*info) );
return *info;
}
magma_queue_create( &stream[igpu][0] );
magma_queue_create( &stream[igpu][1] );
magma_event_create( &event[igpu][0] );
magma_event_create( &event[igpu][1] );
}
/* Use hybrid CPU-MGPU code */
if (left) {
//copy C to mgpus
for (magma_int_t i = 0; i < nbl; ++i) {
magma_int_t igpu = i%ngpu;
magma_setdevice(igpu);
magma_int_t kb = min(nb_l, n-i*nb_l);
magma_dsetmatrix_async( m, kb,
C(0, i*nb_l), ldc,
dC(igpu, 0, i/ngpu*nb_l), lddc, stream[igpu][0] );
nlocal[igpu] += kb;
}
magma_int_t i1, i2, i3;
if ( !notran ) {
i1 = 0;
i2 = k;
i3 = nb;
} else {
i1 = (k - 1) / nb * nb;
i2 = 0;
i3 = -nb;
}
ind_c = 0;
for (magma_int_t i = i1; (i3 < 0 ? i >= i2 : i < i2); i += i3) {
// start the copy of A panel
magma_int_t kb = min(nb, k - i);
for (igpu = 0; igpu < ngpu; ++igpu) {
magma_setdevice(igpu);
magma_event_sync(event[igpu][ind_c]); // check if the new data can be copied
magma_dsetmatrix_async(nq-i, kb,
A(i, i), lda,
dA_c(igpu, ind_c, i, 0), lddac, stream[igpu][0] );
// set upper triangular part of dA to identity
magmablas_dlaset_band_q( MagmaUpper, kb, kb, kb, c_zero, c_one, dA_c(igpu, ind_c, i, 0), lddac, stream[igpu][0] );
}
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
magma_int_t nqi = nq - i;
lapackf77_dlarft("F", "C", &nqi, &kb, A(i, i), &lda,
&tau[i], T, &kb);
/* H or H' is applied to C(1:m,i:n) */
/* Apply H or H'; First copy T to the GPU */
for (igpu = 0; igpu < ngpu; ++igpu) {
magma_setdevice(igpu);
magma_dsetmatrix_async(kb, kb,
T, kb,
dT(igpu, ind_c), kb, stream[igpu][0] );
}
for (igpu = 0; igpu < ngpu; ++igpu) {
magma_setdevice(igpu);
magma_queue_sync( stream[igpu][0] ); // check if the data was copied
magmablasSetKernelStream(stream[igpu][1]);
magma_dlarfb_gpu( side, trans, MagmaForward, MagmaColumnwise,
m-i, nlocal[igpu], kb,
dA_c(igpu, ind_c, i, 0), lddac, dT(igpu, ind_c), kb,
dC(igpu, i, 0), lddc,
dwork(igpu, ind_c), lddwork);
magma_event_record(event[igpu][ind_c], stream[igpu][1] );
}
ind_c = (ind_c+1)%2;
}
for (igpu = 0; igpu < ngpu; ++igpu) {
magma_setdevice(igpu);
magma_queue_sync( stream[igpu][1] );
}
//copy C from mgpus
for (magma_int_t i = 0; i < nbl; ++i) {
magma_int_t igpu = i%ngpu;
magma_setdevice(igpu);
magma_int_t kb = min(nb_l, n-i*nb_l);
magma_dgetmatrix( m, kb,
dC(igpu, 0, i/ngpu*nb_l), lddc,
C(0, i*nb_l), ldc );
// magma_dgetmatrix_async( m, kb,
// dC(igpu, 0, i/ngpu*nb_l), lddc,
// C(0, i*nb_l), ldc, stream[igpu][0] );
}
} else {
// TODO fix memory leak T, dw, event, stream
fprintf(stderr, "The case (side == right) is not implemented\n");
*info = MAGMA_ERR_NOT_IMPLEMENTED;
magma_xerbla( __func__, -(*info) );
return *info;
/*
if ( notran ) {
i1 = 0;
i2 = k;
i3 = nb;
} else {
i1 = (k - 1) / nb * nb;
i2 = 0;
i3 = -nb;
}
mi = m;
ic = 0;
for (i = i1; (i3 < 0 ? i >= i2 : i < i2); i += i3) {
ib = min(nb, k - i);
// Form the triangular factor of the block reflector
// H = H(i) H(i+1) . . . H(i+ib-1)
i__4 = nq - i;
lapackf77_dlarft("F", "C", &i__4, &ib, A(i, i), &lda,
&tau[i], T, &ib);
// 1) copy the panel from A to the GPU, and
// 2) set upper triangular part of dA to identity
magma_dsetmatrix( i__4, ib, A(i, i), lda, dA(i, 0), ldda );
magmablas_dlaset_band( MagmaUpper, ib, ib, ib, c_zero, c_one, dA(i, 0), ldda );
// H or H' is applied to C(1:m,i:n)
ni = n - i;
jc = i;
// Apply H or H'; First copy T to the GPU
magma_dsetmatrix( ib, ib, T, ib, dT, ib );
magma_dlarfb_gpu( side, trans, MagmaForward, MagmaColumnwise,
mi, ni, ib,
dA(i, 0), ldda, dT, ib,
dC(ic, jc), lddc,
dwork, lddwork);
}
*/
}
work[0] = MAGMA_D_MAKE( lwkopt, 0 );
for (igpu = 0; igpu < ngpu; ++igpu) {
magma_setdevice(igpu);
magma_event_destroy( event[igpu][0] );
magma_event_destroy( event[igpu][1] );
magma_queue_destroy( stream[igpu][0] );
magma_queue_destroy( stream[igpu][1] );
magma_free( dw[igpu] );
}
magma_setdevice( orig_dev );
magmablasSetKernelStream( orig_stream );
return *info;
} /* magma_dormqr */
/**
Purpose
-------
DORGQR generates an M-by-N DOUBLE_PRECISION matrix Q with orthonormal columns,
which is defined as the first N columns of a product of K elementary
reflectors of order M
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF.
This version recomputes the T matrices on the CPU and sends them to the GPU.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix Q. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix Q. M >= N >= 0.
@param[in]
k INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
@param[in,out]
A DOUBLE_PRECISION array A, dimension (LDDA,N).
On entry, the i-th column must contain the vector
which defines the elementary reflector H(i), for
i = 1,2,...,k, as returned by DGEQRF_GPU in the
first k columns of its array argument A.
On exit, the M-by-N matrix Q.
@param[in]
lda INTEGER
The first dimension of the array A. LDA >= max(1,M).
@param[in]
tau DOUBLE_PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQRF_GPU.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument has an illegal value
@ingroup magma_dgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_dorgqr2(magma_int_t m, magma_int_t n, magma_int_t k,
double *A, magma_int_t lda,
double *tau,
magma_int_t *info)
{
#define A(i,j) ( A + (i) + (j)*lda )
#define dA(i,j) (dA + (i) + (j)*ldda)
double c_zero = MAGMA_D_ZERO;
double c_one = MAGMA_D_ONE;
magma_int_t nb = magma_get_dgeqrf_nb(min(m, n));
magma_int_t m_kk, n_kk, k_kk, mi;
magma_int_t lwork, ldda;
magma_int_t i, ib, ki, kk; //, iinfo;
magma_int_t lddwork;
double *dA, *dV, *dW, *dT, *T;
double *work;
*info = 0;
if (m < 0) {
*info = -1;
} else if ((n < 0) || (n > m)) {
*info = -2;
} else if ((k < 0) || (k > n)) {
*info = -3;
} else if (lda < max(1,m)) {
*info = -5;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
if (n <= 0) {
return *info;
}
// first kk columns are handled by blocked method.
// ki is start of 2nd-to-last block
if ((nb > 1) && (nb < k)) {
ki = (k - nb - 1) / nb * nb;
kk = min(k, ki + nb);
} else {
ki = 0;
kk = 0;
}
// Allocate GPU work space
// ldda*n for matrix dA
// ldda*nb for dV
// lddwork*nb for dW larfb workspace
ldda = ((m + 31) / 32) * 32;
lddwork = ((n + 31) / 32) * 32;
if (MAGMA_SUCCESS != magma_dmalloc( &dA, ldda*n + ldda*nb + lddwork*nb + nb*nb)) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
dV = dA + ldda*n;
dW = dA + ldda*n + ldda*nb;
dT = dA + ldda*n + ldda*nb + lddwork*nb;
// Allocate CPU work space
lwork = (n+m+nb) * nb;
magma_dmalloc_cpu( &work, lwork );
T = work;
if (work == NULL) {
magma_free( dA );
magma_free_cpu( work );
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
double *V = work + (n+nb)*nb;
magma_queue_t stream;
magma_queue_create( &stream );
// Use unblocked code for the last or only block.
if (kk < n) {
m_kk = m - kk;
n_kk = n - kk;
k_kk = k - kk;
/*
lapackf77_dorgqr( &m_kk, &n_kk, &k_kk,
A(kk, kk), &lda,
&tau[kk], work, &lwork, &iinfo );
*/
lapackf77_dlacpy( MagmaUpperLowerStr, &m_kk, &k_kk, A(kk,kk), &lda, V, &m_kk);
lapackf77_dlaset( MagmaUpperLowerStr, &m_kk, &n_kk, &c_zero, &c_one, A(kk, kk), &lda );
lapackf77_dlarft( MagmaForwardStr, MagmaColumnwiseStr,
&m_kk, &k_kk,
V, &m_kk, &tau[kk], work, &k_kk);
lapackf77_dlarfb( MagmaLeftStr, MagmaNoTransStr, MagmaForwardStr, MagmaColumnwiseStr,
&m_kk, &n_kk, &k_kk,
V, &m_kk, work, &k_kk, A(kk, kk), &lda, work+k_kk*k_kk, &n_kk );
if (kk > 0) {
magma_dsetmatrix( m_kk, n_kk,
A(kk, kk), lda,
dA(kk, kk), ldda );
// Set A(1:kk,kk+1:n) to zero.
magmablas_dlaset( MagmaFull, kk, n - kk, c_zero, c_zero, dA(0, kk), ldda );
}
}
if (kk > 0) {
// Use blocked code
// stream: set Aii (V) --> laset --> laset --> larfb --> [next]
// CPU has no computation
magmablasSetKernelStream( stream );
for (i = ki; i >= 0; i -= nb) {
ib = min(nb, k - i);
// Send current panel to the GPU
mi = m - i;
lapackf77_dlaset( "Upper", &ib, &ib, &c_zero, &c_one, A(i, i), &lda );
magma_dsetmatrix_async( mi, ib,
A(i, i), lda,
dV, ldda, stream );
lapackf77_dlarft( MagmaForwardStr, MagmaColumnwiseStr,
&mi, &ib,
A(i,i), &lda, &tau[i], T, &nb);
magma_dsetmatrix_async( ib, ib,
T, nb,
dT, nb, stream );
// set panel to identity
magmablas_dlaset( MagmaFull, i, ib, c_zero, c_zero, dA(0, i), ldda );
magmablas_dlaset( MagmaFull, mi, ib, c_zero, c_one, dA(i, i), ldda );
magma_queue_sync( stream );
if (i < n) {
// Apply H to A(i:m,i:n) from the left
magma_dlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise,
mi, n-i, ib,
dV, ldda, dT, nb,
dA(i, i), ldda, dW, lddwork );
}
}
// copy result back to CPU
magma_dgetmatrix( m, n,
dA(0, 0), ldda, A(0, 0), lda);
}
magmablasSetKernelStream( NULL );
magma_queue_destroy( stream );
magma_free( dA );
magma_free_cpu( work );
return *info;
} /* magma_dorgqr */
extern "C" magma_int_t
magma_dgeqp3( magma_int_t m, magma_int_t n,
double *A, magma_int_t lda,
magma_int_t *jpvt, double *tau,
double *work, magma_int_t lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
double *rwork,
#endif
magma_int_t *info )
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
DGEQP3 computes a QR factorization with column pivoting of a
matrix A: A*P = Q*R using Level 3 BLAS.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input/output) DOUBLE_PRECISION array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the upper triangle of the array contains the
min(M,N)-by-N upper trapezoidal matrix R; the elements below
the diagonal, together with the array TAU, represent the
unitary matrix Q as a product of min(M,N) elementary
reflectors.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
JPVT (input/output) INTEGER array, dimension (N)
On entry, if JPVT(J).ne.0, the J-th column of A is permuted
to the front of A*P (a leading column); if JPVT(J)=0,
the J-th column of A is a free column.
On exit, if JPVT(J)=K, then the J-th column of A*P was the
the K-th column of A.
TAU (output) DOUBLE_PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors.
WORK (workspace/output) DOUBLE_PRECISION 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.
For [sd]geqp3, LWORK >= (N+1)*NB + 2*N;
for [cz]geqp3, LWORK >= (N+1)*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.
For [cz]geqp3 only:
RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
Further Details
===============
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector
with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
A(i+1:m,i), and tau in TAU(i).
===================================================================== */
#define A(i, j) (A + (i) + (j)*(lda ))
#define dA(i, j) (dwork + (i) + (j)*(ldda))
double *dwork, *df;
magma_int_t ione = 1;
magma_int_t n_j, ldda, ldwork;
magma_int_t j, jb, na, nb, sm, sn, fjb, nfxd, minmn;
magma_int_t topbmn, sminmn, lwkopt, lquery;
*info = 0;
lquery = (lwork == -1);
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,m)) {
*info = -4;
}
nb = magma_get_dgeqp3_nb(min(m, n));
if (*info == 0) {
minmn = min(m,n);
if (minmn == 0) {
lwkopt = 1;
} else {
lwkopt = (n + 1)*nb;
#if defined(PRECISION_d) || defined(PRECISION_s)
lwkopt += 2*n;
#endif
}
work[0] = MAGMA_D_MAKE( lwkopt, 0. );
if (lwork < lwkopt && ! lquery) {
*info = -8;
}
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
} else if (lquery) {
return *info;
}
if (minmn == 0)
return *info;
#if defined(PRECISION_d) || defined(PRECISION_s)
double *rwork = work + (n + 1)*nb;
#endif
ldda = ((m+31)/32)*32;
ldwork = n*ldda + (n+1)*nb;
if (MAGMA_SUCCESS != magma_dmalloc( &dwork, ldwork )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
df = dwork + n*ldda;
// dwork used for dA
magma_queue_t stream;
magma_queue_create( &stream );
/* Move initial columns up front.
* Note jpvt uses 1-based indices for historical compatibility. */
nfxd = 0;
for (j = 0; j < n; ++j) {
if (jpvt[j] != 0) {
if (j != nfxd) {
blasf77_dswap(&m, A(0, j), &ione, A(0, nfxd), &ione);
jpvt[j] = jpvt[nfxd];
jpvt[nfxd] = j + 1;
}
else {
jpvt[j] = j + 1;
}
++nfxd;
}
else {
jpvt[j] = j + 1;
}
}
/* Factorize fixed columns
=======================
Compute the QR factorization of fixed columns and update
remaining columns. */
if (nfxd > 0) {
na = min(m,nfxd);
lapackf77_dgeqrf(&m, &na, A, &lda, tau, work, &lwork, info);
if (na < n) {
n_j = n - na;
lapackf77_dormqr( MagmaLeftStr, MagmaTransStr, &m, &n_j, &na,
A, &lda, tau, A(0, na), &lda,
work, &lwork, info );
}
}
/* Factorize free columns */
if (nfxd < minmn) {
sm = m - nfxd;
sn = n - nfxd;
sminmn = minmn - nfxd;
if (nb < sminmn) {
j = nfxd;
// Set the original matrix to the GPU
magma_dsetmatrix_async( m, sn,
A (0,j), lda,
dA(0,j), ldda, stream );
}
/* Initialize partial column norms. */
for (j = nfxd; j < n; ++j) {
rwork[j] = cblas_dnrm2(sm, A(nfxd, j), ione);
rwork[n + j] = rwork[j];
}
j = nfxd;
if (nb < sminmn) {
/* Use blocked code initially. */
magma_queue_sync( stream );
/* Compute factorization: while loop. */
topbmn = minmn - nb;
while(j < topbmn) {
jb = min(nb, topbmn - j);
/* Factorize JB columns among columns J:N. */
n_j = n - j;
if (j>nfxd) {
// Get panel to the CPU
magma_dgetmatrix( m-j, jb,
dA(j,j), ldda,
A (j,j), lda );
// Get the rows
magma_dgetmatrix( jb, n_j - jb,
dA(j,j + jb), ldda,
A (j,j + jb), lda );
}
magma_dlaqps( m, n_j, j, jb, &fjb,
A (0, j), lda,
dA(0, j), ldda,
&jpvt[j], &tau[j], &rwork[j], &rwork[n + j],
work,
&work[jb], n_j,
&df[jb], n_j );
j += fjb; /* fjb is actual number of columns factored */
}
}
/* Use unblocked code to factor the last or only block. */
if (j < minmn) {
n_j = n - j;
if (j > nfxd) {
magma_dgetmatrix( m-j, n_j,
dA(j,j), ldda,
A (j,j), lda );
}
lapackf77_dlaqp2(&m, &n_j, &j, A(0, j), &lda, &jpvt[j],
&tau[j], &rwork[j], &rwork[n+j], work );
}
}
work[0] = MAGMA_D_MAKE( lwkopt, 0. );
magma_free( dwork );
magma_queue_destroy( stream );
return *info;
} /* dgeqp3 */
extern "C" magma_int_t
magma_dsyevd(
magma_vec_t jobz, magma_uplo_t uplo,
magma_int_t n,
double *a, magma_int_t lda,
double *w,
double *work, magma_int_t lwork,
magma_int_t *iwork, magma_int_t liwork,
magma_queue_t queue,
magma_int_t *info)
{
/* -- MAGMA (version 1.3.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
@date November 2014
Purpose
=======
DSYEVD computes all eigenvalues and, optionally, eigenvectors of
a real symmetric 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
=========
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
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.
A (input/output) DOUBLE_PRECISION array, dimension (LDA, N)
On entry, the symmetric matrix A. If UPLO = 'U', the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = 'L',
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
On exit, if JOBZ = 'V', then if INFO = 0, A contains the
orthonormal eigenvectors of the matrix A.
If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
or the upper triangle (if UPLO='U') of A, including the
diagonal, is destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
WORK (workspace/output) DOUBLE_PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
LWORK (input) INTEGER
The length of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = 'N' and N > 1, LWORK >= 2*N + N*NB.
If JOBZ = 'V' and N > 1, LWORK >= max( 2*N + N*NB, 1 + 6*N + 2*N**2 ).
NB can be obtained through magma_get_dsytrd_nb(N).
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK and IWORK
arrays, returns these values as the first entries of the WORK
and IWORK arrays, and no error message related to LWORK or
LIWORK is issued by XERBLA.
IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK.
LIWORK (input) INTEGER
The dimension of the array IWORK.
If N <= 1, LIWORK >= 1.
If JOBZ = 'N' and N > 1, LIWORK >= 1.
If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK and
IWORK arrays, returns these values as the first entries of
the WORK and IWORK arrays, and no error message related to
LWORK or LIWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i and JOBZ = 'N', 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 = 'V', 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.
===================================================================== */
const char* uplo_ = lapack_uplo_const( uplo );
const char* jobz_ = lapack_vec_const( jobz );
magma_int_t ione = 1;
magma_int_t izero = 0;
double d_one = 1.;
double d__1;
double eps;
magma_int_t inde;
double anrm;
double rmin, rmax;
double sigma;
magma_int_t iinfo, lwmin;
magma_int_t lower;
magma_int_t wantz;
magma_int_t indwk2, llwrk2;
magma_int_t iscale;
double safmin;
double bignum;
magma_int_t indtau;
magma_int_t indwrk, liwmin;
magma_int_t llwork;
double smlnum;
magma_int_t lquery;
magmaDouble_ptr dwork;
wantz = (jobz == MagmaVec);
lower = (uplo == MagmaLower);
lquery = (lwork == -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 (lda < max(1,n)) {
*info = -5;
}
magma_int_t nb = magma_get_dsytrd_nb( n );
if ( n <= 1 ) {
lwmin = 1;
liwmin = 1;
}
else if ( wantz ) {
lwmin = max( 2*n + n*nb, 1 + 6*n + 2*n*n );
liwmin = 3 + 5*n;
}
else {
lwmin = 2*n + n*nb;
liwmin = 1;
}
// multiply by 1+eps to ensure length gets rounded up,
// if it cannot be exactly represented in floating point.
double one_eps = 1. + lapackf77_dlamch("Epsilon");
work[0] = lwmin * one_eps;
iwork[0] = liwmin;
if ((lwork < lwmin) && !lquery) {
*info = -8;
} else if ((liwork < liwmin) && ! lquery) {
*info = -10;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
return *info;
}
if (n == 1) {
w[0] = a[0];
if (wantz) {
a[0] = 1.;
}
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
lapackf77_dsyevd(jobz_, uplo_,
&n, a, &lda,
w, work, &lwork,
iwork, &liwork, info);
return *info;
}
/* Get machine constants. */
safmin = lapackf77_dlamch("Safe minimum");
eps = lapackf77_dlamch("Precision");
smlnum = safmin / eps;
bignum = 1. / smlnum;
rmin = magma_dsqrt(smlnum);
rmax = magma_dsqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = lapackf77_dlansy("M", uplo_, &n, a, &lda, work );
iscale = 0;
if (anrm > 0. && anrm < rmin) {
iscale = 1;
sigma = rmin / anrm;
} else if (anrm > rmax) {
iscale = 1;
sigma = rmax / anrm;
}
if (iscale == 1) {
lapackf77_dlascl(uplo_, &izero, &izero, &d_one, &sigma, &n, &n, a,
&lda, info);
}
/* Call DSYTRD to reduce symmetric matrix to tridiagonal form. */
// dsytrd work: e (n) + tau (n) + llwork (n*nb) ==> 2n + n*nb
// dstedx work: e (n) + tau (n) + z (n*n) + llwrk2 (1 + 4*n + n^2) ==> 1 + 6n + 2n^2
inde = 0;
indtau = inde + n;
indwrk = indtau + n;
indwk2 = indwrk + n*n;
llwork = lwork - indwrk;
llwrk2 = lwork - indwk2;
magma_timer_t time;
timer_start( time );
magma_dsytrd(uplo, n, a, lda, w, &work[inde],
&work[indtau], &work[indwrk], llwork, queue, &iinfo);
timer_stop( time );
timer_printf( "time dsytrd = %6.2f\n", time );
/* For eigenvalues only, call DSTERF. For eigenvectors, first call
DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
tridiagonal matrix, then call DORMTR to multiply it to the Householder
transformations represented as Householder vectors in A. */
if (! wantz) {
lapackf77_dsterf(&n, w, &work[inde], info);
}
else {
timer_start( time );
if (MAGMA_SUCCESS != magma_dmalloc( &dwork, 3*n*(n/2 + 1) )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
// TTT Possible bug for n < 128
magma_dstedx(MagmaRangeAll, n, 0., 0., 0, 0, w, &work[inde],
&work[indwrk], n, &work[indwk2],
llwrk2, iwork, liwork, dwork, queue, info);
magma_free( dwork );
timer_stop( time );
timer_printf( "time dstedx = %6.2f\n", time );
timer_start( time );
magma_dormtr(MagmaLeft, uplo, MagmaNoTrans, n, n, a, lda, &work[indtau],
&work[indwrk], n, &work[indwk2], llwrk2, queue, &iinfo);
lapackf77_dlacpy("A", &n, &n, &work[indwrk], &n, a, &lda);
timer_stop( time );
timer_printf( "time dormtr + copy = %6.2f\n", time );
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
d__1 = 1. / sigma;
blasf77_dscal(&n, &d__1, w, &ione);
}
work[0] = lwmin * one_eps; // round up
iwork[0] = liwmin;
return *info;
} /* magma_dsyevd */
extern "C" magma_int_t
magma_dsytrf_nopiv(magma_uplo_t uplo, magma_int_t n,
double *A, magma_int_t lda,
magma_int_t *info)
{
/* -- MAGMA (version 1.6.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
November 2011
Purpose
=======
DSYTRF_nopiv computes the LDLt factorization of a real symmetric
matrix A. This version does not require work space on the GPU passed
as input. GPU memory is allocated in the routine.
The factorization has the form
A = U\*\*H * D * U, if UPLO = 'U', or
A = L * D * L\*\*H, if UPLO = 'L',
where U is an upper triangular matrix, L is lower triangular, and
D is a diagonal matrix.
This is the block version of the algorithm, calling Level 3 BLAS.
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.
A (input/output) DOUBLE_PRECISION array, dimension (LDA,N)
On entry, the symmetric 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 INFO = 0, the factor U or L from the Cholesky
factorization A = U\*\*H*U or A = L*L\*\*H.
Higher performance is achieved if A is in pinned memory, e.g.
allocated using cudaMallocHost.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
if INFO = -6, the GPU memory allocation failed
> 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.
===================================================================== */
/* Local variables */
double zone = MAGMA_D_ONE;
double mzone = MAGMA_D_NEG_ONE;
int upper = (uplo == MagmaUpper);
magma_int_t j, k, jb, ldda, nb, ib, iinfo;
magmaDouble_ptr dA;
magmaDouble_ptr dW;
*info = 0;
if (! upper && uplo != MagmaLower) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,n)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return MAGMA_ERR_ILLEGAL_VALUE;
}
/* Quick return */
if ( n == 0 )
return MAGMA_SUCCESS;
ldda = ((n+31)/32)*32;
nb = magma_get_dsytrf_nopiv_nb(n);
ib = min(32, nb); // inner-block for diagonal factorization
if ((MAGMA_SUCCESS != magma_dmalloc(&dA, n *ldda)) ||
(MAGMA_SUCCESS != magma_dmalloc(&dW, nb*ldda))) {
/* alloc failed so call the non-GPU-resident version */
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_queue_t stream[2];
magma_event_t event;
magma_queue_create(&stream[0]);
magma_queue_create(&stream[1]);
magma_event_create( &event );
trace_init( 1, 1, 2, (CUstream_st**)stream );
//if (nb <= 1 || nb >= n)
//{
// lapackf77_dpotrf(uplo_, &n, a, &lda, info);
//} else
{
/* Use hybrid blocked code. */
if (upper) {
//=========================================================
// Compute the LDLt factorization A = U'*D*U without pivoting.
// copy matrix to GPU
for (j=0; j<n; j+=nb) {
jb = min(nb, (n-j));
trace_gpu_start( 0, 0, "set", "set" );
magma_dsetmatrix_async(j+jb, jb, A(0, j), lda, dA(0, j), ldda, stream[0]);
trace_gpu_end( 0, 0 );
}
// main loop
for (j=0; j<n; j += nb) {
jb = min(nb, (n-j));
// copy A(j,j) back to CPU
trace_gpu_start( 0, 0, "get", "get" );
magma_dgetmatrix_async(jb, jb, dA(j, j), ldda, A(j,j), lda, stream[0]);
trace_gpu_end( 0, 0 );
// copy j-th column of U back to CPU
magma_queue_wait_event( stream[1], event );
trace_gpu_start( 0, 1, "get", "get" );
magma_dgetmatrix_async(j, jb, dA(0, j), ldda, A(0, j), lda, stream[1]);
trace_gpu_end( 0, 1 );
// factorize the diagonal block
magma_queue_sync(stream[0]);
trace_cpu_start( 0, "potrf", "potrf" );
dsytrf_nopiv_cpu(MagmaUpper, jb, ib, A(j, j), lda, info);
trace_cpu_end( 0 );
if (*info != 0){
*info = *info + j;
break;
}
// copy A(j,j) back to GPU
trace_gpu_start( 0, 0, "set", "set" );
magma_dsetmatrix_async(jb, jb, A(j, j), lda, dA(j, j), ldda, stream[0]);
trace_gpu_end( 0, 0 );
if ( (j+jb) < n) {
// compute the off-diagonal blocks of current block column
magmablasSetKernelStream( stream[0] );
trace_gpu_start( 0, 0, "trsm", "trsm" );
magma_dtrsm(MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaUnit,
jb, (n-j-jb),
zone, dA(j, j), ldda,
dA(j, j+jb), ldda);
magma_dcopymatrix( jb, n-j-jb, dA( j, j+jb ), ldda, dWt( 0, j+jb ), nb );
// update the trailing submatrix with D
magmablas_dlascl_diag(MagmaUpper, jb, n-j-jb,
dA(j, j), ldda,
dA(j, j+jb), ldda,
&iinfo);
magma_event_record( event, stream[0] );
trace_gpu_end( 0, 0 );
// update the trailing submatrix with U and W
trace_gpu_start( 0, 0, "gemm", "gemm" );
for (k=j+jb; k<n; k+=nb)
{
magma_int_t kb = min(nb,n-k);
magma_dgemm(MagmaConjTrans, MagmaNoTrans, kb, n-k, jb,
mzone, dWt(0, k), nb,
dA(j, k), ldda,
zone, dA(k, k), ldda);
}
trace_gpu_end( 0, 0 );
}
}
} else {
//=========================================================
// Compute the LDLt factorization A = L*D*L' without pivoting.
// copy the matrix to GPU
for (j=0; j<n; j+=nb) {
jb = min(nb, (n-j));
trace_gpu_start( 0, 0, "set", "set" );
magma_dsetmatrix_async((n-j), jb, A(j, j), lda, dA(j, j), ldda, stream[0]);
trace_gpu_end( 0, 0 );
}
// main loop
for (j=0; j<n; j+=nb) {
jb = min(nb, (n-j));
// copy A(j,j) back to CPU
trace_gpu_start( 0, 0, "get", "get" );
magma_dgetmatrix_async(jb, jb, dA(j, j), ldda, A(j,j), lda, stream[0]);
trace_gpu_end( 0, 0 );
// copy j-th row of L back to CPU
magma_queue_wait_event( stream[1], event );
trace_gpu_start( 0, 1, "get", "get" );
magma_dgetmatrix_async(jb, j, dA(j, 0), ldda, A(j, 0), lda, stream[1]);
trace_gpu_end( 0, 1 );
// factorize the diagonal block
magma_queue_sync(stream[0]);
trace_cpu_start( 0, "potrf", "potrf" );
dsytrf_nopiv_cpu(MagmaLower, jb, ib, A(j, j), lda, info);
trace_cpu_end( 0 );
if (*info != 0){
*info = *info + j;
break;
}
// copy A(j,j) back to GPU
trace_gpu_start( 0, 0, "set", "set" );
magma_dsetmatrix_async(jb, jb, A(j, j), lda, dA(j, j), ldda, stream[0]);
trace_gpu_end( 0, 0 );
if ( (j+jb) < n) {
// compute the off-diagonal blocks of current block column
magmablasSetKernelStream( stream[0] );
trace_gpu_start( 0, 0, "trsm", "trsm" );
magma_dtrsm(MagmaRight, MagmaLower, MagmaConjTrans, MagmaUnit,
(n-j-jb), jb,
zone, dA(j, j), ldda,
dA(j+jb, j), ldda);
magma_dcopymatrix( n-j-jb,jb, dA( j+jb, j ), ldda, dW( j+jb, 0 ), ldda );
// update the trailing submatrix with D
magmablas_dlascl_diag(MagmaLower, n-j-jb, jb,
dA(j, j), ldda,
dA(j+jb, j), ldda,
&iinfo);
magma_event_record( event, stream[0] );
trace_gpu_end( 0, 0 );
// update the trailing submatrix with L and W
trace_gpu_start( 0, 0, "gemm", "gemm" );
for (k=j+jb; k<n; k+=nb)
{
magma_int_t kb = min(nb,n-k);
magma_dgemm(MagmaNoTrans, MagmaConjTrans, n-k, kb, jb,
mzone, dA(k, j), ldda,
dW(k, 0), ldda,
zone, dA(k, k), ldda);
}
trace_gpu_end( 0, 0 );
}
}
}
}
trace_finalize( "dsytrf.svg","trace.css" );
magma_queue_destroy(stream[0]);
magma_queue_destroy(stream[1]);
magma_event_destroy( event );
magma_free(dW);
magma_free(dA);
return MAGMA_SUCCESS;
} /* magma_dsytrf_nopiv */
extern "C" magma_int_t
magma_dgelqf( magma_int_t m, magma_int_t n,
double *a, magma_int_t lda, double *tau,
double *work, magma_int_t lwork, magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
DGELQF computes an LQ factorization of a DOUBLE_PRECISION M-by-N matrix A:
A = L * Q.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input/output) DOUBLE_PRECISION array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and below the diagonal of the array
contain the m-by-min(m,n) lower trapezoidal matrix L (L is
lower triangular if m <= n); the elements above the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of elementary reflectors (see Further Details).
Higher performance is achieved if A is in pinned memory, e.g.
allocated using magma_malloc_pinned.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (output) DOUBLE_PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace/output) DOUBLE_PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
Higher performance is achieved if WORK is in pinned memory, e.g.
allocated using magma_malloc_pinned.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,M).
For optimum performance LWORK >= M*NB, where NB is the
optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
if INFO = -10 internal GPU memory allocation failed.
Further Details
===============
The matrix Q is represented as a product of elementary reflectors
Q = H(k) . . . H(2) H(1), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
and tau in TAU(i).
===================================================================== */
#define a_ref(a_1,a_2) ( a+(a_2)*(lda) + (a_1))
double *dA, *dAT;
double c_one = MAGMA_D_ONE;
magma_int_t maxm, maxn, maxdim, nb;
magma_int_t iinfo, ldda;
int lquery;
/* Function Body */
*info = 0;
nb = magma_get_dgelqf_nb(m);
work[0] = MAGMA_D_MAKE( (double)(m*nb), 0 );
lquery = (lwork == -1);
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,m)) {
*info = -4;
} else if (lwork < max(1,m) && ! lquery) {
*info = -7;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Quick return if possible */
if (min(m, n) == 0) {
work[0] = c_one;
return *info;
}
maxm = ((m + 31)/32)*32;
maxn = ((n + 31)/32)*32;
maxdim = max(maxm, maxn);
if (maxdim*maxdim < 2*maxm*maxn)
{
ldda = maxdim;
if (MAGMA_SUCCESS != magma_dmalloc( &dA, maxdim*maxdim )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_dsetmatrix( m, n, a, lda, dA, ldda );
dAT = dA;
magmablas_dtranspose_inplace( ldda, dAT, ldda );
}
else
{
ldda = maxn;
if (MAGMA_SUCCESS != magma_dmalloc( &dA, 2*maxn*maxm )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_dsetmatrix( m, n, a, lda, dA, maxm );
dAT = dA + maxn * maxm;
magmablas_dtranspose2( dAT, ldda, dA, maxm, m, n );
}
magma_dgeqrf2_gpu(n, m, dAT, ldda, tau, &iinfo);
if (maxdim*maxdim < 2*maxm*maxn) {
magmablas_dtranspose_inplace( ldda, dAT, ldda );
magma_dgetmatrix( m, n, dA, ldda, a, lda );
} else {
magmablas_dtranspose2( dA, maxm, dAT, ldda, n, m );
magma_dgetmatrix( m, n, dA, maxm, a, lda );
}
magma_free( dA );
return *info;
} /* magma_dgelqf */
/**
Purpose
-------
DPOTRF computes the Cholesky factorization of a real symmetric
positive definite matrix dA.
The factorization has the form
dA = U**H * U, if UPLO = MagmaUpper, or
dA = L * L**H, if UPLO = MagmaLower,
where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
Arguments
---------
@param[in]
ngpu INTEGER
Number of GPUs to use. ngpu > 0.
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of dA is stored;
- = MagmaLower: Lower triangle of dA is stored.
@param[in]
n INTEGER
The order of the matrix dA. N >= 0.
@param[in,out]
d_lA DOUBLE_PRECISION array of pointers on the GPU, dimension (ngpu)
On entry, the symmetric matrix dA distributed over GPUs
(d_lA[d] points to the local matrix on the d-th GPU).
It is distributed in 1D block column or row cyclic (with the
block size of nb) if UPLO = MagmaUpper or MagmaLower, respectively.
If UPLO = MagmaUpper, the leading N-by-N upper triangular
part of dA contains the upper triangular part of the matrix dA,
and the strictly lower triangular part of dA is not referenced.
If UPLO = MagmaLower, the leading N-by-N lower triangular part
of dA contains the lower triangular part of the matrix dA, and
the strictly upper triangular part of dA is not referenced.
\n
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization dA = U**H * U or dA = L * L**H.
@param[in]
ldda INTEGER
The leading dimension of the array d_lA. LDDA >= max(1,N).
To benefit from coalescent memory accesses LDDA must be
divisible by 16.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.
@ingroup magma_dposv_comp
********************************************************************/
extern "C" magma_int_t
magma_dpotrf_mgpu(
magma_int_t ngpu,
magma_uplo_t uplo, magma_int_t n,
magmaDouble_ptr d_lA[], magma_int_t ldda,
magma_int_t *info)
{
magma_int_t j, nb, d, lddp, h;
const char* uplo_ = lapack_uplo_const( uplo );
double *work;
int upper = (uplo == MagmaUpper);
double *dwork[MagmaMaxGPUs];
magma_queue_t stream[MagmaMaxGPUs][3];
magma_event_t event[MagmaMaxGPUs][5];
*info = 0;
nb = magma_get_dpotrf_nb(n);
if (! upper && uplo != MagmaLower) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (!upper) {
lddp = nb*(n/(nb*ngpu));
if ( n%(nb*ngpu) != 0 ) lddp += min(nb, n-ngpu*lddp);
if ( ldda < lddp ) *info = -4;
} else if ( ldda < n ) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
if (ngpu == 1 && ((nb <= 1) || (nb >= n)) ) {
/* Use unblocked code. */
magma_setdevice(0);
if (MAGMA_SUCCESS != magma_dmalloc_pinned( &work, n*nb )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
magma_dgetmatrix( n, n, d_lA[0], ldda, work, n );
lapackf77_dpotrf(uplo_, &n, work, &n, info);
magma_dsetmatrix( n, n, work, n, d_lA[0], ldda );
magma_free_pinned( work );
}
else {
lddp = nb*((n+nb-1)/nb);
for( d=0; d < ngpu; d++ ) {
magma_setdevice(d);
if (MAGMA_SUCCESS != magma_dmalloc( &dwork[d], ngpu*nb*lddp )) {
for( j=0; j < d; j++ ) {
magma_setdevice(j);
magma_free( dwork[j] );
}
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
for( j=0; j < 3; j++ )
magma_queue_create( &stream[d][j] );
for( j=0; j < 5; j++ )
magma_event_create( &event[d][j] );
}
magma_setdevice(0);
h = 1; //ngpu; //(n+nb-1)/nb;
if (MAGMA_SUCCESS != magma_dmalloc_pinned( &work, n*nb*h )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
if (upper) {
/* with three streams */
magma_dpotrf3_mgpu(ngpu, uplo, n, n, 0, 0, nb, d_lA, ldda, dwork, lddp, work, n,
h, stream, event, info);
} else {
/* with three streams */
magma_dpotrf3_mgpu(ngpu, uplo, n, n, 0, 0, nb, d_lA, ldda, dwork, lddp, work, nb*h,
h, stream, event, info);
}
/* clean up */
for( d=0; d < ngpu; d++ ) {
magma_setdevice(d);
for( j=0; j < 3; j++ ) {
magma_queue_sync( stream[d][j] );
magma_queue_destroy( stream[d][j] );
}
for( j=0; j < 5; j++ )
magma_event_destroy( event[d][j] );
magma_free( dwork[d] );
}
magma_free_pinned( work );
} /* end of not lapack */
magma_setdevice( orig_dev );
return *info;
} /* magma_dpotrf_mgpu */
/**
Purpose
-------
DGERBT 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.
Random Butterfly Tranformation is applied on A and B, then
the LU decomposition with no pivoting is
used to factor A as
A = L * U,
where 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.
This is a batched version that solves batchCount matrices in parallel.
dA, dB, and info become arrays with one entry per matrix.
Arguments
---------
@param[in]
gen magma_bool_t
- = MagmaTrue: new matrices are generated for U and V
- = MagmaFalse: matrices U and V given as parameter are used
@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]
dA_array Array of pointers, dimension (batchCount).
Each is a DOUBLE PRECISION array on the GPU, dimension (LDDA,N).
On entry, each pointer is an 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]
ldda INTEGER
The leading dimension of each array A. LDDA >= max(1,M).
@param[in,out]
dB_array Array of pointers, dimension (batchCount).
Each is a DOUBLE PRECISION array on the GPU, dimension (LDDB,N).
On entry, each pointer is an right hand side matrix B.
On exit, each pointer is the solution matrix X.
@param[in]
lddb INTEGER
The leading dimension of the array B. LDB >= max(1,N).
@param[in,out]
U DOUBLE PRECISION array, dimension (2,n)
Random butterfly matrix, if gen = MagmaTrue U is generated and returned as output;
else we use U given as input.
CPU memory
@param[in,out]
V DOUBLE PRECISION array, dimension (2,n)
Random butterfly matrix, if gen = MagmaTrue V is generated and returned as output;
else we use U given as input.
CPU memory
@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.
@param[in]
batchCount INTEGER
The number of matrices to operate on.
@param[in]
queue magma_queue_t
Queue to execute in.
@ingroup magma_dgesv_comp
********************************************************************/
extern "C" magma_int_t
magma_dgerbt_batched(
magma_bool_t gen, magma_int_t n, magma_int_t nrhs,
double **dA_array, magma_int_t ldda,
double **dB_array, magma_int_t lddb,
double *U, double *V,
magma_int_t *info, magma_int_t batchCount, magma_queue_t queue)
{
double *du, *dv;
magma_int_t i;
/* Function Body */
*info = 0;
if ( ! (gen == MagmaTrue) &&
! (gen == MagmaFalse) ) {
*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 = -7;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (nrhs == 0 || n == 0)
return *info;
/* Allocate memory for the buterfly matrices */
if (MAGMA_SUCCESS != magma_dmalloc( &du, 2*n )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
if (MAGMA_SUCCESS != magma_dmalloc( &dv, 2*n )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
/* Initialize Butterfly matrix on the CPU*/
if (gen == MagmaTrue)
init_butterfly(2*n, U, V);
/* Copy the butterfly to the GPU */
magma_dsetvector( 2*n, U, 1, du, 1, queue );
magma_dsetvector( 2*n, V, 1, dv, 1, queue );
/* Perform Partial Random Butterfly Transformation on the GPU*/
magmablas_dprbt_batched(n, dA_array, ldda, du, dv, batchCount, queue);
/* Compute U^T.b on the GPU*/
// TODO fix for multiple RHS
for (i= 0; i < nrhs; i++)
magmablas_dprbt_mtv_batched(n, du, dB_array, batchCount, queue);
magma_free( du );
magma_free( dv );
return *info;
}
extern "C" magma_int_t
magma_dorgqr(
magma_int_t m, magma_int_t n, magma_int_t k,
double *a, magma_int_t lda,
double *tau, magmaDouble_ptr dT, size_t dT_offset,
magma_int_t nb,
magma_queue_t queue,
magma_int_t *info )
{
/* -- clMAGMA (version 1.3.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
@date November 2014
Purpose
=======
DORGQR generates an M-by-N DOUBLE_PRECISION matrix Q with orthonormal columns,
which is defined as the first N columns of a product of K elementary
reflectors of order M
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix Q. M >= 0.
N (input) INTEGER
The number of columns of the matrix Q. M >= N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
A (input/output) DOUBLE_PRECISION array A, dimension (LDDA,N).
On entry, the i-th column must contain the vector
which defines the elementary reflector H(i), for
i = 1,2,...,k, as returned by DGEQRF_GPU in the
first k columns of its array argument A.
On exit, the M-by-N matrix Q.
LDA (input) INTEGER
The first dimension of the array A. LDA >= max(1,M).
TAU (input) DOUBLE_PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQRF_GPU.
DT (input) DOUBLE_PRECISION array on the GPU device.
DT contains the T matrices used in blocking the elementary
reflectors H(i), e.g., this can be the 6th argument of
magma_dgeqrf_gpu.
NB (input) INTEGER
This is the block size used in DGEQRF_GPU, and correspondingly
the size of the T matrices, used in the factorization, and
stored in DT.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument has an illegal value
===================================================================== */
#define a_ref(i,j) ( a + (j)*lda + (i))
#define da_ref(i,j) da, (da_offset + (j)*ldda + (i))
#define t_ref(a_1) dT, (dT_offset + (a_1)*nb)
double c_zero = MAGMA_D_ZERO;
magma_int_t i__1, i__2, i__3;
magma_int_t lwork, ldda;
magma_int_t i, ib, ki, kk, iinfo;
magma_int_t lddwork = min(m, n);
double *work;
magmaDouble_ptr da, dwork;
size_t da_offset, dwork_offset;
magma_event_t event = NULL;
*info = 0;
if (m < 0) {
*info = -1;
} else if ((n < 0) || (n > m)) {
*info = -2;
} else if ((k < 0) || (k > n)) {
*info = -3;
} else if (lda < max(1,m)) {
*info = -5;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
if (n <= 0)
return *info;
/* Allocate GPU work space */
ldda = ((m+31)/32)*32;
lddwork = ((lddwork+31)/32)*32;
if (MAGMA_SUCCESS != magma_dmalloc( &da, ((n)*ldda + nb*lddwork ) )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
da_offset = 0;
dwork = da;
dwork_offset = da_offset + (n)*ldda;
/* Allocate CPU work space */
lwork = n * nb;
magma_dmalloc_cpu( &work, lwork );
if( work == NULL ) {
magma_free( da );
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
if ( (nb > 1) && (nb < k) )
{
/* Use blocked code after the last block.
The first kk columns are handled by the block method. */
ki = (k - nb - 1) / nb * nb;
kk = min(k, ki + nb);
/* Set A(1:kk,kk+1:n) to zero. */
magmablas_dlaset(MagmaFull, kk, n-kk, c_zero, c_zero, da_ref(0,kk), ldda, queue);
}
else
kk = 0;
/* Use unblocked code for the last or only block. */
if (kk < n)
{
i__1 = m - kk;
i__2 = n - kk;
i__3 = k - kk;
lapackf77_dorgqr(&i__1, &i__2, &i__3,
a_ref(kk, kk), &lda,
&tau[kk], work, &lwork, &iinfo);
magma_dsetmatrix(i__1, i__2, a_ref(kk, kk), lda, da_ref(kk, kk), ldda, queue);
}
if (kk > 0)
{
/* Use blocked code */
for (i = ki; i >= 0; i-=nb)
{
ib = min(nb, k - i);
/* Send the current panel to the GPU */
i__2 = m - i;
dpanel_to_q(MagmaUpper, ib, a_ref(i,i), lda, work);
magma_dsetmatrix(i__2, ib, a_ref(i, i), lda, da_ref(i, i), ldda, queue);
if (i + ib < n)
{
/* Apply H to A(i:m,i+ib:n) from the left */
i__3 = n - i - ib;
magma_dlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise,
i__2, i__3, ib,
da_ref(i, i ), ldda, t_ref(i), nb,
da_ref(i, i+ib), ldda, dwork, dwork_offset, lddwork, queue);
}
/* Apply H to rows i:m of current block on the CPU */
lapackf77_dorgqr(&i__2, &ib, &ib,
a_ref(i, i), &lda,
&tau[i], work, &lwork, &iinfo);
magma_dsetmatrix_async( i__2, ib,
a_ref(i,i), lda,
da_ref(i,i), ldda, queue, &event );
/* Set rows 1:i-1 of current block to zero */
i__2 = i + ib;
magmablas_dlaset(MagmaFull, i, i__2 - i, c_zero, c_zero, da_ref(0,i), ldda, queue);
}
}
magma_dgetmatrix(m, n, da_ref(0, 0), ldda, a_ref(0, 0), lda, queue);
//cudaStreamDestroy(stream);
magma_free( da );
magma_free_cpu(work);
return *info;
} /* magma_dorgqr */
/**
Purpose
-------
DGEBRD reduces a general real M-by-N matrix A to upper or lower
bidiagonal form B by an orthogonal transformation: Q**H * A * P = B.
If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
Arguments
---------
@param[in]
m INTEGER
The number of rows in the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns in the matrix A. N >= 0.
@param[in,out]
A DOUBLE_PRECISION array, dimension (LDA,N)
On entry, the M-by-N general matrix to be reduced.
On exit,
if m >= n, the diagonal and the first superdiagonal are
overwritten with the upper bidiagonal matrix B; the
elements below the diagonal, with the array TAUQ, represent
the orthogonal matrix Q as a product of elementary
reflectors, and the elements above the first superdiagonal,
with the array TAUP, represent the orthogonal matrix P as
a product of elementary reflectors;
\n
if m < n, the diagonal and the first subdiagonal are
overwritten with the lower bidiagonal matrix B; the
elements below the first subdiagonal, with the array TAUQ,
represent the orthogonal matrix Q as a product of
elementary reflectors, and the elements above the diagonal,
with the array TAUP, represent the orthogonal matrix P as
a product of elementary reflectors.
See Further Details.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,M).
@param[out]
d double precision array, dimension (min(M,N))
The diagonal elements of the bidiagonal matrix B:
D(i) = A(i,i).
@param[out]
e double precision array, dimension (min(M,N)-1)
The off-diagonal elements of the bidiagonal matrix B:
if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1;
if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1.
@param[out]
tauq DOUBLE_PRECISION array dimension (min(M,N))
The scalar factors of the elementary reflectors which
represent the orthogonal matrix Q. See Further Details.
@param[out]
taup DOUBLE_PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors which
represent the orthogonal matrix P. See Further Details.
@param[out]
work (workspace) DOUBLE_PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The length of the array WORK. LWORK >= (M+N)*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.
Further Details
---------------
The matrices Q and P are represented as products of elementary
reflectors:
If m >= n,
Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1)
Each H(i) and G(i) has the form:
H(i) = I - tauq * v * v' and G(i) = I - taup * u * u'
where tauq and taup are real scalars, and v and u are real vectors;
v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i);
u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n);
tauq is stored in TAUQ(i) and taup in TAUP(i).
If m < n,
Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m)
Each H(i) and G(i) has the form:
H(i) = I - tauq * v * v' and G(i) = I - taup * u * u'
where tauq and taup are real scalars, and v and u are real vectors;
v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i);
u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n);
tauq is stored in TAUQ(i) and taup in TAUP(i).
The contents of A on exit are illustrated by the following examples:
@verbatim
m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n):
( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 )
( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 )
( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 )
( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 )
( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 )
( v1 v2 v3 v4 v5 )
@endverbatim
where d and e denote diagonal and off-diagonal elements of B, vi
denotes an element of the vector defining H(i), and ui an element of
the vector defining G(i).
@ingroup magma_dgesvd_comp
********************************************************************/
extern "C" magma_int_t
magma_dgebrd(magma_int_t m, magma_int_t n,
double *A, magma_int_t lda, double *d, double *e,
double *tauq, double *taup,
double *work, magma_int_t lwork,
magma_int_t *info)
{
#define A(i, j) (A + (j)*lda + (i))
#define dA(i, j) (dA + (j)*ldda + (i))
double c_neg_one = MAGMA_D_NEG_ONE;
double c_one = MAGMA_D_ONE;
double *dA, *dwork;
magma_int_t ncol, nrow, jmax, nb, ldda;
magma_int_t i, j, nx;
magma_int_t iinfo;
magma_int_t minmn;
magma_int_t ldwrkx, ldwrky, lwkopt;
magma_int_t lquery;
nb = magma_get_dgebrd_nb(n);
ldda = m;
lwkopt = (m + n) * nb;
work[0] = MAGMA_D_MAKE( lwkopt, 0. );
lquery = (lwork == -1);
/* Check arguments */
*info = 0;
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,m)) {
*info = -4;
} else if (lwork < lwkopt && (! lquery) ) {
*info = -10;
}
if (*info < 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
/* Quick return if possible */
minmn = min(m,n);
if (minmn == 0) {
work[0] = c_one;
return *info;
}
if (MAGMA_SUCCESS != magma_dmalloc( &dA, n*ldda + (m + n)*nb )) {
fprintf (stderr, "!!!! device memory allocation error in dgebrd\n" );
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
dwork = dA + n*ldda;
ldwrkx = m;
ldwrky = n;
/* Set the block/unblock crossover point NX. */
nx = 128;
/* Copy the matrix to the GPU */
if (minmn - nx >= 1) {
magma_dsetmatrix( m, n, A, lda, dA, ldda );
}
for (i=0; i < (minmn - nx); i += nb) {
/* Reduce rows and columns i:i+nb-1 to bidiagonal form and return
the matrices X and Y which are needed to update the unreduced
part of the matrix */
nrow = m - i;
ncol = n - i;
/* Get the current panel (no need for the 1st iteration) */
if ( i > 0 ) {
magma_dgetmatrix( nrow, nb, dA(i, i), ldda, A( i, i), lda );
magma_dgetmatrix( nb, ncol - nb,
dA(i, i+nb), ldda,
A( i, i+nb), lda );
}
magma_dlabrd_gpu(nrow, ncol, nb,
A(i, i), lda, dA(i, i), ldda,
d+i, e+i, tauq+i, taup+i,
work, ldwrkx, dwork, ldwrkx, // x, dx
work+(ldwrkx*nb), ldwrky, dwork+(ldwrkx*nb), ldwrky); // y, dy
/* Update the trailing submatrix A(i+nb:m,i+nb:n), using an update
of the form A := A - V*Y' - X*U' */
nrow = m - i - nb;
ncol = n - i - nb;
// Send Y back to the GPU
magma_dsetmatrix( nrow, nb, work + nb, ldwrkx, dwork + nb, ldwrkx );
magma_dsetmatrix( ncol, nb,
work + (ldwrkx+1)*nb, ldwrky,
dwork + (ldwrkx+1)*nb, ldwrky );
magma_dgemm( MagmaNoTrans, MagmaConjTrans,
nrow, ncol, nb,
c_neg_one, dA(i+nb, i ), ldda,
dwork+(ldwrkx+1)*nb, ldwrky,
c_one, dA(i+nb, i+nb), ldda);
magma_dgemm( MagmaNoTrans, MagmaNoTrans,
nrow, ncol, nb,
c_neg_one, dwork+nb, ldwrkx,
dA( i, i+nb ), ldda,
c_one, dA( i+nb, i+nb ), ldda);
/* Copy diagonal and off-diagonal elements of B back into A */
if (m >= n) {
jmax = i + nb;
for (j = i; j < jmax; ++j) {
*A(j, j ) = MAGMA_D_MAKE( d[j], 0. );
*A(j, j+1) = MAGMA_D_MAKE( e[j], 0. );
}
} else {
jmax = i + nb;
for (j = i; j < jmax; ++j) {
*A(j, j ) = MAGMA_D_MAKE( d[j], 0. );
*A(j+1, j ) = MAGMA_D_MAKE( e[j], 0. );
}
}
}
/* Use unblocked code to reduce the remainder of the matrix */
nrow = m - i;
ncol = n - i;
if ( 0 < minmn - nx ) {
magma_dgetmatrix( nrow, ncol, dA(i, i), ldda, A(i, i), lda );
}
lapackf77_dgebrd( &nrow, &ncol,
A(i, i), &lda, d+i, e+i,
tauq+i, taup+i, work, &lwork, &iinfo);
work[0] = MAGMA_D_MAKE( lwkopt, 0. );
magma_free( dA );
return *info;
} /* magma_dgebrd */
extern "C" magma_int_t
magma_dormqr_gpu_2stages(const char side, const char trans,
magma_int_t m, magma_int_t n, magma_int_t k,
double *da, magma_int_t ldda,
double *dc, magma_int_t lddc,
double *dT, magma_int_t nb,
magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
DORMQR_GPU overwrites the general real M-by-N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'T': Q**T * C C * Q**T
where Q is a real orthogonal matrix defined as the product of k
elementary reflectors
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF. Q is of order M if SIDE = 'L' and of order N
if SIDE = 'R'.
Arguments
=========
SIDE (input) CHARACTER*1
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.
TRANS (input) CHARACTER*1
= 'N': No transpose, apply Q;
= 'T': Transpose, apply Q**T.
M (input) INTEGER
The number of rows of the matrix C. M >= 0.
N (input) INTEGER
The number of columns of the matrix C. N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = 'L', M >= K >= 0;
if SIDE = 'R', N >= K >= 0.
DA (input) DOUBLE_PRECISION array on the GPU, dimension (LDDA,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
DGEQRF in the first k columns of its array argument DA.
DA is modified by the routine but restored on exit.
LDDA (input) INTEGER
The leading dimension of the array DA.
If SIDE = 'L', LDDA >= max(1,M);
if SIDE = 'R', LDDA >= max(1,N).
DC (input/output) DOUBLE_PRECISION array on the GPU, dimension (LDDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**T * C or C * Q**T or C*Q.
LDDC (input) INTEGER
The leading dimension of the array DC. LDDC >= max(1,M).
DT (input) DOUBLE_PRECISION array on the GPU that is the output
(the 9th argument) of magma_dgeqrf_gpu.
NB (input) INTEGER
This is the blocking size that was used in pre-computing DT, e.g.,
the blocking size used in magma_dgeqrf_gpu.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
===================================================================== */
char side_[2] = {side, 0};
char trans_[2] = {trans, 0};
double *dwork;
magma_int_t i1, i2, i3, ib, ic, jc, mi, ni, nq, nw, ret;
int left, notran;
//magma_int_t lwkopt;
*info = 0;
left = lapackf77_lsame(side_, "L");
notran = lapackf77_lsame(trans_, "N");
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left) {
nq = m;
nw = n;
} else {
nq = n;
nw = m;
}
if ( (!left) && (!lapackf77_lsame(side_, "R")) ) {
*info = -1;
} else if ( (!notran) && (!lapackf77_lsame(trans_, MagmaTransStr)) ) {
*info = -2;
} else if (m < 0) {
*info = -3;
} else if (n < 0) {
*info = -4;
} else if (k < 0 || k > nq) {
*info = -5;
} else if (ldda < max(1,nq)) {
*info = -7;
} else if (lddc < max(1,m)) {
*info = -10;
}
if(MAGMA_SUCCESS != magma_dmalloc( &dwork, n*nb )) {
printf ("!!!! dorgqr_2stage magma_alloc failed for: dwork\n" );
exit(-1);
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0 || k == 0) {
return *info;
}
if ( (left && (! notran)) || ( (!left) && notran ) ) {
i1 = 0;
i2 = k;
i3 = nb;
} else {
i1 = (k - 1) / nb * nb;
i2 = 0;
i3 = -nb;
}
// silence "uninitialized" warnings
mi = 0;
ni = 0;
if (left) {
ni = n;
jc = 0;
} else {
mi = m;
ic = 0;
}
for (magma_int_t i=i1; (i3<0 ? i>=i2 : i<i2); i+=i3)
{
ib = min(nb, k - i);
if (left){
mi = m - i;
ic = i;
}
else {
ni = n - i;
jc = i;
}
ret = magma_dlarfb_gpu( MagmaLeft, trans, MagmaForward, MagmaColumnwise,
mi, ni, ib, da+i+i*ldda, ldda, dT+i*nb, nb,
dc+ic+jc*lddc, lddc, dwork, nw);
if ( ret != MAGMA_SUCCESS ){
magma_free(dwork);
return ret;
}
}
return MAGMA_SUCCESS;
} /* End of MAGMA_DORMQR_GPU_2stages */
magma_int_t
magma_dcg_merge( magma_d_sparse_matrix A, magma_d_vector b, magma_d_vector *x,
magma_d_solver_par *solver_par ){
// prepare solver feedback
solver_par->solver = Magma_CGMERGE;
solver_par->numiter = 0;
solver_par->info = 0;
// some useful variables
double c_zero = MAGMA_D_ZERO, c_one = MAGMA_D_ONE;
magma_int_t dofs = A.num_rows;
// GPU stream
magma_queue_t stream[2];
magma_event_t event[1];
magma_queue_create( &stream[0] );
magma_queue_create( &stream[1] );
magma_event_create( &event[0] );
// GPU workspace
magma_d_vector r, d, z;
magma_d_vinit( &r, Magma_DEV, dofs, c_zero );
magma_d_vinit( &d, Magma_DEV, dofs, c_zero );
magma_d_vinit( &z, Magma_DEV, dofs, c_zero );
double *d1, *d2, *skp;
magma_dmalloc( &d1, dofs*(1) );
magma_dmalloc( &d2, dofs*(1) );
// array for the parameters
magma_dmalloc( &skp, 6 ); // skp = [alpha|beta|gamma|rho|tmp1|tmp2]
// solver variables
double alpha, beta, gamma, rho, tmp1, *skp_h;
double nom, nom0, r0, betanom, den;
// solver setup
magma_dscal( dofs, c_zero, x->val, 1) ; // x = 0
magma_dcopy( dofs, b.val, 1, r.val, 1 ); // r = b
magma_dcopy( dofs, b.val, 1, d.val, 1 ); // d = b
nom0 = betanom = magma_dnrm2( dofs, r.val, 1 );
nom = nom0 * nom0; // nom = r' * r
magma_d_spmv( c_one, A, d, c_zero, z ); // z = A d
den = MAGMA_D_REAL( magma_ddot(dofs, d.val, 1, z.val, 1) ); // den = d'* z
solver_par->init_res = nom0;
// array on host for the parameters
magma_dmalloc_cpu( &skp_h, 6 );
alpha = rho = gamma = tmp1 = c_one;
beta = magma_ddot(dofs, r.val, 1, r.val, 1);
skp_h[0]=alpha;
skp_h[1]=beta;
skp_h[2]=gamma;
skp_h[3]=rho;
skp_h[4]=tmp1;
skp_h[5]=MAGMA_D_MAKE(nom, 0.0);
magma_dsetvector( 6, skp_h, 1, skp, 1 );
if ( (r0 = nom * solver_par->epsilon) < ATOLERANCE )
r0 = ATOLERANCE;
if ( nom < r0 )
return MAGMA_SUCCESS;
// check positive definite
if (den <= 0.0) {
printf("Operator A is not postive definite. (Ar,r) = %f\n", den);
return -100;
}
//Chronometry
real_Double_t tempo1, tempo2;
magma_device_sync(); tempo1=magma_wtime();
if( solver_par->verbose > 0 ){
solver_par->res_vec[0] = (real_Double_t) nom0;
solver_par->timing[0] = 0.0;
}
// start iteration
for( solver_par->numiter= 1; solver_par->numiter<solver_par->maxiter;
solver_par->numiter++ ){
magmablasSetKernelStream(stream[0]);
// computes SpMV and dot product
magma_dcgmerge_spmv1( A, d1, d2, d.val, z.val, skp );
// updates x, r, computes scalars and updates d
magma_dcgmerge_xrbeta( dofs, d1, d2, x->val, r.val, d.val, z.val, skp );
// check stopping criterion (asynchronous copy)
magma_dgetvector_async( 1 , skp+1, 1,
skp_h+1, 1, stream[1] );
betanom = sqrt(MAGMA_D_REAL(skp_h[1]));
if( solver_par->verbose > 0 ){
magma_device_sync(); tempo2=magma_wtime();
if( (solver_par->numiter)%solver_par->verbose==0 ) {
solver_par->res_vec[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) betanom;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
if ( betanom < r0 ) {
break;
}
}
magma_device_sync(); tempo2=magma_wtime();
solver_par->runtime = (real_Double_t) tempo2-tempo1;
double residual;
magma_dresidual( A, b, *x, &residual );
solver_par->iter_res = betanom;
solver_par->final_res = residual;
if( solver_par->numiter < solver_par->maxiter){
solver_par->info = 0;
}else if( solver_par->init_res > solver_par->final_res ){
if( solver_par->verbose > 0 ){
if( (solver_par->numiter)%solver_par->verbose==0 ) {
solver_par->res_vec[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) betanom;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
solver_par->info = -2;
}
else{
if( solver_par->verbose > 0 ){
if( (solver_par->numiter)%solver_par->verbose==0 ) {
solver_par->res_vec[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) betanom;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
solver_par->info = -1;
}
magma_d_vfree(&r);
magma_d_vfree(&z);
magma_d_vfree(&d);
magma_free( d1 );
magma_free( d2 );
magma_free( skp );
magma_free_cpu( skp_h );
return MAGMA_SUCCESS;
} /* magma_dcg_merge */
/**
Purpose
-------
DSYEVD computes all eigenvalues and, optionally, eigenvectors of a
real symmetric 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]
nrgpu INTEGER
Number of GPUs to use.
@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]
A DOUBLE_PRECISION array, dimension (LDA, N)
On entry, the symmetric 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]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[out]
w DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
@param[out]
work (workspace) DOUBLE_PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The length of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LWORK >= 2*N + N*NB.
If JOBZ = MagmaVec and N > 1, LWORK >= max( 2*N + N*NB, 1 + 6*N + 2*N**2 ).
NB can be obtained through magma_get_dsytrd_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]
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_dsyev_driver
********************************************************************/
extern "C" magma_int_t
magma_dsyevd_m(magma_int_t nrgpu, magma_vec_t jobz, magma_uplo_t uplo,
magma_int_t n,
double *A, magma_int_t lda,
double *w,
double *work, magma_int_t lwork,
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;
magma_int_t izero = 0;
double d_one = 1.;
double d__1;
double eps;
magma_int_t inde;
double anrm;
double rmin, rmax;
double sigma;
magma_int_t iinfo, lwmin;
magma_int_t lower;
magma_int_t wantz;
magma_int_t indwk2, llwrk2;
magma_int_t iscale;
double safmin;
double bignum;
magma_int_t indtau;
magma_int_t indwrk, liwmin;
magma_int_t llwork;
double smlnum;
magma_int_t lquery;
wantz = (jobz == MagmaVec);
lower = (uplo == MagmaLower);
lquery = (lwork == -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 (lda < max(1,n)) {
*info = -5;
}
magma_int_t nb = magma_get_dsytrd_nb( n );
if ( n <= 1 ) {
lwmin = 1;
liwmin = 1;
}
else if ( wantz ) {
lwmin = max( 2*n + n*nb, 1 + 6*n + 2*n*n );
liwmin = 3 + 5*n;
}
else {
lwmin = 2*n + n*nb;
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_dlamch("Epsilon");
work[0] = lwmin * one_eps;
iwork[0] = liwmin;
if ((lwork < lwmin) && !lquery) {
*info = -8;
} else if ((liwork < liwmin) && ! lquery) {
*info = -10;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
return *info;
}
if (n == 1) {
w[0] = A[0];
if (wantz) {
A[0] = 1.;
}
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
lapackf77_dsyevd(jobz_, uplo_,
&n, A, &lda,
w, work, &lwork,
iwork, &liwork, info);
return *info;
}
/* Get machine constants. */
safmin = lapackf77_dlamch("Safe minimum");
eps = lapackf77_dlamch("Precision");
smlnum = safmin / eps;
bignum = 1. / smlnum;
rmin = magma_dsqrt(smlnum);
rmax = magma_dsqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = lapackf77_dlansy("M", uplo_, &n, A, &lda, work);
iscale = 0;
if (anrm > 0. && anrm < rmin) {
iscale = 1;
sigma = rmin / anrm;
} else if (anrm > rmax) {
iscale = 1;
sigma = rmax / anrm;
}
if (iscale == 1) {
lapackf77_dlascl(uplo_, &izero, &izero, &d_one, &sigma, &n, &n, A,
&lda, info);
}
/* Call DSYTRD to reduce symmetric matrix to tridiagonal form. */
// dsytrd work: e (n) + tau (n) + llwork (n*nb) ==> 2n + n*nb
// dstedx work: e (n) + tau (n) + z (n*n) + llwrk2 (1 + 4*n + n^2) ==> 1 + 6n + 2n^2
inde = 0;
indtau = inde + n;
indwrk = indtau + n;
indwk2 = indwrk + n*n;
llwork = lwork - indwrk;
llwrk2 = lwork - indwk2;
magma_timer_t time=0;
timer_start( time );
magma_dsytrd_mgpu(nrgpu, 1, uplo, n, A, lda, w, &work[inde],
&work[indtau], &work[indwrk], llwork, &iinfo);
timer_stop( time );
timer_printf( "time dsytrd = %6.2f\n", time );
/* For eigenvalues only, call DSTERF. For eigenvectors, first call
DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
tridiagonal matrix, then call DORMTR to multiply it to the Householder
transformations represented as Householder vectors in A. */
if (! wantz) {
lapackf77_dsterf(&n, w, &work[inde], info);
}
else {
timer_start( time );
#ifdef USE_SINGLE_GPU
if (MAGMA_SUCCESS != magma_dmalloc( &dwork, 3*n*(n/2 + 1) )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_dstedx(MagmaRangeAll, n, 0., 0., 0, 0, w, &work[inde],
&work[indwrk], n, &work[indwk2],
llwrk2, iwork, liwork, dwork, info);
magma_free( dwork );
#else
magma_dstedx_m(nrgpu, MagmaRangeAll, n, 0., 0., 0, 0, w, &work[inde],
&work[indwrk], n, &work[indwk2],
llwrk2, iwork, liwork, info);
#endif
timer_stop( time );
timer_printf( "time dstedc = %6.2f\n", time );
timer_start( time );
magma_dormtr_m(nrgpu, MagmaLeft, uplo, MagmaNoTrans, n, n, A, lda, &work[indtau],
&work[indwrk], n, &work[indwk2], llwrk2, &iinfo);
lapackf77_dlacpy("A", &n, &n, &work[indwrk], &n, A, &lda);
timer_stop( time );
timer_printf( "time dormtr + copy = %6.2f\n", time );
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
d__1 = 1. / sigma;
blasf77_dscal(&n, &d__1, w, &ione);
}
work[0] = lwmin * one_eps; // round up
iwork[0] = liwmin;
return *info;
} /* magma_dsyevd_m */
/**
Purpose
-------
DORGQR generates an M-by-N DOUBLE_PRECISION matrix Q with orthonormal columns,
which is defined as the first N columns of a product of K elementary
reflectors of order M
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF_GPU.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix Q. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix Q. M >= N >= 0.
@param[in]
k INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
@param[in,out]
dA DOUBLE_PRECISION array A on the GPU device,
dimension (LDDA,N). On entry, the i-th column must contain
the vector which defines the elementary reflector H(i), for
i = 1,2,...,k, as returned by DGEQRF_GPU in the first k
columns of its array argument A.
On exit, the M-by-N matrix Q.
@param[in]
ldda INTEGER
The first dimension of the array A. LDDA >= max(1,M).
@param[in]
tau DOUBLE_PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQRF_GPU.
@param[in]
dT DOUBLE_PRECISION work space array on the GPU device,
dimension (MIN(M, N) )*NB.
This must be the 6th argument of magma_dgeqrf_gpu
[ note that if N here is bigger than N in magma_dgeqrf_gpu,
the workspace requirement DT in magma_dgeqrf_gpu must be
as specified in this routine ].
@param[in]
nb INTEGER
This is the block size used in DGEQRF_GPU, and correspondingly
the size of the T matrices, used in the factorization, and
stored in DT.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument has an illegal value
@ingroup magma_dsyev_2stage
********************************************************************/
extern "C" magma_int_t
magma_dorgqr_2stage_gpu(magma_int_t m, magma_int_t n, magma_int_t k,
double *dA, magma_int_t ldda,
double *tau, double *dT,
magma_int_t nb, magma_int_t *info)
{
#define dA(a_1,a_2) (dA + (a_2)*(ldda) + (a_1))
#define dT(a_1) (dT + (a_1)*nb)
double c_zero = MAGMA_D_ZERO;
double c_one = MAGMA_D_ONE;
magma_int_t i__1, i__2, i__3;
//magma_int_t lwork;
magma_int_t i, ib, ki, kk; //, iinfo;
//magma_int_t lddwork = min(m, n);
//double *work, *panel;
double *dwork;
//magma_queue_t stream[2];
magma_int_t ldt=nb; // need to be an input parameter
*info = 0;
if (m < 0) {
*info = -1;
} else if ((n < 0) || (n > m)) {
*info = -2;
} else if ((k < 0) || (k > n)) {
*info = -3;
} else if (ldda < max(1,m)) {
*info = -5;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
if (n <= 0)
return *info;
if (MAGMA_SUCCESS != magma_dmalloc( &dwork, n*nb )) {
printf ("!!!! dorgqr_2stage magma_alloc failed for: dwork\n" );
exit(-1);
}
if ( (nb > 1) && (nb < k) ) {
/* Use blocked code after the last block.
The first kk columns are handled by the block method.
ki is start of 2nd-to-last block. */
ki = (k - nb - 1) / nb * nb;
kk = min(k, ki + nb);
/* Set A(1:kk,kk+1:n) to zero. */
/* and A(kk+1:m, kk+1:n) = I */
magmablas_dlaset( MagmaFull, kk, n-kk, c_zero, c_zero, dA(0, kk), ldda );
magmablas_dlaset( MagmaFull, m-kk, n-kk, c_zero, c_one, dA(kk,kk), ldda );
}
else {
ki = 0;
kk = 0;
}
/* Allocate work space on CPU in pinned memory */
//lwork = (n+m) * nb;
//if (kk < n)
// lwork = max(lwork, n * nb + (m-kk)*(n-kk));
//if (MAGMA_SUCCESS != magma_dmalloc_pinned( &work, (lwork) )) {
// *info = MAGMA_ERR_HOST_ALLOC;
// return *info;
//}
//panel = work + n * nb;
//magma_queue_create( &stream[0] );
//magma_queue_create( &stream[1] );
/* Use unblocked code for the last or only block. */
if (kk < n) {
i__1 = m - kk;
i__2 = n - kk;
i__3 = k - kk;
//magma_dgetmatrix(i__1, i__2, dA(kk, kk), ldda, panel, i__1);
//lapackf77_dorgqr(&i__1, &i__2, &i__3, panel, &i__1, &tau[kk],
// work, &lwork, &iinfo);
//
//magma_dsetmatrix(i__1, i__2, panel, i__1, dA(kk, kk), ldda);
magma_dlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise,
i__1, i__2, i__3,
dA(kk, kk-nb), ldda, dT(kk-nb), ldt,
dA(kk, kk), ldda, dwork, i__2);
//magmablas_dlaset(MagmaFull, kk-nb, nb, c_zero, c_zero, dA(0,kk-nb), ldda);
//magmablas_dlaset(MagmaFull, m-(kk-nb), nb, c_zero, c_one, dA(kk-nb,kk-nb), ldda);
}
if (kk > 0) {
/* Use blocked code */
for (i = ki; i >= nb; i -= nb) {
ib = min(nb, k - i);
/* Send current panel to the CPU for update */
i__2 = m - i;
//magma_dgetmatrix_async( i__2, ib, dA(i,i), ldda, panel, i__2, stream[0] ); // verify
if (i + ib < n) {
/* Apply H to A(i:m,i+ib:n) from the left */
i__3 = n - i;
magmablas_dlaset( MagmaFull, i, ib, c_zero, c_zero, dA(0,i), ldda );
magmablas_dlaset( MagmaFull, m-i, ib, c_zero, c_one, dA(i,i), ldda );
magma_dlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise,
i__2, i__3, ib,
dA(i, i-nb), ldda, dT(i-nb), ldt,
dA(i, i), ldda, dwork, i__3);
}
/* Apply H to rows i:m of current block on the CPU */
//magma_queue_sync( stream[0] );
//lapackf77_dorgqr(&i__2, &ib, &ib, panel, &i__2, &tau[i],
// work, &lwork, &iinfo);
//magma_dsetmatrix_async( i__2, ib, panel, i__2, dA(i,i), ldda, stream[1] ); // verify
/* Set rows 1:i-1 of current block to zero */
i__2 = i + ib;
//magmablas_dlaset(MagmaFull, i-ib, ib, c_zero, c_zero, dA(0,i-ib), ldda);
//magmablas_dlaset(MagmaFull, m-(i-ib), ib, c_zero, c_one, dA(i-ib,i-ib), ldda);
}
}
magmablas_dlaset( MagmaFull, m, nb, c_zero, c_one, dA(0,0), ldda );
magma_free( dwork );
//magma_free_pinned( work );
//magma_queue_destroy( stream[0] );
//magma_queue_destroy( stream[1] );
return *info;
} /* magma_dorgqr_gpu */
/***************************************************************************//**
Purpose
-------
DGEQRF computes a QR factorization of a real M-by-N matrix A:
A = Q * R.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. N >= 0.
@param[in,out]
dA_array Array of pointers, dimension (batchCount).
Each is a DOUBLE PRECISION array on the GPU, dimension (LDDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of min(m,n) elementary reflectors (see Further
Details).
@param[in]
ldda INTEGER
The leading dimension of the array dA. LDDA >= max(1,M).
To benefit from coalescent memory accesses LDDA must be
divisible by 16.
@param[in,out]
dR_array Array of pointers, dimension (batchCount).
Each is a DOUBLE PRECISION array on the GPU, dimension (LDDR, N/NB)
dR should be of size (LDDR, N) when provide_RT > 0 and
of size (LDDT, NB) otherwise. NB is the local blocking size.
On exit, the elements of R are stored in dR only when provide_RT > 0.
@param[in]
lddr INTEGER
The leading dimension of the array dR.
LDDR >= min(M,N) when provide_RT == 1
otherwise LDDR >= min(NB, min(M,N)).
NB is the local blocking size.
To benefit from coalescent memory accesses LDDR must be
divisible by 16.
@param[in,out]
dT_array Array of pointers, dimension (batchCount).
Each is a DOUBLE PRECISION array on the GPU, dimension (LDDT, N/NB)
dT should be of size (LDDT, N) when provide_RT > 0 and
of size (LDDT, NB) otherwise. NB is the local blocking size.
On exit, the elements of T are stored in dT only when provide_RT > 0.
@param[in]
lddt INTEGER
The leading dimension of the array dT.
LDDT >= min(NB,min(M,N)). NB is the local blocking size.
To benefit from coalescent memory accesses LDDR must be
divisible by 16.
@param[out]
dtau_array Array of pointers, dimension (batchCount).
Each is a DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
@param[in]
provide_RT INTEGER
provide_RT = 0 no R and no T in output.
dR and dT are used as local workspace to store the R and T of each step.
provide_RT = 1 the whole R of size (min(M,N), N) and the nbxnb block of T are provided in output.
provide_RT = 2 the nbxnb diag block of R and of T are provided in output.
@param[out]
info_array Array of INTEGERs, dimension (batchCount), for corresponding matrices.
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
@param[in]
batchCount INTEGER
The number of matrices to operate on.
@param[in]
queue magma_queue_t
Queue to execute in.
Further Details
---------------
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
@ingroup magma_geqrf_batched
*******************************************************************************/
extern "C" magma_int_t
magma_dgeqrf_expert_batched(
magma_int_t m, magma_int_t n,
double **dA_array, magma_int_t ldda,
double **dR_array, magma_int_t lddr,
double **dT_array, magma_int_t lddt,
double **dtau_array, magma_int_t provide_RT,
magma_int_t *info_array, magma_int_t batchCount, magma_queue_t queue)
{
#define dA(i, j) (dA + (i) + (j)*ldda)
/* Local Parameter */
magma_int_t nb = magma_get_dgeqrf_batched_nb(m);
magma_int_t nnb = 8;
magma_int_t min_mn = min(m, n);
/* Check arguments */
cudaMemset(info_array, 0, batchCount*sizeof(magma_int_t));
magma_int_t arginfo = 0;
if (m < 0)
arginfo = -1;
else if (n < 0)
arginfo = -2;
else if (ldda < max(1,m))
arginfo = -4;
else if (lddr < min_mn && provide_RT == 1)
arginfo = -6;
else if (lddr < min(min_mn, nb))
arginfo = -6;
else if (lddt < min(min_mn, nb))
arginfo = -8;
if (arginfo != 0) {
magma_xerbla( __func__, -(arginfo) );
return arginfo;
}
/* Quick return if possible */
if (m == 0 || n == 0)
if (min_mn == 0 ) return arginfo;
if ( m > 2048 || n > 2048 ) {
printf("=========================================================================================\n");
printf(" WARNING batched routines are designed for small sizes it might be better to use the\n Native/Hybrid classical routines if you want performance\n");
printf("=========================================================================================\n");
}
magma_int_t i, k, ib=nb, jb=nnb, offset_RT=0, use_stream;
magma_int_t ldw, offset;
double **dW0_displ = NULL;
double **dW1_displ = NULL;
double **dW2_displ = NULL;
double **dW3_displ = NULL;
double **dW4_displ = NULL;
double **dW5_displ = NULL;
double **dR_displ = NULL;
double **dT_displ = NULL;
double *dwork = NULL;
double **cpuAarray = NULL;
double **cpuTarray = NULL;
magma_malloc((void**)&dW0_displ, batchCount * sizeof(*dW0_displ));
magma_malloc((void**)&dW1_displ, batchCount * sizeof(*dW1_displ));
magma_malloc((void**)&dW2_displ, batchCount * sizeof(*dW2_displ));
magma_malloc((void**)&dW3_displ, batchCount * sizeof(*dW3_displ));
magma_malloc((void**)&dW4_displ, batchCount * sizeof(*dW4_displ));
magma_malloc((void**)&dW5_displ, batchCount * sizeof(*dW5_displ));
magma_malloc((void**)&dR_displ, batchCount * sizeof(*dR_displ));
magma_malloc((void**)&dT_displ, batchCount * sizeof(*dT_displ));
magma_dmalloc(&dwork, (2 * nb * n) * batchCount);
magma_malloc_cpu((void**) &cpuAarray, batchCount*sizeof(double*));
magma_malloc_cpu((void**) &cpuTarray, batchCount*sizeof(double*));
/* check allocation */
if ( dW0_displ == NULL || dW1_displ == NULL || dW2_displ == NULL ||
dW3_displ == NULL || dW4_displ == NULL || dW5_displ == NULL ||
dR_displ == NULL || dT_displ == NULL || dwork == NULL ||
cpuAarray == NULL || cpuTarray == NULL ) {
magma_free(dW0_displ);
magma_free(dW1_displ);
magma_free(dW2_displ);
magma_free(dW3_displ);
magma_free(dW4_displ);
magma_free(dW5_displ);
magma_free(dR_displ);
magma_free(dT_displ);
magma_free(dwork);
magma_free_cpu(cpuAarray);
magma_free_cpu(cpuTarray);
magma_int_t info = MAGMA_ERR_DEVICE_ALLOC;
magma_xerbla( __func__, -(info) );
return info;
}
magma_ddisplace_pointers(dR_displ, dR_array, lddr, 0, 0, batchCount, queue);
magma_ddisplace_pointers(dT_displ, dT_array, lddt, 0, 0, batchCount, queue);
// set dwork to zero because our GEMM routine does propagate NAN when C=betaC+alphaA*B and beta=0
magmablas_dlaset_q( MagmaFull, 2*nb, n*batchCount, MAGMA_D_ZERO, MAGMA_D_ZERO, dwork, 2*nb, queue );
// set dR and dT to zero. if provide_RT == 0 only a tile of size nbxnb is used and overwritten at each step
magmablas_dlaset_batched( MagmaFull, lddr, (provide_RT > 0 ? n:min(min_mn,nb)), MAGMA_D_ZERO, MAGMA_D_ZERO, dR_displ, lddr, batchCount, queue );
magmablas_dlaset_batched( MagmaFull, lddt, (provide_RT > 0 ? n:min(min_mn,nb)), MAGMA_D_ZERO, MAGMA_D_ZERO, dT_displ, lddt, batchCount, queue );
/*
if ( provide_RT > 0 )
{
magmablas_dlaset_q( MagmaFull, lddr, n*batchCount, MAGMA_D_ZERO, MAGMA_D_ZERO, dR, lddr, queue );
magmablas_dlaset_q( MagmaFull, lddt, n*batchCount, MAGMA_D_ZERO, MAGMA_D_ZERO, dT, lddt, queue );
}
else
{
magmablas_dlaset_q( MagmaFull, lddr, nb*batchCount, MAGMA_D_ZERO, MAGMA_D_ZERO, dR, lddr, queue );
magmablas_dlaset_q( MagmaFull, lddt, nb*batchCount, MAGMA_D_ZERO, MAGMA_D_ZERO, dT, lddt, queue );
}
*/
magma_int_t streamid;
const magma_int_t nbstreams=10;
magma_queue_t queues[nbstreams];
for (i=0; i < nbstreams; i++) {
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queues[i] );
}
magma_getvector( batchCount, sizeof(double*), dA_array, 1, cpuAarray, 1, queue);
magma_getvector( batchCount, sizeof(double*), dT_array, 1, cpuTarray, 1, queue);
for (i=0; i < min_mn; i += nb)
{
ib = min(nb, min_mn-i);
//===============================================
// panel factorization
//===============================================
magma_ddisplace_pointers(dW0_displ, dA_array, ldda, i, i, batchCount, queue);
magma_ddisplace_pointers(dW2_displ, dtau_array, 1, i, 0, batchCount, queue);
if ( provide_RT > 0 )
{
offset_RT = i;
magma_ddisplace_pointers(dR_displ, dR_array, lddr, (provide_RT == 1 ? offset_RT:0), offset_RT, batchCount, queue);
magma_ddisplace_pointers(dT_displ, dT_array, lddt, 0, offset_RT, batchCount, queue);
}
//dwork is used in panel factorization and trailing matrix update
//dW4_displ, dW5_displ are used as workspace and configured inside
magma_dgeqrf_panel_batched(m-i, ib, jb,
dW0_displ, ldda,
dW2_displ,
dT_displ, lddt,
dR_displ, lddr,
dW1_displ,
dW3_displ,
dwork,
dW4_displ, dW5_displ,
info_array,
batchCount, queue);
//===============================================
// end of panel
//===============================================
//===============================================
// update trailing matrix
//===============================================
if ( (n-ib-i) > 0)
{
//dwork is used in panel factorization and trailing matrix update
//reset dW4_displ
ldw = nb;
magma_dset_pointer( dW4_displ, dwork, 1, 0, 0, ldw*n, batchCount, queue );
offset = ldw*n*batchCount;
magma_dset_pointer( dW5_displ, dwork + offset, 1, 0, 0, ldw*n, batchCount, queue );
// set the diagonal of v as one and the upper triangular part as zero already set inside geqrf_panel
//magmablas_dlaset_batched( MagmaUpper, ib, ib, MAGMA_D_ZERO, MAGMA_D_ONE, dW0_displ, ldda, batchCount, queue );
//magma_ddisplace_pointers(dW2_displ, dtau_array, 1, i, 0, batchCount, queue);
// it is faster since it is using BLAS-3 GEMM routines, different from lapack implementation
magma_dlarft_batched(m-i, ib, 0,
dW0_displ, ldda,
dW2_displ,
dT_displ, lddt,
dW4_displ, nb*lddt,
batchCount, queue);
// perform C = (I-V T^H V^H) * C, C is the trailing matrix
//-------------------------------------------
// USE STREAM GEMM
//-------------------------------------------
use_stream = magma_drecommend_cublas_gemm_stream(MagmaNoTrans, MagmaNoTrans, m-i-ib, n-i-ib, ib);
if ( use_stream )
{
magma_queue_sync(queue);
for (k=0; k < batchCount; k++)
{
streamid = k%nbstreams;
// the queue gemm must take cpu pointer
magma_dlarfb_gpu_gemm( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
m-i, n-i-ib, ib,
cpuAarray[k] + i + i * ldda, ldda,
cpuTarray[k] + offset_RT*lddt, lddt,
cpuAarray[k] + i + (i+ib) * ldda, ldda,
dwork + nb * n * k, -1,
dwork + nb * n * batchCount + nb * n * k, -1, queues[streamid] );
}
// need to synchronise to be sure that panel does not start before
// finishing the update at least of the next panel
// if queue is NULL, no need to sync
if ( queue != NULL ) {
for (magma_int_t s=0; s < nbstreams; s++)
magma_queue_sync(queues[s]);
}
}
//-------------------------------------------
// USE BATCHED GEMM
//-------------------------------------------
else
{
//direct trailing matrix in dW1_displ
magma_ddisplace_pointers(dW1_displ, dA_array, ldda, i, i+ib, batchCount, queue);
magma_dlarfb_gemm_batched(
MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
m-i, n-i-ib, ib,
(const double**)dW0_displ, ldda,
(const double**)dT_displ, lddt,
dW1_displ, ldda,
dW4_displ, ldw,
dW5_displ, ldw,
batchCount, queue );
}
}// update the trailing matrix
//===============================================
// copy dR back to V after the trailing matrix update,
// only when provide_RT=0 otherwise the nbxnb block of V is set to diag=1/0
// The upper portion of V could be set totaly to 0 here
if ( provide_RT == 0 )
{
magmablas_dlacpy_batched( MagmaUpper, ib, ib, dR_displ, lddr, dW0_displ, ldda, batchCount, queue );
}
}
magma_queue_sync(queue);
for (k=0; k < nbstreams; k++) {
magma_queue_destroy( queues[k] );
}
magma_free(dW0_displ);
magma_free(dW1_displ);
magma_free(dW2_displ);
magma_free(dW3_displ);
magma_free(dW4_displ);
magma_free(dW5_displ);
magma_free(dR_displ);
magma_free(dT_displ);
magma_free(dwork);
magma_free_cpu(cpuAarray);
magma_free_cpu(cpuTarray);
return arginfo;
}
extern "C" magma_int_t
magma_dgehrd2(magma_int_t n, magma_int_t ilo, magma_int_t ihi,
double *a, magma_int_t lda,
double *tau, double *work,
magma_int_t lwork, magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
DGEHRD2 reduces a DOUBLE_PRECISION 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 DGEBAL; 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) DOUBLE_PRECISION 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) DOUBLE_PRECISION 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) DOUBLE_PRECISION 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 real scalar, and v is a real 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.
===================================================================== */
double c_one = MAGMA_D_ONE;
double c_zero = MAGMA_D_ZERO;
magma_int_t nb = magma_get_dgehrd_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_D_SET2REAL( work[0], (double) 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;
}
double *da;
if (MAGMA_SUCCESS != magma_dmalloc( &da, N*ldda + 2*N*nb + nb*nb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
double *d_A = da;
double *d_work = da + (N+nb)*ldda;
magma_int_t i__;
double *t, *d_t;
magma_dmalloc_cpu( &t, nb*nb );
if ( t == NULL ) {
magma_free( da );
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
d_t = d_work + nb * ldda;
dzero_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_dsetmatrix( 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_dgetmatrix( ihi-i__+1, ib,
d_A + (i__ - ilo)*ldda + i__ - 1, ldda,
a + (i__ - 1 )*lda + i__ - 1, lda );
magma_dlahr2(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_dsetmatrix( nb, nb, t, nb, d_t, nb );
magma_dlahru(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_dgetmatrix( n, n-i__+1,
d_A+ (i__-ilo)*ldda, ldda,
a + (i__-1)*(lda), lda );
}
lapackf77_dgehd2(&n, &i__, &ihi, a, &lda, &tau[1], work, &iinfo);
MAGMA_D_SET2REAL( work[0], (double) iws );
magma_free( da );
magma_free_cpu(t);
return *info;
} /* magma_dgehrd2 */
/**
Purpose
-------
DGEQLF computes a QL factorization of a DOUBLE_PRECISION M-by-N matrix A:
A = Q * L.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. N >= 0.
@param[in,out]
A DOUBLE_PRECISION array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, if m >= n, the lower triangle of the subarray
A(m-n+1:m,1:n) contains the N-by-N lower triangular matrix L;
if m <= n, the elements on and below the (n-m)-th
superdiagonal contain the M-by-N lower trapezoidal matrix L;
the remaining elements, with the array TAU, represent the
orthogonal matrix Q as a product of elementary reflectors
(see Further Details).
\n
Higher performance is achieved if A is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,M).
@param[out]
tau DOUBLE_PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
@param[out]
work (workspace) DOUBLE_PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
\n
Higher performance is achieved if WORK is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lwork INTEGER
The dimension of the array WORK. LWORK >= max(1,N,2*NB^2).
For optimum performance LWORK >= max(N*NB, 2*NB^2) where NB can be obtained
through magma_get_dgeqlf_nb(M).
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
Further Details
---------------
The matrix Q is represented as a product of elementary reflectors
Q = H(k) . . . H(2) H(1), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
A(1:m-k+i-1,n-k+i), and tau in TAU(i).
@ingroup magma_dgeqlf_comp
********************************************************************/
extern "C" magma_int_t
magma_dgeqlf(
magma_int_t m, magma_int_t n,
double *A, magma_int_t lda, double *tau,
double *work, magma_int_t lwork,
magma_int_t *info)
{
#define A(i_,j_) ( A + (i_) + (j_)*lda)
#define dA(i_,j_) (dA + (i_) + (j_)*ldda)
#define dwork(i_) (dwork + (i_))
magmaDouble_ptr dA, dwork;
double c_one = MAGMA_D_ONE;
magma_int_t i, k, lddwork, old_i, old_ib, nb;
magma_int_t rows, cols;
magma_int_t ib, ki, kk, mu, nu, iinfo, ldda;
int lquery;
nb = magma_get_dgeqlf_nb(m);
*info = 0;
lquery = (lwork == -1);
// silence "uninitialized" warnings
old_ib = nb;
old_i = 0;
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,m)) {
*info = -4;
}
k = min(m,n);
if (*info == 0) {
if (k == 0)
work[0] = c_one;
else {
work[0] = MAGMA_D_MAKE( max(n*nb, 2*nb*nb), 0 );
}
if (lwork < max(max(1,n), 2*nb*nb) && ! lquery)
*info = -7;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
/* Quick return if possible */
if (k == 0)
return *info;
lddwork = ((n+31)/32)*32;
ldda = ((m+31)/32)*32;
if (MAGMA_SUCCESS != magma_dmalloc( &dA, (n)*ldda + nb*lddwork )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
dwork = dA + ldda*n;
magma_queue_t queues[2];
magma_queue_create( &queues[0] );
magma_queue_create( &queues[1] );
if ( (nb > 1) && (nb < k) ) {
/* Use blocked code initially.
The last kk columns are handled by the block method.
First, copy the matrix on the GPU except the last kk columns */
magma_dsetmatrix_async( m, n-nb,
A(0, 0), lda,
dA(0, 0), ldda, queues[0] );
ki = ((k - nb - 1) / nb) * nb;
kk = min(k, ki + nb);
for (i = k - kk + ki; i >= k -kk; i -= nb) {
ib = min(k-i,nb);
if (i < k - kk + ki) {
/* 1. Copy asynchronously the current panel to the CPU.
2. Copy asynchronously the submatrix below the panel
to the CPU) */
rows = m - k + i + ib;
magma_dgetmatrix_async( rows, ib,
dA(0, n-k+i), ldda,
A(0, n-k+i), lda, queues[1] );
magma_dgetmatrix_async( m-rows, ib,
dA(rows, n-k+i), ldda,
A(rows, n-k+i), lda, queues[0] );
/* Apply H' to A(1:m-k+i+ib-1,1:n-k+i-1) from the left in
two steps - implementing the lookahead techniques.
This is the main update from the lookahead techniques. */
rows = m - k + old_i + old_ib;
cols = n - k + old_i - old_ib;
magma_dlarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaBackward, MagmaColumnwise,
rows, cols, old_ib,
dA(0, cols+old_ib), ldda, dwork(0), lddwork,
dA(0, 0 ), ldda, dwork(old_ib), lddwork);
}
magma_queue_sync( queues[1] );
/* Compute the QL factorization of the current block
A(1:m-k+i+ib-1,n-k+i:n-k+i+ib-1) */
rows = m - k + i + ib;
cols = n - k + i;
lapackf77_dgeqlf( &rows, &ib, A(0,cols), &lda, tau+i, work, &lwork, &iinfo );
if (cols > 0) {
/* Form the triangular factor of the block reflector
H = H(i+ib-1) . . . H(i+1) H(i) */
lapackf77_dlarft( MagmaBackwardStr, MagmaColumnwiseStr,
&rows, &ib,
A(0, cols), &lda, tau + i, work, &ib);
dpanel_to_q( MagmaLower, ib, A(rows-ib,cols), lda, work+ib*ib);
magma_dsetmatrix( rows, ib,
A(0,cols), lda,
dA(0,cols), ldda );
dq_to_panel( MagmaLower, ib, A(rows-ib,cols), lda, work+ib*ib);
// Send the triangular part on the GPU
magma_dsetmatrix( ib, ib, work, ib, dwork(0), lddwork );
/* Apply H' to A(1:m-k+i+ib-1,1:n-k+i-1) from the left in
two steps - implementing the lookahead techniques.
This is the update of first ib columns. */
if (i-ib >= k -kk)
magma_dlarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaBackward, MagmaColumnwise,
rows, ib, ib,
dA(0, cols), ldda, dwork(0), lddwork,
dA(0,cols-ib), ldda, dwork(ib), lddwork);
else {
magma_dlarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaBackward, MagmaColumnwise,
rows, cols, ib,
dA(0, cols), ldda, dwork(0), lddwork,
dA(0, 0 ), ldda, dwork(ib), lddwork);
}
old_i = i;
old_ib = ib;
}
}
mu = m - k + i + nb;
nu = n - k + i + nb;
magma_dgetmatrix( m, nu, dA(0,0), ldda, A(0,0), lda );
} else {
mu = m;
nu = n;
}
/* Use unblocked code to factor the last or only block */
if (mu > 0 && nu > 0)
lapackf77_dgeqlf(&mu, &nu, A(0,0), &lda, tau, work, &lwork, &iinfo);
magma_queue_destroy( queues[0] );
magma_queue_destroy( queues[1] );
magma_free( dA );
return *info;
} /* magma_dgeqlf */
extern "C" magma_int_t
magma_dlobpcg( magma_d_sparse_matrix A, magma_d_solver_par *solver_par ){
#define residualNorms(i,iter) ( residualNorms + (i) + (iter)*n )
#define magmablas_swap(x, y) { pointer = x; x = y; y = pointer; }
#define hresidualNorms(i,iter) (hresidualNorms + (i) + (iter)*n )
#define gramA( m, n) (gramA + (m) + (n)*ldgram)
#define gramB( m, n) (gramB + (m) + (n)*ldgram)
#define gevectors(m, n) (gevectors + (m) + (n)*ldgram)
#define h_gramB( m, n) (h_gramB + (m) + (n)*ldgram)
#define magma_d_bspmv_tuned(m, n, alpha, A, X, beta, AX) { \
magmablas_dtranspose( m, n, X, m, blockW, n ); \
magma_d_vector x, ax; \
x.memory_location = Magma_DEV; x.num_rows = m*n; x.nnz = m*n; x.val = blockW; \
ax.memory_location= Magma_DEV; ax.num_rows = m*n; ax.nnz = m*n; ax.val = AX; \
magma_d_spmv(alpha, A, x, beta, ax ); \
magmablas_dtranspose( n, m, blockW, n, X, m ); \
}
//**************************************************************
// Memory allocation for the eigenvectors, eigenvalues, and workspace
solver_par->solver = Magma_LOBPCG;
magma_int_t m = A.num_rows;
magma_int_t n =(solver_par->num_eigenvalues);
double *blockX = solver_par->eigenvectors;
double *evalues = solver_par->eigenvalues;
double *dwork, *hwork;
double *blockP, *blockAP, *blockR, *blockAR, *blockAX, *blockW;
double *gramA, *gramB, *gramM;
double *gevectors, *h_gramB;
double *pointer, *origX = blockX;
double *eval_gpu;
magma_int_t lwork = max( 2*n+n*magma_get_dsytrd_nb(n),
1 + 6*3*n + 2* 3*n* 3*n);
magma_dmalloc_pinned( &hwork , lwork );
magma_dmalloc( &blockAX , m*n );
magma_dmalloc( &blockAR , m*n );
magma_dmalloc( &blockAP , m*n );
magma_dmalloc( &blockR , m*n );
magma_dmalloc( &blockP , m*n );
magma_dmalloc( &blockW , m*n );
magma_dmalloc( &dwork , m*n );
magma_dmalloc( &eval_gpu , 3*n );
//**********************************************************+
magma_int_t verbosity = 1;
magma_int_t *iwork, liwork = 15*n+9;
// === Set solver parameters ===
double residualTolerance = solver_par->epsilon;
magma_int_t maxIterations = solver_par->maxiter;
// === Set some constants & defaults ===
double c_one = MAGMA_D_ONE, c_zero = MAGMA_D_ZERO;
double *residualNorms, *condestGhistory, condestG;
double *gevalues;
magma_int_t *activeMask;
// === Check some parameters for possible quick exit ===
solver_par->info = 0;
if (m < 2)
solver_par->info = -1;
else if (n > m)
solver_par->info = -2;
if (solver_par->info != 0) {
magma_xerbla( __func__, -(solver_par->info) );
return solver_par->info;
}
magma_int_t *info = &(solver_par->info); // local info variable;
// === Allocate GPU memory for the residual norms' history ===
magma_dmalloc(&residualNorms, (maxIterations+1) * n);
magma_malloc( (void **)&activeMask, (n+1) * sizeof(magma_int_t) );
// === Allocate CPU work space ===
magma_dmalloc_cpu(&condestGhistory, maxIterations+1);
magma_dmalloc_cpu(&gevalues, 3 * n);
magma_malloc_cpu((void **)&iwork, liwork * sizeof(magma_int_t));
double *hW;
magma_dmalloc_pinned(&hW, n*n);
magma_dmalloc_pinned(&gevectors, 9*n*n);
magma_dmalloc_pinned(&h_gramB , 9*n*n);
// === Allocate GPU workspace ===
magma_dmalloc(&gramM, n * n);
magma_dmalloc(&gramA, 9 * n * n);
magma_dmalloc(&gramB, 9 * n * n);
#if defined(PRECISION_z) || defined(PRECISION_c)
double *rwork;
magma_int_t lrwork = 1 + 5*(3*n) + 2*(3*n)*(3*n);
magma_dmalloc_cpu(&rwork, lrwork);
#endif
// === Set activemask to one ===
for(int k =0; k<n; k++)
iwork[k]=1;
magma_setmatrix(n, 1, sizeof(magma_int_t), iwork, n ,activeMask, n);
magma_int_t gramDim, ldgram = 3*n, ikind = 4;
// === Make the initial vectors orthonormal ===
magma_dgegqr_gpu(ikind, m, n, blockX, m, dwork, hwork, info );
//magma_dorthomgs( m, n, blockX );
magma_d_bspmv_tuned(m, n, c_one, A, blockX, c_zero, blockAX );
// === Compute the Gram matrix = (X, AX) & its eigenstates ===
magma_dgemm(MagmaConjTrans, MagmaNoTrans, n, n, m,
c_one, blockX, m, blockAX, m, c_zero, gramM, n);
magma_dsyevd_gpu( MagmaVec, MagmaUpper,
n, gramM, n, evalues, hW, n, hwork, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork, info );
// === Update X = X * evectors ===
magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, n, n,
c_one, blockX, m, gramM, n, c_zero, blockW, m);
magmablas_swap(blockW, blockX);
// === Update AX = AX * evectors ===
magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, n, n,
c_one, blockAX, m, gramM, n, c_zero, blockW, m);
magmablas_swap(blockW, blockAX);
condestGhistory[1] = 7.82;
magma_int_t iterationNumber, cBlockSize, restart = 1, iter;
//Chronometry
real_Double_t tempo1, tempo2;
magma_device_sync(); tempo1=magma_wtime();
// === Main LOBPCG loop ============================================================
for(iterationNumber = 1; iterationNumber < maxIterations; iterationNumber++)
{
// === compute the residuals (R = Ax - x evalues )
magmablas_dlacpy( MagmaUpperLower, m, n, blockAX, m, blockR, m);
/*
for(int i=0; i<n; i++){
magma_daxpy(m, MAGMA_D_MAKE(-evalues[i],0), blockX+i*m, 1, blockR+i*m, 1);
}
*/
#if defined(PRECISION_z) || defined(PRECISION_d)
magma_dsetmatrix( 3*n, 1, evalues, 3*n, eval_gpu, 3*n );
#else
magma_ssetmatrix( 3*n, 1, evalues, 3*n, eval_gpu, 3*n );
#endif
magma_dlobpcg_res( m, n, eval_gpu, blockX, blockR, eval_gpu);
magmablas_dnrm2_cols(m, n, blockR, m, residualNorms(0, iterationNumber));
// === remove the residuals corresponding to already converged evectors
magma_dcompact(m, n, blockR, m,
residualNorms(0, iterationNumber), residualTolerance,
activeMask, &cBlockSize);
if (cBlockSize == 0)
break;
// === apply a preconditioner P to the active residulas: R_new = P R_old
// === for now set P to be identity (no preconditioner => nothing to be done )
// magmablas_dlacpy( MagmaUpperLower, m, cBlockSize, blockR, m, blockW, m);
/*
// === make the preconditioned residuals orthogonal to X
magma_dgemm(MagmaConjTrans, MagmaNoTrans, n, cBlockSize, m,
c_one, blockX, m, blockR, m, c_zero, gramB(0,0), ldgram);
magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, cBlockSize, n,
c_mone, blockX, m, gramB(0,0), ldgram, c_one, blockR, m);
*/
// === make the active preconditioned residuals orthonormal
magma_dgegqr_gpu(ikind, m, cBlockSize, blockR, m, dwork, hwork, info );
//magma_dorthomgs( m, cBlockSize, blockR );
// === compute AR
magma_d_bspmv_tuned(m, cBlockSize, c_one, A, blockR, c_zero, blockAR );
if (!restart) {
// === compact P & AP as well
magma_dcompactActive(m, n, blockP, m, activeMask);
magma_dcompactActive(m, n, blockAP, m, activeMask);
/*
// === make P orthogonal to X ?
magma_dgemm(MagmaConjTrans, MagmaNoTrans, n, cBlockSize, m,
c_one, blockX, m, blockP, m, c_zero, gramB(0,0), ldgram);
magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, cBlockSize, n,
c_mone, blockX, m, gramB(0,0), ldgram, c_one, blockP, m);
// === make P orthogonal to R ?
magma_dgemm(MagmaConjTrans, MagmaNoTrans, cBlockSize, cBlockSize, m,
c_one, blockR, m, blockP, m, c_zero, gramB(0,0), ldgram);
magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, cBlockSize, cBlockSize,
c_mone, blockR, m, gramB(0,0), ldgram, c_one, blockP, m);
*/
// === Make P orthonormal & properly change AP (without multiplication by A)
magma_dgegqr_gpu(ikind, m, cBlockSize, blockP, m, dwork, hwork, info );
//magma_dorthomgs( m, cBlockSize, blockP );
//magma_d_bspmv_tuned(m, cBlockSize, c_one, A, blockP, c_zero, blockAP );
magma_dsetmatrix( cBlockSize, cBlockSize, hwork, cBlockSize, dwork, cBlockSize);
// magma_dtrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaNonUnit,
// m, cBlockSize, c_one, dwork, cBlockSize, blockAP, m);
// replacement according to Stan
#if defined(PRECISION_s) || defined(PRECISION_d)
magmablas_dtrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaNonUnit,
m, cBlockSize, c_one, dwork, cBlockSize, blockAP, m);
#else
magma_dtrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaNonUnit, m,
cBlockSize, c_one, dwork, cBlockSize, blockAP, m);
#endif
}
iter = max(1,iterationNumber-10- (int)(log(1.*cBlockSize)));
double condestGmean = 0.;
for(int i = 0; i<iterationNumber-iter+1; i++)
condestGmean += condestGhistory[i];
condestGmean = condestGmean / (iterationNumber-iter+1);
if (restart)
gramDim = n+cBlockSize;
else
gramDim = n+2*cBlockSize;
/* --- The Raileight-Ritz method for [X R P] -----------------------
[ X R P ]' [AX AR AP] y = evalues [ X R P ]' [ X R P ], i.e.,
GramA GramB
/ X'AX X'AR X'AP \ / X'X X'R X'P \
| R'AX R'AR R'AP | y = evalues | R'X R'R R'P |
\ P'AX P'AR P'AP / \ P'X P'R P'P /
----------------------------------------------------------------- */
// === assemble GramB; first, set it to I
magmablas_dlaset(MagmaFull, ldgram, ldgram, c_zero, c_one, gramB, ldgram); // identity
if (!restart) {
magma_dgemm(MagmaConjTrans, MagmaNoTrans, cBlockSize, n, m,
c_one, blockP, m, blockX, m, c_zero, gramB(n+cBlockSize,0), ldgram);
magma_dgemm(MagmaConjTrans, MagmaNoTrans, cBlockSize, cBlockSize, m,
c_one, blockP, m, blockR, m, c_zero, gramB(n+cBlockSize,n), ldgram);
}
magma_dgemm(MagmaConjTrans, MagmaNoTrans, cBlockSize, n, m,
c_one, blockR, m, blockX, m, c_zero, gramB(n,0), ldgram);
// === get GramB from the GPU to the CPU and compute its eigenvalues only
magma_dgetmatrix(gramDim, gramDim, gramB, ldgram, h_gramB, ldgram);
lapackf77_dsyev("N", "L", &gramDim, h_gramB, &ldgram, gevalues,
hwork, &lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork,
#endif
info);
// === check stability criteria if we need to restart
condestG = log10( gevalues[gramDim-1]/gevalues[0] ) + 1.;
if ((condestG/condestGmean>2 && condestG>2) || condestG>8) {
// Steepest descent restart for stability
restart=1;
printf("restart at step #%d\n", (int) iterationNumber);
}
// === assemble GramA; first, set it to I
magmablas_dlaset(MagmaFull, ldgram, ldgram, c_zero, c_one, gramA, ldgram); // identity
magma_dgemm(MagmaConjTrans, MagmaNoTrans, cBlockSize, n, m,
c_one, blockR, m, blockAX, m, c_zero, gramA(n,0), ldgram);
magma_dgemm(MagmaConjTrans, MagmaNoTrans, cBlockSize, cBlockSize, m,
c_one, blockR, m, blockAR, m, c_zero, gramA(n,n), ldgram);
if (!restart) {
magma_dgemm(MagmaConjTrans, MagmaNoTrans, cBlockSize, n, m,
c_one, blockP, m, blockAX, m, c_zero,
gramA(n+cBlockSize,0), ldgram);
magma_dgemm(MagmaConjTrans, MagmaNoTrans, cBlockSize, cBlockSize, m,
c_one, blockP, m, blockAR, m, c_zero,
gramA(n+cBlockSize,n), ldgram);
magma_dgemm(MagmaConjTrans, MagmaNoTrans, cBlockSize, cBlockSize, m,
c_one, blockP, m, blockAP, m, c_zero,
gramA(n+cBlockSize,n+cBlockSize), ldgram);
}
/*
// === Compute X' AX or just use the eigenvalues below ?
magma_dgemm(MagmaConjTrans, MagmaNoTrans, n, n, m,
c_one, blockX, m, blockAX, m, c_zero,
gramA(0,0), ldgram);
*/
if (restart==0) {
magma_dgetmatrix(gramDim, gramDim, gramA, ldgram, gevectors, ldgram);
}
else {
gramDim = n+cBlockSize;
magma_dgetmatrix(gramDim, gramDim, gramA, ldgram, gevectors, ldgram);
}
for(int k=0; k<n; k++)
*gevectors(k,k) = MAGMA_D_MAKE(evalues[k], 0);
// === the previous eigensolver destroyed what is in h_gramB => must copy it again
magma_dgetmatrix(gramDim, gramDim, gramB, ldgram, h_gramB, ldgram);
magma_int_t itype = 1;
lapackf77_dsygvd(&itype, "V", "L", &gramDim,
gevectors, &ldgram, h_gramB, &ldgram,
gevalues, hwork, &lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, &lrwork,
#endif
iwork, &liwork, info);
for(int k =0; k<n; k++)
evalues[k] = gevalues[k];
// === copy back the result to gramA on the GPU and use it for the updates
magma_dsetmatrix(gramDim, gramDim, gevectors, ldgram, gramA, ldgram);
if (restart == 0) {
// === contribution from P to the new X (in new search direction P)
magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize,
c_one, blockP, m, gramA(n+cBlockSize,0), ldgram, c_zero, dwork, m);
magmablas_swap(dwork, blockP);
// === contribution from R to the new X (in new search direction P)
magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize,
c_one, blockR, m, gramA(n,0), ldgram, c_one, blockP, m);
// === corresponding contribution from AP to the new AX (in AP)
magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize,
c_one, blockAP, m, gramA(n+cBlockSize,0), ldgram, c_zero, dwork, m);
magmablas_swap(dwork, blockAP);
// === corresponding contribution from AR to the new AX (in AP)
magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize,
c_one, blockAR, m, gramA(n,0), ldgram, c_one, blockAP, m);
}
else {
// === contribution from R (only) to the new X
magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize,
c_one, blockR, m, gramA(n,0), ldgram, c_zero, blockP, m);
// === corresponding contribution from AR (only) to the new AX
magma_dgemm(MagmaNoTrans, MagmaNoTrans,m, n, cBlockSize,
c_one, blockAR, m, gramA(n,0), ldgram, c_zero, blockAP, m);
}
// === contribution from old X to the new X + the new search direction P
magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, n, n,
c_one, blockX, m, gramA, ldgram, c_zero, dwork, m);
magmablas_swap(dwork, blockX);
//magma_daxpy(m*n, c_one, blockP, 1, blockX, 1);
magma_dlobpcg_maxpy( m, n, blockP, blockX );
// === corresponding contribution from old AX to new AX + AP
magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, n, n,
c_one, blockAX, m, gramA, ldgram, c_zero, dwork, m);
magmablas_swap(dwork, blockAX);
//magma_daxpy(m*n, c_one, blockAP, 1, blockAX, 1);
magma_dlobpcg_maxpy( m, n, blockAP, blockAX );
condestGhistory[iterationNumber+1]=condestG;
if (verbosity==1) {
// double res;
// magma_dgetmatrix(1, 1,
// (double*)residualNorms(0, iterationNumber), 1,
// (double*)&res, 1);
//
// printf("Iteration %4d, CBS %4d, Residual: %10.7f\n",
// iterationNumber, cBlockSize, res);
printf("%4d-%2d ", (int) iterationNumber, (int) cBlockSize);
magma_dprint_gpu(1, n, residualNorms(0, iterationNumber), 1);
}
restart = 0;
} // === end for iterationNumber = 1,maxIterations =======================
// fill solver info
magma_device_sync(); tempo2=magma_wtime();
solver_par->runtime = (real_Double_t) tempo2-tempo1;
solver_par->numiter = iterationNumber;
if( solver_par->numiter < solver_par->maxiter){
solver_par->info = 0;
}else if( solver_par->init_res > solver_par->final_res )
solver_par->info = -2;
else
solver_par->info = -1;
// =============================================================================
// === postprocessing;
// =============================================================================
// === compute the real AX and corresponding eigenvalues
magma_d_bspmv_tuned(m, n, c_one, A, blockX, c_zero, blockAX );
magma_dgemm(MagmaConjTrans, MagmaNoTrans, n, n, m,
c_one, blockX, m, blockAX, m, c_zero, gramM, n);
magma_dsyevd_gpu( MagmaVec, MagmaUpper,
n, gramM, n, gevalues, dwork, n, hwork, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork, info );
for(int k =0; k<n; k++)
evalues[k] = gevalues[k];
// === update X = X * evectors
magmablas_swap(blockX, dwork);
magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, n, n,
c_one, dwork, m, gramM, n, c_zero, blockX, m);
// === update AX = AX * evectors to compute the final residual
magmablas_swap(blockAX, dwork);
magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, n, n,
c_one, dwork, m, gramM, n, c_zero, blockAX, m);
// === compute R = AX - evalues X
magmablas_dlacpy( MagmaUpperLower, m, n, blockAX, m, blockR, m);
for(int i=0; i<n; i++)
magma_daxpy(m, MAGMA_D_MAKE(-evalues[i], 0), blockX+i*m, 1, blockR+i*m, 1);
// === residualNorms[iterationNumber] = || R ||
magmablas_dnrm2_cols(m, n, blockR, m, residualNorms(0, iterationNumber));
// === restore blockX if needed
if (blockX != origX)
magmablas_dlacpy( MagmaUpperLower, m, n, blockX, m, origX, m);
printf("Eigenvalues:\n");
for(int i =0; i<n; i++)
printf("%e ", evalues[i]);
printf("\n\n");
printf("Final residuals:\n");
magma_dprint_gpu(1, n, residualNorms(0, iterationNumber), 1);
printf("\n\n");
//=== Print residual history in a file for plotting ====
double *hresidualNorms;
magma_dmalloc_cpu(&hresidualNorms, (iterationNumber+1) * n);
magma_dgetmatrix(n, iterationNumber,
(double*)residualNorms, n,
(double*)hresidualNorms, n);
printf("Residuals are stored in file residualNorms\n");
printf("Plot the residuals using: myplot \n");
FILE *residuals_file;
residuals_file = fopen("residualNorms", "w");
for(int i =1; i<iterationNumber; i++) {
for(int j = 0; j<n; j++)
fprintf(residuals_file, "%f ", *hresidualNorms(j,i));
fprintf(residuals_file, "\n");
}
fclose(residuals_file);
magma_free_cpu(hresidualNorms);
// === free work space
magma_free( residualNorms );
magma_free_cpu( condestGhistory );
magma_free_cpu( gevalues );
magma_free_cpu( iwork );
magma_free_pinned( hW );
magma_free_pinned( gevectors );
magma_free_pinned( h_gramB );
magma_free( gramM );
magma_free( gramA );
magma_free( gramB );
magma_free( activeMask );
magma_free( blockAX );
magma_free( blockAR );
magma_free( blockAP );
magma_free( blockR );
magma_free( blockP );
magma_free( blockW );
magma_free( dwork );
magma_free( eval_gpu );
magma_free_pinned( hwork );
#if defined(PRECISION_z) || defined(PRECISION_c)
magma_free_cpu( rwork );
#endif
return MAGMA_SUCCESS;
}
extern "C" magma_int_t
magma_zheevx_gpu(char jobz, char range, char uplo, magma_int_t n,
magmaDoubleComplex *da, magma_int_t ldda, double vl, double vu,
magma_int_t il, magma_int_t iu, double abstol, magma_int_t *m,
double *w, magmaDoubleComplex *dz, magma_int_t lddz,
magmaDoubleComplex *wa, magma_int_t ldwa,
magmaDoubleComplex *wz, magma_int_t ldwz,
magmaDoubleComplex *work, magma_int_t lwork,
double *rwork, magma_int_t *iwork, magma_int_t *ifail, magma_int_t *info)
{
/* -- MAGMA (version 1.4.1) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
December 2013
Purpose
=======
ZHEEVX computes selected eigenvalues and, optionally, eigenvectors
of a complex Hermitian matrix A. Eigenvalues and eigenvectors can
be selected by specifying either a range of values or a range of
indices for the desired eigenvalues.
Arguments
=========
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
RANGE (input) CHARACTER*1
= 'A': all eigenvalues will be found.
= 'V': all eigenvalues in the half-open interval (VL,VU]
will be found.
= 'I': the IL-th through IU-th eigenvalues will be found.
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_16 array, dimension (LDDA, 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. If UPLO = 'L',
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
On exit, the lower triangle (if UPLO='L') or the upper
triangle (if UPLO='U') of A, including the diagonal, is
destroyed.
LDDA (input) INTEGER
The leading dimension of the array DA. LDDA >= max(1,N).
VL (input) DOUBLE PRECISION
VU (input) DOUBLE PRECISION
If RANGE='V', the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = 'A' or 'I'.
IL (input) INTEGER
IU (input) INTEGER
If RANGE='I', 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 = 'A' or 'V'.
ABSTOL (input) DOUBLE PRECISION
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
ABSTOL + EPS * max( |a|,|b| ) ,
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.
Eigenvalues will be computed most accurately when ABSTOL is
set to twice the underflow threshold 2*DLAMCH('S'), not zero.
If this routine returns with INFO>0, indicating that some
eigenvectors did not converge, try setting ABSTOL to
2*DLAMCH('S').
See "Computing Small Singular Values of Bidiagonal Matrices
with Guaranteed High Relative Accuracy," by Demmel and
Kahan, LAPACK Working Note #3.
M (output) INTEGER
The total number of eigenvalues found. 0 <= M <= N.
If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
W (output) DOUBLE PRECISION array, dimension (N)
On normal exit, the first M elements contain the selected
eigenvalues in ascending order.
DZ (device output) COMPLEX_16 array, dimension (LDDZ, max(1,M))
If JOBZ = 'V', 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).
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.
If JOBZ = 'N', then Z is not referenced.
Note: the user must ensure that at least max(1,M) columns are
supplied in the array Z; if RANGE = 'V', the exact value of M
is not known in advance and an upper bound must be used.
********* (workspace) If FAST_HEMV is defined DZ should be (LDDZ, max(1,N)) in both cases.
LDDZ (input) INTEGER
The leading dimension of the array DZ. LDDZ >= 1, and if
JOBZ = 'V', LDDZ >= max(1,N).
WA (workspace) COMPLEX_16 array, dimension (LDWA, N)
LDWA (input) INTEGER
The leading dimension of the array WA. LDWA >= max(1,N).
WZ (workspace) COMPLEX_16 array, dimension (LDWZ, max(1,M))
LDWZ (input) INTEGER
The leading dimension of the array DZ. LDWZ >= 1, and if
JOBZ = 'V', LDWZ >= max(1,N).
WORK (workspace/output) COMPLEX_16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The length of the array WORK. LWORK >= (NB+1)*N,
where NB is the max of the blocksize for ZHETRD.
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.
RWORK (workspace) DOUBLE PRECISION array, dimension (7*N)
IWORK (workspace) INTEGER array, dimension (5*N)
IFAIL (output) INTEGER array, dimension (N)
If JOBZ = 'V', 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 = 'N', then IFAIL is not referenced.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, then i eigenvectors failed to converge.
Their indices are stored in array IFAIL.
===================================================================== */
char uplo_[2] = {uplo, 0};
char jobz_[2] = {jobz, 0};
char range_[2] = {range, 0};
magma_int_t ione = 1;
char order[1];
magma_int_t indd, inde;
magma_int_t imax;
magma_int_t lopt, itmp1, indee;
magma_int_t lower, wantz;
magma_int_t i, j, jj, i__1;
magma_int_t alleig, valeig, indeig;
magma_int_t iscale, indibl;
magma_int_t indiwk, indisp, indtau;
magma_int_t indrwk, indwrk;
magma_int_t llwork, nsplit;
magma_int_t lquery;
magma_int_t iinfo;
double safmin;
double bignum;
double smlnum;
double eps, tmp1;
double anrm;
double sigma, d__1;
double rmin, rmax;
double *dwork;
/* Function Body */
lower = lapackf77_lsame(uplo_, MagmaLowerStr);
wantz = lapackf77_lsame(jobz_, MagmaVecStr);
alleig = lapackf77_lsame(range_, "A");
valeig = lapackf77_lsame(range_, "V");
indeig = lapackf77_lsame(range_, "I");
lquery = lwork == -1;
*info = 0;
if (! (wantz || lapackf77_lsame(jobz_, MagmaNoVecStr))) {
*info = -1;
} else if (! (alleig || valeig || indeig)) {
*info = -2;
} else if (! (lower || lapackf77_lsame(uplo_, MagmaUpperStr))) {
*info = -3;
} else if (n < 0) {
*info = -4;
} else if (ldda < max(1,n)) {
*info = -6;
} else if (lddz < 1 || (wantz && lddz < n)) {
*info = -15;
} else if (ldwa < max(1,n)) {
*info = -17;
} else if (ldwz < 1 || (wantz && ldwz < n)) {
*info = -19;
} else {
if (valeig) {
if (n > 0 && vu <= vl) {
*info = -8;
}
} else if (indeig) {
if (il < 1 || il > max(1,n)) {
*info = -9;
} else if (iu < min(n,il) || iu > n) {
*info = -10;
}
}
}
magma_int_t nb = magma_get_zhetrd_nb(n);
lopt = n * (nb + 1);
work[0] = MAGMA_Z_MAKE( lopt, 0 );
if (lwork < lopt && ! lquery) {
*info = -21;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info));
return *info;
} else if (lquery) {
return *info;
}
*m = 0;
/* 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
magmaDoubleComplex *a = (magmaDoubleComplex *) malloc( n * n * sizeof(magmaDoubleComplex) );
magma_zgetmatrix(n, n, da, ldda, a, n);
lapackf77_zheevx(jobz_, range_, uplo_,
&n, a, &n, &vl, &vu, &il, &iu, &abstol, m,
w, wz, &ldwz, work, &lwork,
rwork, iwork, ifail, info);
magma_zsetmatrix( n, n, a, n, da, ldda);
magma_zsetmatrix( n, *m, wz, ldwz, dz, lddz);
free(a);
return *info;
}
if (MAGMA_SUCCESS != magma_dmalloc( &dwork, n )) {
fprintf (stderr, "!!!! device memory allocation error (magma_zheevx_gpu)\n");
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
--w;
--work;
--rwork;
--iwork;
--ifail;
/* Get machine constants. */
safmin = lapackf77_dlamch("Safe minimum");
eps = lapackf77_dlamch("Precision");
smlnum = safmin / eps;
bignum = 1. / smlnum;
rmin = magma_dsqrt(smlnum);
rmax = magma_dsqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = magmablas_zlanhe('M', 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) {
d__1 = 1.;
magmablas_zlascl(uplo, 0, 0, 1., sigma, n, n, da,
ldda, info);
if (abstol > 0.) {
abstol *= sigma;
}
if (valeig) {
vl *= sigma;
vu *= sigma;
}
}
/* Call ZHETRD to reduce Hermitian matrix to tridiagonal form. */
indd = 1;
inde = indd + n;
indrwk = inde + n;
indtau = 1;
indwrk = indtau + n;
llwork = lwork - indwrk + 1;
#ifdef FAST_HEMV
magma_zhetrd2_gpu(uplo, n, da, ldda, &rwork[indd], &rwork[inde],
&work[indtau], wa, ldwa, &work[indwrk], llwork, dz, lddz*n, &iinfo);
#else
magma_zhetrd_gpu (uplo, n, da, ldda, &rwork[indd], &rwork[inde],
&work[indtau], wa, ldwa, &work[indwrk], llwork, &iinfo);
#endif
lopt = n + (magma_int_t)MAGMA_Z_REAL(work[indwrk]);
/* If all eigenvalues are desired and ABSTOL is less than or equal to
zero, then call DSTERF or ZUNGTR and ZSTEQR. If this fails for
some eigenvalue, then try DSTEBZ. */
if ((alleig || (indeig && il == 1 && iu == n)) && abstol <= 0.) {
blasf77_dcopy(&n, &rwork[indd], &ione, &w[1], &ione);
indee = indrwk + 2*n;
if (! wantz) {
i__1 = n - 1;
blasf77_dcopy(&i__1, &rwork[inde], &ione, &rwork[indee], &ione);
lapackf77_dsterf(&n, &w[1], &rwork[indee], info);
}
else {
lapackf77_zlacpy("A", &n, &n, wa, &ldwa, wz, &ldwz);
lapackf77_zungtr(uplo_, &n, wz, &ldwz, &work[indtau], &work[indwrk], &llwork, &iinfo);
i__1 = n - 1;
blasf77_dcopy(&i__1, &rwork[inde], &ione, &rwork[indee], &ione);
lapackf77_zsteqr(jobz_, &n, &w[1], &rwork[indee], wz, &ldwz, &rwork[indrwk], info);
if (*info == 0) {
for (i = 1; i <= n; ++i) {
ifail[i] = 0;
}
magma_zsetmatrix( n, n, wz, ldwz, dz, lddz );
}
}
if (*info == 0) {
*m = n;
}
}
/* Otherwise, call DSTEBZ and, if eigenvectors are desired, ZSTEIN. */
if (*m == 0) {
*info = 0;
if (wantz) {
*(unsigned char *)order = 'B';
} else {
*(unsigned char *)order = 'E';
}
indibl = 1;
indisp = indibl + n;
indiwk = indisp + n;
lapackf77_dstebz(range_, order, &n, &vl, &vu, &il, &iu, &abstol, &rwork[indd], &rwork[inde], m,
&nsplit, &w[1], &iwork[indibl], &iwork[indisp], &rwork[indrwk], &iwork[indiwk], info);
if (wantz) {
lapackf77_zstein(&n, &rwork[indd], &rwork[inde], m, &w[1], &iwork[indibl], &iwork[indisp],
wz, &ldwz, &rwork[indrwk], &iwork[indiwk], &ifail[1], info);
magma_zsetmatrix( n, *m, wz, ldwz, dz, lddz );
/* Apply unitary matrix used in reduction to tridiagonal
form to eigenvectors returned by ZSTEIN. */
magma_zunmtr_gpu(MagmaLeft, uplo, MagmaNoTrans, n, *m, da, ldda, &work[indtau],
dz, lddz, wa, ldwa, &iinfo);
}
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
if (*info == 0) {
imax = *m;
} else {
imax = *info - 1;
}
d__1 = 1. / sigma;
blasf77_dscal(&imax, &d__1, &w[1], &ione);
}
/* If eigenvalues are not in order, then sort them, along with
eigenvectors. */
if (wantz) {
for (j = 1; j <= *m-1; ++j) {
i = 0;
tmp1 = w[j];
for (jj = j + 1; jj <= *m; ++jj) {
if (w[jj] < tmp1) {
i = jj;
tmp1 = w[jj];
}
}
if (i != 0) {
itmp1 = iwork[indibl + i - 1];
w[i] = w[j];
iwork[indibl + i - 1] = iwork[indibl + j - 1];
w[j] = tmp1;
iwork[indibl + j - 1] = itmp1;
magma_zswap(n, dz + (i-1)*lddz, ione, dz + (j-1)*lddz, ione);
if (*info != 0) {
itmp1 = ifail[i];
ifail[i] = ifail[j];
ifail[j] = itmp1;
}
}
}
}
/* Set WORK(1) to optimal complex workspace size. */
work[1] = MAGMA_Z_MAKE( lopt, 0 );
return *info;
} /* magma_zheevx_gpu */
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, t1, t2;
double c_neg_one = MAGMA_D_NEG_ONE;
magma_int_t ione = 1;
const char trans[] = { 'N', 'C', 'T' };
const char uplo[] = { 'L', 'U' };
const char diag[] = { 'U', 'N' };
const char side[] = { 'L', 'R' };
double *A, *B, *C, *C2, *LU;
double *dA, *dB, *dC1, *dC2;
double alpha = MAGMA_D_MAKE( 0.5, 0.1 );
double beta = MAGMA_D_MAKE( 0.7, 0.2 );
double dalpha = 0.6;
double dbeta = 0.8;
double 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_err_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 i = 0; i < opts.ntest; ++i ) {
m = opts.msize[i];
n = opts.nsize[i];
k = opts.ksize[i];
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 = maxn;
size = maxn*maxn;
err = magma_malloc_cpu( (void**) &piv, maxn*sizeof(magma_int_t) ); assert( err == 0 );
err = magma_dmalloc_pinned( &A, size ); assert( err == 0 );
err = magma_dmalloc_pinned( &B, size ); assert( err == 0 );
err = magma_dmalloc_pinned( &C, size ); assert( err == 0 );
err = magma_dmalloc_pinned( &C2, size ); assert( err == 0 );
err = magma_dmalloc_pinned( &LU, size ); assert( err == 0 );
err = magma_dmalloc( &dA, size ); assert( err == 0 );
err = magma_dmalloc( &dB, size ); assert( err == 0 );
err = magma_dmalloc( &dC1, size ); assert( err == 0 );
err = magma_dmalloc( &dC2, size ); assert( err == 0 );
// initialize matrices
size = maxn*maxn;
lapackf77_dlarnv( &ione, ISEED, &size, A );
lapackf77_dlarnv( &ione, ISEED, &size, B );
lapackf77_dlarnv( &ione, ISEED, &size, C );
printf( "========== Level 1 BLAS ==========\n" );
// ----- test DSWAP
// swap 2nd and 3rd columns of dA, then copy to C2 and compare with A
assert( n >= 4 );
magma_dsetmatrix( m, n, A, ld, dA, ld );
magma_dsetmatrix( m, n, A, ld, dB, ld );
magma_dswap( m, dA(0,1), 1, dA(0,2), 1 );
magma_dswap( m, dB(0,1), 1, dB(0,2), 1 );
// check results, storing diff between magma and cuda calls in C2
cublasDaxpy( ld*n, c_neg_one, dA, 1, dB, 1 );
magma_dgetmatrix( m, n, dB, ld, C2, ld );
error = lapackf77_dlange( "F", &m, &k, C2, &ld, work );
total_error += error;
printf( "dswap diff %.2g\n", error );
// ----- test IDAMAX
// get argmax of column of A
magma_dsetmatrix( m, k, A, ld, dA, ld );
error = 0;
for( int j = 0; j < k; ++j ) {
magma_int_t i1 = magma_idamax( m, dA(0,j), 1 );
magma_int_t i2 = cublasIdamax( m, dA(0,j), 1 );
assert( i1 == i2 );
error += abs( i1 - i2 );
}
total_error += error;
gflops = (double)m * k / 1e9;
printf( "idamax diff %.2g\n", error );
printf( "\n" );
printf( "========== Level 2 BLAS ==========\n" );
// ----- test DGEMV
// 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_dsetmatrix( m, n, A, ld, dA, ld );
magma_dsetvector( maxn, B, 1, dB, 1 );
magma_dsetvector( maxn, C, 1, dC1, 1 );
magma_dsetvector( maxn, C, 1, dC2, 1 );
t1 = magma_sync_wtime( 0 );
magma_dgemv( trans[ia], m, n, alpha, dA, ld, dB, 1, beta, dC1, 1 );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasDgemv( 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] == 'N' ? m : n);
cublasDaxpy( size, c_neg_one, dC1, 1, dC2, 1 );
magma_dgetvector( size, dC2, 1, C2, 1 );
error = lapackf77_dlange( "F", &size, &ione, C2, &ld, work );
total_error += error;
gflops = FLOPS_DGEMV( m, n ) / 1e9;
printf( "dgemv( %c ) diff %.2g, Gflop/s %6.2f, %6.2f\n",
trans[ia], error, gflops/t1, gflops/t2 );
}
printf( "\n" );
// ----- test DSYMV
// 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_dsetmatrix( m, m, A, ld, dA, ld );
magma_dsetvector( m, B, 1, dB, 1 );
magma_dsetvector( m, C, 1, dC1, 1 );
magma_dsetvector( m, C, 1, dC2, 1 );
t1 = magma_sync_wtime( 0 );
magma_dsymv( uplo[iu], m, alpha, dA, ld, dB, 1, beta, dC1, 1 );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasDsymv( 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
cublasDaxpy( m, c_neg_one, dC1, 1, dC2, 1 );
magma_dgetvector( m, dC2, 1, C2, 1 );
error = lapackf77_dlange( "F", &m, &ione, C2, &ld, work );
total_error += error;
gflops = FLOPS_DSYMV( m ) / 1e9;
printf( "dsymv( %c ) diff %.2g, Gflop/s %6.2f, %6.2f\n",
uplo[iu], error, gflops/t1, gflops/t2 );
}
printf( "\n" );
// ----- test DTRSV
// 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_dlacpy( "Full", &maxn, &maxn, A, &ld, LU, &ld );
lapackf77_dgetrf( &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_dsetmatrix( m, m, LU, ld, dA, ld );
magma_dsetvector( m, C, 1, dC1, 1 );
magma_dsetvector( m, C, 1, dC2, 1 );
t1 = magma_sync_wtime( 0 );
magma_dtrsv( uplo[iu], trans[it], diag[id], m, dA, ld, dC1, 1 );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasDtrsv( uplo[iu], trans[it], diag[id], m, dA, ld, dC2, 1 );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasDaxpy( m, c_neg_one, dC1, 1, dC2, 1 );
magma_dgetvector( m, dC2, 1, C2, 1 );
error = lapackf77_dlange( "F", &m, &ione, C2, &ld, work );
total_error += error;
gflops = FLOPS_DTRSM( MagmaLeft, m, 1 ) / 1e9;
printf( "dtrsv( %c, %c, %c ) diff %.2g, Gflop/s %6.2f, %6.2f\n",
uplo[iu], trans[it], diag[id], error, gflops/t1, gflops/t2 );
}}}
printf( "\n" );
printf( "========== Level 3 BLAS ==========\n" );
// ----- test DGEMM
// 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] == 'N');
bool ntb = (trans[ib] == 'N');
magma_dsetmatrix( (nta ? m : k), (nta ? m : k), A, ld, dA, ld );
magma_dsetmatrix( (ntb ? k : n), (ntb ? n : k), B, ld, dB, ld );
magma_dsetmatrix( m, n, C, ld, dC1, ld );
magma_dsetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_dgemm( 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 );
cublasDgemm( trans[ia], 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
cublasDaxpy( ld*n, c_neg_one, dC1, 1, dC2, 1 );
magma_dgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_dlange( "F", &m, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_DGEMM( m, n, k ) / 1e9;
printf( "dgemm( %c, %c ) diff %.2g, Gflop/s %6.2f, %6.2f\n",
trans[ia], trans[ib], error, gflops/t1, gflops/t2 );
}}
printf( "\n" );
// ----- test DSYMM
// 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_dsetmatrix( m, m, A, ld, dA, ld );
magma_dsetmatrix( m, n, B, ld, dB, ld );
magma_dsetmatrix( m, n, C, ld, dC1, ld );
magma_dsetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_dsymm( 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 );
cublasDsymm( side[is], 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
cublasDaxpy( ld*n, c_neg_one, dC1, 1, dC2, 1 );
magma_dgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_dlange( "F", &m, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_DSYMM( side[is], m, n ) / 1e9;
printf( "dsymm( %c, %c ) diff %.2g, Gflop/s %6.2f, %6.2f\n",
side[is], uplo[iu], error, gflops/t1, gflops/t2 );
}}
printf( "\n" );
// ----- test DSYRK
// 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_dsetmatrix( n, k, A, ld, dA, ld );
magma_dsetmatrix( n, n, C, ld, dC1, ld );
magma_dsetmatrix( n, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_dsyrk( uplo[iu], trans[it], n, k, dalpha, dA, ld, dbeta, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasDsyrk( uplo[iu], 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
cublasDaxpy( ld*n, c_neg_one, dC1, 1, dC2, 1 );
magma_dgetmatrix( n, n, dC2, ld, C2, ld );
error = lapackf77_dlange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_DSYRK( k, n ) / 1e9;
printf( "dsyrk( %c, %c ) diff %.2g, Gflop/s %6.2f, %6.2f\n",
uplo[iu], trans[it], error, gflops/t1, gflops/t2 );
}}
printf( "\n" );
// ----- test DSYR2K
// 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] == 'N');
magma_dsetmatrix( (nt ? n : k), (nt ? n : k), A, ld, dA, ld );
magma_dsetmatrix( n, n, C, ld, dC1, ld );
magma_dsetmatrix( n, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_dsyr2k( 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 );
cublasDsyr2k( uplo[iu], 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
cublasDaxpy( ld*n, c_neg_one, dC1, 1, dC2, 1 );
magma_dgetmatrix( n, n, dC2, ld, C2, ld );
error = lapackf77_dlange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_DSYR2K( k, n ) / 1e9;
printf( "dsyr2k( %c, %c ) diff %.2g, Gflop/s %6.2f, %6.2f\n",
uplo[iu], trans[it], error, gflops/t1, gflops/t2 );
}}
printf( "\n" );
// ----- test DTRMM
// 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] == 'L');
magma_dsetmatrix( (left ? m : n), (left ? m : n), A, ld, dA, ld );
magma_dsetmatrix( m, n, C, ld, dC1, ld );
magma_dsetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_dtrmm( 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 );
cublasDtrmm( side[is], uplo[iu], trans[it], 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
cublasDaxpy( ld*n, c_neg_one, dC1, 1, dC2, 1 );
magma_dgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_dlange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_DTRMM( side[is], m, n ) / 1e9;
printf( "dtrmm( %c, %c ) diff %.2g, Gflop/s %6.2f, %6.2f\n",
uplo[iu], trans[it], error, gflops/t1, gflops/t2 );
}}}}
printf( "\n" );
// ----- test DTRSM
// 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] == 'L');
magma_dsetmatrix( (left ? m : n), (left ? m : n), LU, ld, dA, ld );
magma_dsetmatrix( m, n, C, ld, dC1, ld );
magma_dsetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_dtrsm( 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 );
cublasDtrsm( side[is], uplo[iu], trans[it], 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
cublasDaxpy( ld*n, c_neg_one, dC1, 1, dC2, 1 );
magma_dgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_dlange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_DTRSM( side[is], m, n ) / 1e9;
printf( "dtrsm( %c, %c ) diff %.2g, Gflop/s %6.2f, %6.2f\n",
uplo[iu], 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();
return 0;
}
