SEXP magQR(SEXP a)
{
SEXP gpu = GET_SLOT(a, install("gpu")),
b = PROTECT(NEW_OBJECT(MAKE_CLASS("magmaQR")));
int *DIMA = INTEGER(GET_DIM(a)), M = DIMA[0], N = DIMA[1],
MIN_MN = (M < N ? M : N), NB = magma_get_dgeqrf_nb(M), *pivot, info;
double *A, *tau;
A = REAL(SET_VECTOR_ELT(b, 0, AS_NUMERIC(duplicate(a))));
SET_VECTOR_ELT(b, 1, ScalarInteger(MIN_MN));
tau = REAL(SET_VECTOR_ELT(b, 2, NEW_NUMERIC(MIN_MN)));
pivot = INTEGER(SET_VECTOR_ELT(b, 3, NEW_INTEGER(N)));
int i;
for(i = 1; i <= N; i++) *pivot++ = i;
if(LOGICAL_VALUE(gpu)) {
int LENT = (2*MIN_MN + (N+31)/32*32)*NB;
double *dA, *dT, *work;
SET_SLOT(b, install("work"), NEW_NUMERIC(LENT));
work = REAL(GET_SLOT(b, install("work")));
magma_malloc((void**)&dA, (M*N)*sizeof(double));
magma_malloc((void**)&dT, LENT*sizeof(double));
magma_dsetmatrix(M, N, A, M, dA, M);
magma_dgeqrf3_gpu(M, N, dA, M, tau, dT, &info);
magma_dgetmatrix(M, N, dA, M, A, M);
magma_dgetvector(LENT, dT, 1, work, 1);
magma_free(dA);
magma_free(dT);
} else {
int LWORK = N * NB;
double *hA, *hwork;
magma_malloc_pinned((void**)&hA, (M*N)*sizeof(double));
magma_malloc_pinned((void**)&hwork, LWORK*sizeof(double));
lapackf77_dlacpy(MagmaUpperLowerStr, &M, &N, A, &M, hA, &M);
magma_dgeqrf_ooc(M, N, hA, M, tau, hwork, LWORK, &info);
lapackf77_dlacpy(MagmaUpperLowerStr, &M, &N, hA, &M, A, &M);
magma_free_pinned(hA);
magma_free_pinned(hwork);
}
if(info < 0) error("illegal argument %d in 'magQR'", -1 * info);
UNPROTECT(1);
return b;
}
SEXP magChol(SEXP a)
{
SEXP gpu = GET_SLOT(a, install("gpu")),
b = PROTECT(NEW_OBJECT(MAKE_CLASS("magma")));
int *DIMA = INTEGER(GET_DIM(a)), N = DIMA[0], N2 = N * N, LDB = N, info;
double *B;
if(DIMA[1] != N) error("non-square matrix");
b = SET_SLOT(b, install(".Data"), AS_NUMERIC(a));
SET_SLOT(b, install("gpu"), duplicate(gpu));
B = REAL(b);
if(LOGICAL_VALUE(gpu)) {
double *dB;
magma_malloc((void**)&dB, N2*sizeof(double));
magma_dsetmatrix(N, N, B, LDB, dB, LDB);
magma_dpotrf_gpu(magma_uplo_const('U'), N, dB, LDB, &info);
magma_dgetmatrix(N, N, dB, LDB, B, LDB);
magma_free(dB);
} else {
double *hB;
magma_malloc_pinned((void**)&hB, N2*sizeof(double));
lapackf77_dlacpy(MagmaUpperStr, &N, &N, B, &LDB, hB, &LDB);
magma_dpotrf(magma_uplo_const('U'), N, hB, N, &info);
lapackf77_dlacpy(MagmaUpperStr, &N, &N, hB, &LDB, B, &LDB);
magma_free_pinned(hB);
}
if(info < 0) error("illegal argument %d in 'magChol", -1 * info);
else if(info > 0) error("leading minor of order %d is not positive definite", info);
int i, j;
for(j = 0; j < N; j++) {
for(i = j + 1; i < N; i++) {
B[i + j * N] = 0.0;
}
}
UNPROTECT(1);
return b;
}
// On input, LU and ipiv is LU factorization of A. On output, LU is overwritten.
// Works for any m, n.
// Uses init_matrix() to re-generate original A as needed.
// Returns error in factorization, |PA - LU| / (n |A|)
// This allocates 3 more matrices to store A, L, and U.
double get_LU_error(magma_int_t M, magma_int_t N,
double *LU, magma_int_t lda,
magma_int_t *ipiv)
{
magma_int_t min_mn = min(M,N);
magma_int_t ione = 1;
magma_int_t i, j;
double alpha = MAGMA_D_ONE;
double beta = MAGMA_D_ZERO;
double *A, *L, *U;
double work[1], matnorm, residual;
TESTING_MALLOC_CPU( A, double, lda*N );
TESTING_MALLOC_CPU( L, double, M*min_mn );
TESTING_MALLOC_CPU( U, double, min_mn*N );
memset( L, 0, M*min_mn*sizeof(double) );
memset( U, 0, min_mn*N*sizeof(double) );
// set to original A
init_matrix( M, N, A, lda );
lapackf77_dlaswp( &N, A, &lda, &ione, &min_mn, ipiv, &ione);
// copy LU to L and U, and set diagonal to 1
lapackf77_dlacpy( MagmaLowerStr, &M, &min_mn, LU, &lda, L, &M );
lapackf77_dlacpy( MagmaUpperStr, &min_mn, &N, LU, &lda, U, &min_mn );
for(j=0; j<min_mn; j++)
L[j+j*M] = MAGMA_D_MAKE( 1., 0. );
matnorm = lapackf77_dlange("f", &M, &N, A, &lda, work);
blasf77_dgemm("N", "N", &M, &N, &min_mn,
&alpha, L, &M, U, &min_mn, &beta, LU, &lda);
for( j = 0; j < N; j++ ) {
for( i = 0; i < M; i++ ) {
LU[i+j*lda] = MAGMA_D_SUB( LU[i+j*lda], A[i+j*lda] );
}
}
residual = lapackf77_dlange("f", &M, &N, LU, &lda, work);
TESTING_FREE_CPU( A );
TESTING_FREE_CPU( L );
TESTING_FREE_CPU( U );
return residual / (matnorm * N);
}
SEXP magLU(SEXP a)
{
SEXP gpu = GET_SLOT(a, install("gpu")),
b = PROTECT(NEW_OBJECT(MAKE_CLASS("magmaLU")));
int *DIMA = INTEGER(GET_DIM(a)), M = DIMA[0], N = DIMA[1], LDA = M,
MIN_MN = M < N ? M : N, *ipiv, info;
double *A = REAL(PROTECT(AS_NUMERIC(a)));
b = SET_SLOT(b, install(".Data"), AS_NUMERIC(a));
SET_SLOT(b, install("pivot"), NEW_INTEGER(MIN_MN));
ipiv = INTEGER(GET_SLOT(b, install("pivot")));
SET_SLOT(b, install("gpu"), duplicate(gpu));
if(LOGICAL_VALUE(gpu)) {
double *dA;
magma_malloc((void**)&dA, (M*N)*sizeof(double));
magma_dsetmatrix(M, N, A, LDA, dA, LDA);
magma_dgetrf_gpu(M, N, dA, LDA, ipiv, &info);
magma_dgetmatrix(M, N, dA, LDA, REAL(b), LDA);
magma_free(dA);
} else {
double *hA;
magma_malloc_pinned((void**)&hA, (M*N)*sizeof(double));
lapackf77_dlacpy(MagmaUpperLowerStr, &M, &N, A, &LDA, hA, &LDA);
magma_dgetrf(M, N, hA, LDA, ipiv, &info);
lapackf77_dlacpy(MagmaUpperLowerStr, &M, &N, hA, &LDA, REAL(b), &LDA);
magma_free_pinned(hA);
}
if(info < 0) error("illegal argument %d in 'magLU'", -1 * info);
else if(info > 0) error("factor U is singular");
UNPROTECT(2);
return b;
}
double get_LU_error(magma_int_t M, magma_int_t N,
double *A, magma_int_t lda,
double *LU, magma_int_t *IPIV)
{
magma_int_t min_mn = min(M,N);
magma_int_t ione = 1;
magma_int_t i, j;
double alpha = MAGMA_D_ONE;
double beta = MAGMA_D_ZERO;
double *L, *U;
double work[1], matnorm, residual;
TESTING_MALLOC( L, double, M*min_mn);
TESTING_MALLOC( U, double, min_mn*N);
memset( L, 0, M*min_mn*sizeof(double) );
memset( U, 0, min_mn*N*sizeof(double) );
lapackf77_dlaswp( &N, A, &lda, &ione, &min_mn, IPIV, &ione);
lapackf77_dlacpy( MagmaLowerStr, &M, &min_mn, LU, &lda, L, &M );
lapackf77_dlacpy( MagmaUpperStr, &min_mn, &N, LU, &lda, U, &min_mn );
for(j=0; j<min_mn; j++)
L[j+j*M] = MAGMA_D_MAKE( 1., 0. );
matnorm = lapackf77_dlange("f", &M, &N, A, &lda, work);
blasf77_dgemm("N", "N", &M, &N, &min_mn,
&alpha, L, &M, U, &min_mn, &beta, LU, &lda);
for( j = 0; j < N; j++ ) {
for( i = 0; i < M; i++ ) {
LU[i+j*lda] = MAGMA_D_SUB( LU[i+j*lda], A[i+j*lda] );
}
}
residual = lapackf77_dlange("f", &M, &N, LU, &lda, work);
TESTING_FREE(L);
TESTING_FREE(U);
return residual / (matnorm * N);
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dgeqrf_mgpu
*/
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf=0, cpu_time=0;
double error, work[1];
double c_neg_one = MAGMA_D_NEG_ONE;
double *h_A, *h_R, *tau, *h_work, tmp[1];
double *d_lA[ MagmaMaxGPUs ];
magma_int_t M, N, n2, lda, ldda, n_local, ngpu;
magma_int_t info, min_mn, nb, lhwork;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1}, ISEED2[4];
magma_opts opts;
parse_opts( argc, argv, &opts );
opts.lapack |= (opts.check == 2); // check (-c2) implies lapack (-l)
magma_int_t status = 0;
double tol, eps = lapackf77_dlamch("E");
tol = opts.tolerance * eps;
printf("ngpu %d\n", (int) opts.ngpu );
if ( opts.check == 1 ) {
printf(" M N CPU GFlop/s (sec) GPU GFlop/s (sec) ||R-Q'A||_1 / (M*||A||_1) ||I-Q'Q||_1 / M\n");
printf("================================================================================================\n");
} else {
printf(" M N CPU GFlop/s (sec) GPU GFlop/s (sec) ||R||_F /(M*||A||_F)\n");
printf("==========================================================================\n");
}
for( int i = 0; i < opts.ntest; ++i ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[i];
N = opts.nsize[i];
min_mn = min(M, N);
lda = M;
n2 = lda*N;
ldda = ((M+31)/32)*32;
nb = magma_get_dgeqrf_nb( M );
gflops = FLOPS_DGEQRF( M, N ) / 1e9;
// ngpu must be at least the number of blocks
ngpu = min( opts.ngpu, int((N+nb-1)/nb) );
if ( ngpu < opts.ngpu ) {
printf( " * too many GPUs for the matrix size, using %d GPUs\n", (int) ngpu );
}
// query for workspace size
lhwork = -1;
lapackf77_dgeqrf( &M, &N, h_A, &M, tau, tmp, &lhwork, &info );
lhwork = (magma_int_t) MAGMA_D_REAL( tmp[0] );
// Allocate host memory for the matrix
TESTING_MALLOC( tau, double, min_mn );
TESTING_MALLOC( h_A, double, n2 );
TESTING_HOSTALLOC( h_R, double, n2 );
TESTING_MALLOC( h_work, double, lhwork );
// Allocate device memory
for( int dev = 0; dev < ngpu; dev++ ) {
n_local = ((N/nb)/ngpu)*nb;
if (dev < (N/nb) % ngpu)
n_local += nb;
else if (dev == (N/nb) % ngpu)
n_local += N % nb;
magma_setdevice( dev );
TESTING_DEVALLOC( d_lA[dev], double, ldda*n_local );
}
/* Initialize the matrix */
for ( int j=0; j<4; j++ ) ISEED2[j] = ISEED[j]; // saving seeds
lapackf77_dlarnv( &ione, ISEED, &n2, h_A );
lapackf77_dlacpy( MagmaUpperLowerStr, &M, &N, h_A, &lda, h_R, &lda );
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
double *tau;
TESTING_MALLOC( tau, double, min_mn );
cpu_time = magma_wtime();
lapackf77_dgeqrf( &M, &N, h_A, &M, tau, h_work, &lhwork, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapack_dgeqrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
TESTING_FREE( tau );
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
magma_dsetmatrix_1D_col_bcyclic( M, N, h_R, lda, d_lA, ldda, ngpu, nb );
gpu_time = magma_wtime();
magma_dgeqrf2_mgpu( ngpu, M, N, d_lA, ldda, tau, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_dgeqrf2 returned error %d: %s.\n",
(int) info, magma_strerror( info ));
magma_dgetmatrix_1D_col_bcyclic( M, N, d_lA, ldda, h_R, lda, ngpu, nb );
magma_queue_sync( NULL );
if ( opts.check == 1 ) {
/* =====================================================================
Check the result
=================================================================== */
magma_int_t lwork = n2+N;
double *h_W1, *h_W2, *h_W3;
double *h_RW, results[2];
TESTING_MALLOC( h_W1, double, n2 ); // Q
TESTING_MALLOC( h_W2, double, n2 ); // R
TESTING_MALLOC( h_W3, double, lwork ); // WORK
TESTING_MALLOC( h_RW, double, M ); // RWORK
lapackf77_dlarnv( &ione, ISEED2, &n2, h_A );
lapackf77_dqrt02( &M, &N, &min_mn, h_A, h_R, h_W1, h_W2, &lda, tau, h_W3, &lwork,
h_RW, results );
results[0] *= eps;
results[1] *= eps;
if ( opts.lapack ) {
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %8.2e",
(int) M, (int) N, cpu_perf, cpu_time, gpu_perf, gpu_time, results[0],results[1] );
printf("%s\n", (results[0] < tol ? "" : " failed"));
} else {
printf("%5d %5d --- ( --- ) %7.2f (%7.2f) %8.2e %8.2e",
(int) M, (int) N, gpu_perf, gpu_time, results[0],results[1] );
printf("%s\n", (results[0] < tol ? "" : " failed"));
}
status |= ! (results[0] < tol);
TESTING_FREE( h_W1 );
TESTING_FREE( h_W2 );
TESTING_FREE( h_W3 );
TESTING_FREE( h_RW );
} else if ( opts.check == 2 ) {
/* =====================================================================
Check the result compared to LAPACK
=================================================================== */
error = lapackf77_dlange("f", &M, &N, h_A, &lda, work );
blasf77_daxpy( &n2, &c_neg_one, h_A, &ione, h_R, &ione );
error = lapackf77_dlange("f", &M, &N, h_R, &lda, work ) / (min_mn*error);
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e",
(int) M, (int) N, cpu_perf, cpu_time, gpu_perf, gpu_time, error );
printf("%s\n", (error < tol ? "" : " failed"));
status |= ! (error < tol);
}
else {
if ( opts.lapack ) {
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) ---\n",
(int) M, (int) N, cpu_perf, cpu_time, gpu_perf, gpu_time );
} else {
printf("%5d %5d --- ( --- ) %7.2f (%7.2f) --- \n",
(int) M, (int) N, gpu_perf, gpu_time);
}
}
TESTING_FREE( tau );
TESTING_FREE( h_A );
TESTING_FREE( h_work );
TESTING_HOSTFREE( h_R );
for( int dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
TESTING_DEVFREE( d_lA[dev] );
}
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dgels
*/
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
double gpu_error, cpu_error, error, Anorm, work[1];
double c_one = MAGMA_D_ONE;
double c_neg_one = MAGMA_D_NEG_ONE;
double *h_A, *h_A2, *h_B, *h_X, *h_R, *tau, *h_work, tmp[1];
magmaDouble_ptr d_A, d_B;
magma_int_t M, N, size, nrhs, lda, ldb, ldda, lddb, min_mn, max_mn, nb, info;
magma_int_t lworkgpu, lhwork;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_opts opts;
opts.parse_opts( argc, argv );
magma_int_t status = 0;
double tol = opts.tolerance * lapackf77_dlamch("E");
nrhs = opts.nrhs;
printf("%% ||b-Ax|| / (N||A||) ||dx-x||/(N||A||)\n");
printf("%% M N NRHS CPU Gflop/s (sec) GPU Gflop/s (sec) CPU GPU \n");
printf("%%==================================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[itest];
N = opts.nsize[itest];
if ( M < N ) {
printf( "%5d %5d %5d skipping because M < N is not yet supported.\n", (int) M, (int) N, (int) nrhs );
continue;
}
min_mn = min(M, N);
max_mn = max(M, N);
lda = M;
ldb = max_mn;
ldda = magma_roundup( M, opts.align ); // multiple of 32 by default
lddb = magma_roundup( max_mn, opts.align ); // multiple of 32 by default
nb = magma_get_dgeqrf_nb( M, N );
gflops = (FLOPS_DGEQRF( M, N ) + FLOPS_DGEQRS( M, N, nrhs )) / 1e9;
lworkgpu = (M - N + nb)*(nrhs + nb) + nrhs*nb;
// query for workspace size
lhwork = -1;
lapackf77_dgels( MagmaNoTransStr, &M, &N, &nrhs,
NULL, &lda, NULL, &ldb, tmp, &lhwork, &info );
lhwork = (magma_int_t) MAGMA_D_REAL( tmp[0] );
lhwork = max( lhwork, lworkgpu );
TESTING_MALLOC_CPU( tau, double, min_mn );
TESTING_MALLOC_CPU( h_A, double, lda*N );
TESTING_MALLOC_CPU( h_A2, double, lda*N );
TESTING_MALLOC_CPU( h_B, double, ldb*nrhs );
TESTING_MALLOC_CPU( h_X, double, ldb*nrhs );
TESTING_MALLOC_CPU( h_R, double, ldb*nrhs );
TESTING_MALLOC_CPU( h_work, double, lhwork );
TESTING_MALLOC_DEV( d_A, double, ldda*N );
TESTING_MALLOC_DEV( d_B, double, lddb*nrhs );
/* Initialize the matrices */
size = lda*N;
lapackf77_dlarnv( &ione, ISEED, &size, h_A );
lapackf77_dlacpy( MagmaFullStr, &M, &N, h_A, &lda, h_A2, &lda );
// make random RHS
size = ldb*nrhs;
lapackf77_dlarnv( &ione, ISEED, &size, h_B );
lapackf77_dlacpy( MagmaFullStr, &M, &nrhs, h_B, &ldb, h_R, &ldb );
// make consistent RHS
//size = N*nrhs;
//lapackf77_dlarnv( &ione, ISEED, &size, h_X );
//blasf77_dgemm( MagmaNoTransStr, MagmaNoTransStr, &M, &nrhs, &N,
// &c_one, h_A, &lda,
// h_X, &ldb,
// &c_zero, h_B, &ldb );
//lapackf77_dlacpy( MagmaFullStr, &M, &nrhs, h_B, &ldb, h_R, &ldb );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
magma_dsetmatrix( M, N, h_A, lda, d_A, ldda );
magma_dsetmatrix( M, nrhs, h_B, ldb, d_B, lddb );
gpu_time = magma_wtime();
magma_dgels_gpu( MagmaNoTrans, M, N, nrhs, d_A, ldda,
d_B, lddb, h_work, lworkgpu, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0) {
printf("magma_dgels_gpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
// compute the residual
magma_dgetmatrix( N, nrhs, d_B, lddb, h_X, ldb );
blasf77_dgemm( MagmaNoTransStr, MagmaNoTransStr, &M, &nrhs, &N,
&c_neg_one, h_A, &lda,
h_X, &ldb,
&c_one, h_R, &ldb );
Anorm = lapackf77_dlange("f", &M, &N, h_A, &lda, work);
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
lapackf77_dlacpy( MagmaFullStr, &M, &nrhs, h_B, &ldb, h_X, &ldb );
cpu_time = magma_wtime();
lapackf77_dgels( MagmaNoTransStr, &M, &N, &nrhs,
h_A, &lda, h_X, &ldb, h_work, &lhwork, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0) {
printf("lapackf77_dgels returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
blasf77_dgemm( MagmaNoTransStr, MagmaNoTransStr, &M, &nrhs, &N,
&c_neg_one, h_A2, &lda,
h_X, &ldb,
&c_one, h_B, &ldb );
cpu_error = lapackf77_dlange("f", &M, &nrhs, h_B, &ldb, work) / (min_mn*Anorm);
gpu_error = lapackf77_dlange("f", &M, &nrhs, h_R, &ldb, work) / (min_mn*Anorm);
// error relative to LAPACK
size = M*nrhs;
blasf77_daxpy( &size, &c_neg_one, h_B, &ione, h_R, &ione );
error = lapackf77_dlange("f", &M, &nrhs, h_R, &ldb, work) / (min_mn*Anorm);
printf("%5d %5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %8.2e %8.2e",
(int) M, (int) N, (int) nrhs,
cpu_perf, cpu_time, gpu_perf, gpu_time, cpu_error, gpu_error, error );
bool okay;
if ( M == N ) {
okay = (gpu_error < tol && error < tol);
}
else {
okay = (error < tol);
}
status += ! okay;
printf( " %s\n", (okay ? "ok" : "failed"));
TESTING_FREE_CPU( tau );
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_A2 );
TESTING_FREE_CPU( h_B );
TESTING_FREE_CPU( h_X );
TESTING_FREE_CPU( h_R );
TESTING_FREE_CPU( h_work );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_B );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
/**
Purpose
-------
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 */
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dsyevd
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gpu_time, cpu_time;
double *h_A, *h_R, *h_work;
double *w1, *w2;
magma_int_t *iwork;
magma_int_t N, n2, info, lwork, liwork, lda, aux_iwork[1];
magma_int_t izero = 0;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
double result[3], eps, aux_work[1];
eps = lapackf77_dlamch( "E" );
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
double tol = opts.tolerance * lapackf77_dlamch("E");
double tolulp = opts.tolerance * lapackf77_dlamch("P");
if ( opts.check && opts.jobz == MagmaNoVec ) {
fprintf( stderr, "checking results requires vectors; setting jobz=V (option -JV)\n" );
opts.jobz = MagmaVec;
}
printf("using: jobz = %s, uplo = %s\n",
lapack_vec_const(opts.jobz), lapack_uplo_const(opts.uplo));
printf(" N CPU Time (sec) GPU Time (sec)\n");
printf("=======================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
n2 = N*N;
lda = N;
// query for workspace sizes
magma_dsyevd( opts.jobz, opts.uplo,
N, NULL, lda, NULL,
aux_work, -1,
aux_iwork, -1,
opts.queue, &info );
lwork = (magma_int_t) aux_work[0];
liwork = aux_iwork[0];
/* Allocate host memory for the matrix */
TESTING_MALLOC_CPU( h_A, double, N*lda );
TESTING_MALLOC_CPU( w1, double, N );
TESTING_MALLOC_CPU( w2, double, N );
TESTING_MALLOC_CPU( iwork, magma_int_t, liwork );
TESTING_MALLOC_PIN( h_R, double, N*lda );
TESTING_MALLOC_PIN( h_work, double, lwork );
/* Initialize the matrix */
lapackf77_dlarnv( &ione, ISEED, &n2, h_A );
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
/* warm up run */
if ( opts.warmup ) {
magma_dsyevd( opts.jobz, opts.uplo,
N, h_R, lda, w1,
h_work, lwork,
iwork, liwork,
opts.queue, &info );
if (info != 0)
printf("magma_dsyevd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
magma_dsyevd( opts.jobz, opts.uplo,
N, h_R, lda, w1,
h_work, lwork,
iwork, liwork,
opts.queue, &info );
gpu_time = magma_wtime() - gpu_time;
if (info != 0)
printf("magma_dsyevd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
if ( opts.check ) {
/* =====================================================================
Check the results following the LAPACK's [zcds]drvst routine.
A is factored as A = U S U' and the following 3 tests computed:
(1) | A - U S U' | / ( |A| N )
(2) | I - U'U | / ( N )
(3) | S(with U) - S(w/o U) | / | S |
=================================================================== */
double temp1, temp2;
// tau=NULL is unused since itype=1
lapackf77_dsyt21( &ione, lapack_uplo_const(opts.uplo), &N, &izero,
h_A, &lda,
w1, h_work,
h_R, &lda,
h_R, &lda,
NULL, h_work, &result[0] );
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
magma_dsyevd( MagmaNoVec, opts.uplo,
N, h_R, lda, w2,
h_work, lwork,
iwork, liwork,
opts.queue, &info );
if (info != 0)
printf("magma_dsyevd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
temp1 = temp2 = 0;
for( int j=0; j<N; j++ ) {
temp1 = max(temp1, fabs(w1[j]));
temp1 = max(temp1, fabs(w2[j]));
temp2 = max(temp2, fabs(w1[j]-w2[j]));
}
result[2] = temp2 / (((double)N)*temp1);
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
lapackf77_dsyevd( lapack_vec_const(opts.jobz), lapack_uplo_const(opts.uplo),
&N, h_A, &lda, w2,
h_work, &lwork,
iwork, &liwork,
&info );
cpu_time = magma_wtime() - cpu_time;
if (info != 0)
printf("lapackf77_dsyevd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
printf("%5d %7.2f %7.2f\n",
(int) N, cpu_time, gpu_time);
}
else {
printf("%5d --- %7.2f\n",
(int) N, gpu_time);
}
/* =====================================================================
Print execution time
=================================================================== */
if ( opts.check ) {
printf("Testing the factorization A = U S U' for correctness:\n");
printf("(1) | A - U S U' | / (|A| N) = %8.2e %s\n", result[0]*eps, (result[0]*eps < tol ? "ok" : "failed") );
printf("(2) | I - U'U | / N = %8.2e %s\n", result[1]*eps, (result[1]*eps < tol ? "ok" : "failed") );
printf("(3) | S(w/ U) - S(w/o U) | / |S| = %8.2e %s\n\n", result[2] , (result[2] < tolulp ? "ok" : "failed") );
status += ! (result[0]*eps < tol && result[1]*eps < tol && result[2] < tolulp);
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( w1 );
TESTING_FREE_CPU( w2 );
TESTING_FREE_CPU( iwork );
TESTING_FREE_PIN( h_R );
TESTING_FREE_PIN( h_work );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dgeqrs_gpu
*/
int main( int argc, char** argv)
{
//#if defined(PRECISION_s)
/* Initialize */
magma_queue_t queue;
magma_device_t device[ MagmaMaxGPUs ];
int num = 0;
magma_err_t err;
magma_init();
err = magma_get_devices( device, MagmaMaxGPUs, &num );
if ( err != 0 || num < 1 ) {
fprintf( stderr, "magma_get_devices failed: %d\n", err );
exit(-1);
}
err = magma_queue_create( device[0], &queue );
if ( err != 0 ) {
fprintf( stderr, "magma_queue_create failed: %d\n", err );
exit(-1);
}
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
double matnorm, work[1];
double c_one = MAGMA_D_ONE;
double c_neg_one = MAGMA_D_NEG_ONE;
double *h_A, *h_A2, *h_B, *h_X, *h_R, *tau, *hwork, tmp[1];
magmaDouble_ptr d_A, d_B;
/* Matrix size */
magma_int_t M = 0, N = 0, n2;
magma_int_t lda, ldb, ldda, lddb, lworkgpu, lhwork;
magma_int_t size[7] = {1024,2048,3072,4032,5184,6016,7000};
magma_int_t i, info, min_mn, nb, l1, l2;
magma_int_t ione = 1;
magma_int_t nrhs = 3;
magma_int_t ISEED[4] = {0,0,0,1};
if (argc != 1){
for(i = 1; i<argc; i++){
if (strcmp("-N", argv[i])==0)
N = atoi(argv[++i]);
else if (strcmp("-M", argv[i])==0)
M = atoi(argv[++i]);
else if (strcmp("-nrhs", argv[i])==0)
nrhs = atoi(argv[++i]);
}
if (N>0 && M>0 && M >= N)
printf(" testing_dgeqrs_gpu -nrhs %d -M %d -N %d\n\n", nrhs, M, N);
else
{
printf("\nUsage: \n");
printf(" testing_dgeqrs_gpu -nrhs %d -M %d -N %d\n\n", nrhs, M, N);
printf(" M has to be >= N, exit.\n");
exit(1);
}
}
else {
printf("\nUsage: \n");
printf(" testing_dgeqrs_gpu -nrhs %d -M %d -N %d\n\n", nrhs, 1024, 1024);
M = N = size[6];
}
ldda = ((M+31)/32)*32;
lddb = ldda;
n2 = M * N;
min_mn = min(M, N);
nb = magma_get_dgeqrf_nb(M);
lda = ldb = M;
lworkgpu = (M-N + nb)*(nrhs+2*nb);
/* Allocate host memory for the matrix */
TESTING_MALLOC_PIN( tau, double, min_mn );
TESTING_MALLOC_PIN( h_A, double, lda*N );
TESTING_MALLOC_PIN( h_A2, double, lda*N );
TESTING_MALLOC_PIN( h_B, double, ldb*nrhs );
TESTING_MALLOC_PIN( h_X, double, ldb*nrhs );
TESTING_MALLOC_PIN( h_R, double, ldb*nrhs );
TESTING_MALLOC_DEV( d_A, double, ldda*N );
TESTING_MALLOC_DEV( d_B, double, lddb*nrhs );
/*
* Get size for host workspace
*/
lhwork = -1;
lapackf77_dgeqrf(&M, &N, h_A, &M, tau, tmp, &lhwork, &info);
l1 = (magma_int_t)MAGMA_D_REAL( tmp[0] );
lhwork = -1;
lapackf77_dormqr( MagmaLeftStr, MagmaTransStr,
&M, &nrhs, &min_mn, h_A, &lda, tau,
h_X, &ldb, tmp, &lhwork, &info);
l2 = (magma_int_t)MAGMA_D_REAL( tmp[0] );
lhwork = max( max( l1, l2 ), lworkgpu );
TESTING_MALLOC_PIN( hwork, double, lhwork );
printf("\n");
printf(" ||b-Ax|| / (N||A||)\n");
printf(" M N CPU GFlop/s GPU GFlop/s CPU GPU \n");
printf("============================================================\n");
for(i=0; i<7; i++){
if (argc == 1){
M = N = size[i];
}
min_mn= min(M, N);
ldb = lda = M;
n2 = lda*N;
ldda = ((M+31)/32)*32;
gflops = (FLOPS_GEQRF( (double)M, (double)N )
+ FLOPS_GEQRS( (double)M, (double)N, (double)nrhs )) / 1e9;
/* Initialize the matrices */
lapackf77_dlarnv( &ione, ISEED, &n2, h_A );
lapackf77_dlacpy( MagmaUpperLowerStr, &M, &N, h_A, &lda, h_A2, &lda );
n2 = M*nrhs;
lapackf77_dlarnv( &ione, ISEED, &n2, h_B );
lapackf77_dlacpy( MagmaUpperLowerStr, &M, &nrhs, h_B, &ldb, h_R, &ldb );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
/* Warm up to measure the performance */
magma_dsetmatrix( M, N, h_A, 0, lda, d_A, 0, ldda, queue );
magma_dsetmatrix( M, nrhs, h_B, 0, ldb, d_B, 0, lddb, queue );
magma_dgels_gpu( MagmaNoTrans, M, N, nrhs, d_A, 0, ldda,
d_B, 0, lddb, hwork, lworkgpu, &info, queue);
magma_dsetmatrix( M, N, h_A, 0, lda, d_A, 0, ldda, queue );
magma_dsetmatrix( M, nrhs, h_B, 0, ldb, d_B, 0, lddb, queue );
gpu_time = magma_wtime();
magma_dgels_gpu( MagmaNoTrans, M, N, nrhs, d_A, 0, ldda,
d_B, 0, lddb, hwork, lworkgpu, &info, queue);
gpu_time = magma_wtime() - gpu_time;
if (info < 0)
printf("Argument %d of magma_dgels had an illegal value.\n", -info);
gpu_perf = gflops / gpu_time;
// Get the solution in h_X
magma_dgetmatrix( N, nrhs, d_B, 0, lddb, h_X, 0, ldb, queue );
// compute the residual
blasf77_dgemm( MagmaNoTransStr, MagmaNoTransStr, &M, &nrhs, &N,
&c_neg_one, h_A, &lda,
h_X, &ldb,
&c_one, h_R, &ldb);
matnorm = lapackf77_dlange("f", &M, &N, h_A, &lda, work);
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
lapackf77_dlacpy( MagmaUpperLowerStr, &M, &nrhs, h_B, &ldb, h_X, &ldb );
cpu_time = magma_wtime();
lapackf77_dgels( MagmaNoTransStr, &M, &N, &nrhs,
h_A, &lda, h_X, &ldb, hwork, &lhwork, &info);
cpu_time = magma_wtime()-cpu_time;
cpu_perf = gflops / cpu_time;
if (info < 0)
printf("Argument %d of lapackf77_dgels had an illegal value.\n", -info);
blasf77_dgemm( MagmaNoTransStr, MagmaNoTransStr, &M, &nrhs, &N,
&c_neg_one, h_A2, &lda,
h_X, &ldb,
&c_one, h_B, &ldb);
printf("%5d %5d %6.1f %6.1f %7.2e %7.2e\n",
M, N, cpu_perf, gpu_perf,
lapackf77_dlange("f", &M, &nrhs, h_B, &M, work)/(min_mn*matnorm),
lapackf77_dlange("f", &M, &nrhs, h_R, &M, work)/(min_mn*matnorm) );
if (argc != 1)
break;
}
/* Memory clean up */
TESTING_FREE_PIN( tau );
TESTING_FREE_PIN( h_A );
TESTING_FREE_PIN( h_A2 );
TESTING_FREE_PIN( h_B );
TESTING_FREE_PIN( h_X );
TESTING_FREE_PIN( h_R );
TESTING_FREE_PIN( hwork );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_B );
/* Shutdown */
magma_queue_destroy( queue );
magma_finalize();
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dsygvdx
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gpu_time;
double *h_A, *h_R, *h_work;
#if defined(PRECISION_z) || defined(PRECISION_c)
double *rwork;
magma_int_t lrwork;
#endif
/* Matrix size */
double *w1, *w2;
magma_int_t *iwork;
magma_int_t N, n2, info, lwork, liwork;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};;
magma_int_t info_ortho = 0;
magma_int_t info_solution = 0;
magma_int_t info_reduction = 0;
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
magma_range_t range = MagmaRangeAll;
if (opts.fraction != 1)
range = MagmaRangeI;
if ( opts.check && opts.jobz == MagmaNoVec ) {
fprintf( stderr, "checking results requires vectors; setting jobz=V (option -JV)\n" );
opts.jobz = MagmaVec;
}
printf("using: itype = %d, jobz = %s, range = %s, uplo = %s, check = %d, fraction = %6.4f\n",
(int) opts.itype, lapack_vec_const(opts.jobz), lapack_range_const(range), lapack_uplo_const(opts.uplo),
(int) opts.check, opts.fraction);
printf(" N M GPU Time (sec) ||I-Q'Q||/. ||A-QDQ'||/. ||D-D_magma||/.\n");
printf("=======================================================================\n");
magma_int_t threads = magma_get_parallel_numthreads();
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
n2 = N*N;
#if defined(PRECISION_z) || defined(PRECISION_c)
lwork = magma_dbulge_get_lq2(N, threads) + 2*N + N*N;
lrwork = 1 + 5*N +2*N*N;
#else
lwork = magma_dbulge_get_lq2(N, threads) + 1 + 6*N + 2*N*N;
#endif
liwork = 3 + 5*N;
/* Allocate host memory for the matrix */
TESTING_MALLOC_CPU( h_A, double, n2 );
TESTING_MALLOC_CPU( w1, double, N );
TESTING_MALLOC_CPU( w2, double, N );
TESTING_MALLOC_CPU( iwork, magma_int_t, liwork );
TESTING_MALLOC_PIN( h_R, double, n2 );
TESTING_MALLOC_PIN( h_work, double, lwork );
#if defined(PRECISION_z) || defined(PRECISION_c)
TESTING_MALLOC_PIN( rwork, double, lrwork );
#endif
/* Initialize the matrix */
lapackf77_dlarnv( &ione, ISEED, &n2, h_A );
magma_dmake_symmetric( N, h_A, N );
magma_int_t m1 = 0;
double vl = 0;
double vu = 0;
magma_int_t il = 0;
magma_int_t iu = 0;
if (range == MagmaRangeI) {
il = 1;
iu = (int) (opts.fraction*N);
}
if (opts.warmup) {
// ==================================================================
// Warmup using MAGMA
// ==================================================================
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
if (opts.ngpu == 1) {
//printf("calling dsyevdx_2stage 1 GPU\n");
magma_dsyevdx_2stage(opts.jobz, range, opts.uplo, N,
h_R, N,
vl, vu, il, iu,
&m1, w1,
h_work, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork,
&info);
} else {
//printf("calling dsyevdx_2stage_m %d GPU\n", (int) opts.ngpu);
magma_dsyevdx_2stage_m(opts.ngpu, opts.jobz, range, opts.uplo, N,
h_R, N,
vl, vu, il, iu,
&m1, w1,
h_work, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork,
&info);
}
}
// ===================================================================
// Performs operation using MAGMA
// ===================================================================
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
gpu_time = magma_wtime();
if (opts.ngpu == 1) {
//printf("calling dsyevdx_2stage 1 GPU\n");
magma_dsyevdx_2stage(opts.jobz, range, opts.uplo, N,
h_R, N,
vl, vu, il, iu,
&m1, w1,
h_work, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork,
&info);
} else {
//printf("calling dsyevdx_2stage_m %d GPU\n", (int) opts.ngpu);
magma_dsyevdx_2stage_m(opts.ngpu, opts.jobz, range, opts.uplo, N,
h_R, N,
vl, vu, il, iu,
&m1, w1,
h_work, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork,
&info);
}
gpu_time = magma_wtime() - gpu_time;
printf("%5d %5d %7.2f ",
(int) N, (int) m1, gpu_time );
if ( opts.check ) {
double eps = lapackf77_dlamch("E");
//printf("\n");
//printf("------ TESTS FOR MAGMA DSYEVD ROUTINE ------- \n");
//printf(" Size of the Matrix %d by %d\n", (int) N, (int) N);
//printf("\n");
//printf(" The matrix A is randomly generated for each test.\n");
//printf("============\n");
//printf(" The relative machine precision (eps) is %8.2e\n",eps);
//printf(" Computational tests pass if scaled residuals are less than 60.\n");
/* Check the orthogonality, reduction and the eigen solutions */
if (opts.jobz == MagmaVec) {
info_ortho = check_orthogonality(N, N, h_R, N, eps);
info_reduction = check_reduction(opts.uplo, N, 1, h_A, w1, N, h_R, eps);
}
//printf("------ CALLING LAPACK DSYEVD TO COMPUTE only eigenvalue and verify elementswise ------- \n");
lapackf77_dsyevd("N", "L", &N,
h_A, &N, w2,
h_work, &lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, &lrwork,
#endif
iwork, &liwork,
&info);
info_solution = check_solution(N, w2, w1, eps);
if ( (info_solution == 0) && (info_ortho == 0) && (info_reduction == 0) ) {
printf(" ok\n");
//printf("***************************************************\n");
//printf(" ---- TESTING DSYEVD ...................... PASSED !\n");
//printf("***************************************************\n");
}
else {
printf(" failed\n");
status += 1;
//printf("************************************************\n");
//printf(" - TESTING DSYEVD ... FAILED !\n");
//printf("************************************************\n");
}
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( w1 );
TESTING_FREE_CPU( w2 );
TESTING_FREE_CPU( iwork );
TESTING_FREE_PIN( h_R );
TESTING_FREE_PIN( h_work );
#if defined(PRECISION_z) || defined(PRECISION_c)
TESTING_FREE_PIN( rwork );
#endif
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
/* Shutdown */
TESTING_FINALIZE();
return status;
}
/*------------------------------------------------------------
* Check the reduction
*/
static magma_int_t check_reduction(magma_uplo_t uplo, magma_int_t N, magma_int_t bw, double *A, double *D, magma_int_t LDA, double *Q, double eps )
{
double c_one = MAGMA_D_ONE;
double c_neg_one = MAGMA_D_NEG_ONE;
double *TEMP, *Residual;
double *work;
double Anorm, Rnorm, result;
magma_int_t info_reduction;
magma_int_t i;
magma_int_t ione=1;
magma_dmalloc_cpu( &TEMP, N*N );
magma_dmalloc_cpu( &Residual, N*N );
magma_dmalloc_cpu( &work, N );
/* Compute TEMP = Q * LAMBDA */
lapackf77_dlacpy("A", &N, &N, Q, &LDA, TEMP, &N);
for (i = 0; i < N; i++) {
blasf77_dscal(&N, &D[i], &(TEMP[i*N]), &ione);
}
/* Compute Residual = A - Q * LAMBDA * Q^H */
/* A is Hermetian but both upper and lower
* are assumed valable here for checking
* otherwise it need to be symetrized before
* checking.
*/
lapackf77_dlacpy("A", &N, &N, A, &LDA, Residual, &N);
blasf77_dgemm("N", "C", &N, &N, &N, &c_neg_one, TEMP, &N, Q, &LDA, &c_one, Residual, &N);
// since A has been generated by larnv and we did not symmetrize,
// so only the uplo portion of A should be equal to Q*LAMBDA*Q^H
// for that Rnorm use dlansy instead of dlange
Rnorm = lapackf77_dlansy("1", lapack_uplo_const(uplo), &N, Residual, &N, work);
Anorm = lapackf77_dlansy("1", lapack_uplo_const(uplo), &N, A, &LDA, work);
result = Rnorm / ( Anorm * N * eps);
printf(" %12.2e", result );
//if ( uplo == MagmaLower ) {
// printf(" ======================================================\n");
// printf(" ||A-Q*LAMBDA*Q'||_oo/(||A||_oo.N.eps) : %15.3E \n", result );
// printf(" ======================================================\n");
//} else {
// printf(" ======================================================\n");
// printf(" ||A-Q'*LAMBDA*Q||_oo/(||A||_oo.N.eps) : %15.3E \n", result );
// printf(" ======================================================\n");
//}
if ( isnan(result) || isinf(result) || (result > 60.0) ) {
//printf("-- Reduction is suspicious ! \n");
info_reduction = 1;
}
else {
//printf("-- Reduction is CORRECT ! \n");
info_reduction = 0;
}
magma_free_cpu(TEMP);
magma_free_cpu(Residual);
magma_free_cpu(work);
return info_reduction;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dsygvdx
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gpu_time;
double *h_A, *h_R, *h_B, *h_S, *h_work;
#if defined(PRECISION_z) || defined(PRECISION_c)
double *rwork;
magma_int_t lrwork;
#endif
/* Matrix size */
double *w1, *w2, result[2]={0,0};
magma_int_t *iwork;
magma_int_t N, n2, info, lwork, liwork;
double c_zero = MAGMA_D_ZERO;
double c_one = MAGMA_D_ONE;
double c_neg_one = MAGMA_D_NEG_ONE;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
double tol = opts.tolerance * lapackf77_dlamch("E");
double tolulp = opts.tolerance * lapackf77_dlamch("P");
magma_range_t range = MagmaRangeAll;
if (opts.fraction != 1)
range = MagmaRangeI;
if ( opts.check && opts.jobz == MagmaNoVec ) {
fprintf( stderr, "checking results requires vectors; setting jobz=V (option -JV)\n" );
opts.jobz = MagmaVec;
}
printf("using: itype = %d, jobz = %s, range = %s, uplo = %s, opts.check = %d, fraction = %6.4f\n",
(int) opts.itype, lapack_vec_const(opts.jobz), lapack_range_const(range), lapack_uplo_const(opts.uplo),
(int) opts.check, opts.fraction);
printf(" N M GPU Time (sec)\n");
printf("============================\n");
magma_int_t threads = magma_get_parallel_numthreads();
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
n2 = N*N;
#if defined(PRECISION_z) || defined(PRECISION_c)
lwork = magma_dbulge_get_lq2(N, threads) + 2*N + N*N;
lrwork = 1 + 5*N +2*N*N;
#else
lwork = magma_dbulge_get_lq2(N, threads) + 1 + 6*N + 2*N*N;
#endif
liwork = 3 + 5*N;
/* Allocate host memory for the matrix */
TESTING_MALLOC_CPU( h_A, double, n2 );
TESTING_MALLOC_CPU( h_B, double, n2 );
TESTING_MALLOC_CPU( w1, double, N );
TESTING_MALLOC_CPU( w2, double, N );
TESTING_MALLOC_CPU( iwork, magma_int_t, liwork );
TESTING_MALLOC_PIN( h_R, double, n2 );
TESTING_MALLOC_PIN( h_S, double, n2 );
TESTING_MALLOC_PIN( h_work, double, lwork );
#if defined(PRECISION_z) || defined(PRECISION_c)
TESTING_MALLOC_PIN( rwork, double, lrwork);
#endif
/* Initialize the matrix */
lapackf77_dlarnv( &ione, ISEED, &n2, h_A );
lapackf77_dlarnv( &ione, ISEED, &n2, h_B );
magma_dmake_hpd( N, h_B, N );
magma_dmake_symmetric( N, h_A, N );
magma_int_t m1 = 0;
double vl = 0;
double vu = 0;
magma_int_t il = 0;
magma_int_t iu = 0;
if (range == MagmaRangeI) {
il = 1;
iu = (int) (opts.fraction*N);
}
// ==================================================================
// Warmup using MAGMA
// ==================================================================
if (opts.warmup) {
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );
magma_dsygvdx_2stage(opts.itype, opts.jobz, range, opts.uplo,
N, h_R, N, h_S, N, vl, vu, il, iu, &m1, w1,
h_work, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork,
&info);
}
// ===================================================================
// Performs operation using MAGMA
// ===================================================================
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );
gpu_time = magma_wtime();
magma_dsygvdx_2stage(opts.itype, opts.jobz, range, opts.uplo,
N, h_R, N, h_S, N, vl, vu, il, iu, &m1, w1,
h_work, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork,
&info);
gpu_time = magma_wtime() - gpu_time;
if ( opts.check ) {
/* =====================================================================
Check the results following the LAPACK's [zc]hegvdx routine.
A x = lambda B x is solved
and the following 3 tests computed:
(1) | A Z - B Z D | / ( |A||Z| N ) (itype = 1)
| A B Z - Z D | / ( |A||Z| N ) (itype = 2)
| B A Z - Z D | / ( |A||Z| N ) (itype = 3)
(2) | S(with V) - S(w/o V) | / | S |
=================================================================== */
#if defined(PRECISION_d) || defined(PRECISION_s)
double *rwork = h_work + N*N;
#endif
double temp1, temp2;
result[0] = 1.;
result[0] /= lapackf77_dlansy("1", lapack_uplo_const(opts.uplo), &N, h_A, &N, rwork);
result[0] /= lapackf77_dlange("1", &N, &m1, h_R, &N, rwork);
if (opts.itype == 1) {
blasf77_dsymm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_A, &N, h_R, &N, &c_zero, h_work, &N);
for(int i=0; i<m1; ++i)
blasf77_dscal(&N, &w1[i], &h_R[i*N], &ione);
blasf77_dsymm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_neg_one, h_B, &N, h_R, &N, &c_one, h_work, &N);
result[0] *= lapackf77_dlange("1", &N, &m1, h_work, &N, rwork)/N;
}
else if (opts.itype == 2) {
blasf77_dsymm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_B, &N, h_R, &N, &c_zero, h_work, &N);
for(int i=0; i<m1; ++i)
blasf77_dscal(&N, &w1[i], &h_R[i*N], &ione);
blasf77_dsymm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_A, &N, h_work, &N, &c_neg_one, h_R, &N);
result[0] *= lapackf77_dlange("1", &N, &m1, h_R, &N, rwork)/N;
}
else if (opts.itype == 3) {
blasf77_dsymm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_A, &N, h_R, &N, &c_zero, h_work, &N);
for(int i=0; i<m1; ++i)
blasf77_dscal(&N, &w1[i], &h_R[i*N], &ione);
blasf77_dsymm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_B, &N, h_work, &N, &c_neg_one, h_R, &N);
result[0] *= lapackf77_dlange("1", &N, &m1, h_R, &N, rwork)/N;
}
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );
magma_int_t m2 = m1;
lapackf77_dsygvd(&opts.itype, "N", lapack_uplo_const(opts.uplo), &N,
h_R, &N, h_S, &N, w2,
h_work, &lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, &lrwork,
#endif
iwork, &liwork,
&info);
temp1 = temp2 = 0;
for(int j=0; j<m2; j++) {
temp1 = max(temp1, fabs(w1[j]));
temp1 = max(temp1, fabs(w2[j]));
temp2 = max(temp2, fabs(w1[j]-w2[j]));
}
result[1] = temp2 / (((double)m2)*temp1);
}
/* =====================================================================
Print execution time
=================================================================== */
printf("%5d %5d %7.2f\n",
(int) N, (int) m1, gpu_time);
if ( opts.check ) {
printf("Testing the eigenvalues and eigenvectors for correctness:\n");
if (opts.itype==1) {
printf("(1) | A Z - B Z D | / (|A| |Z| N) = %8.2e %s\n", result[0], (result[0] < tol ? "ok" : "failed"));
}
else if (opts.itype==2) {
printf("(1) | A B Z - Z D | / (|A| |Z| N) = %8.2e %s\n", result[0], (result[0] < tol ? "ok" : "failed"));
}
else if (opts.itype==3) {
printf("(1) | B A Z - Z D | / (|A| |Z| N) = %8.2e %s\n", result[0], (result[0] < tol ? "ok" : "failed"));
}
printf( "(2) | D(w/ Z) - D(w/o Z) | / |D| = %8.2e %s\n\n", result[1], (result[1] < tolulp ? "ok" : "failed"));
status += ! (result[0] < tol && result[1] < tolulp);
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_B );
TESTING_FREE_CPU( w1 );
TESTING_FREE_CPU( w2 );
TESTING_FREE_CPU( iwork );
TESTING_FREE_PIN( h_R );
TESTING_FREE_PIN( h_S );
TESTING_FREE_PIN( h_work );
#if defined(PRECISION_z) || defined(PRECISION_c)
TESTING_FREE_PIN( rwork );
#endif
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
/* Shutdown */
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dormlq
*/
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
double error, work[1];
double c_neg_one = MAGMA_D_NEG_ONE;
magma_int_t ione = 1;
magma_int_t mm, m, n, k, size, info;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t nb, ldc, lda, lwork, lwork_max;
double *C, *R, *A, *W, *tau;
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
// need slightly looser bound (60*eps instead of 30*eps) for some tests
opts.tolerance = max( 60., opts.tolerance );
double tol = opts.tolerance * lapackf77_dlamch("E");
// test all combinations of input parameters
magma_side_t side [] = { MagmaLeft, MagmaRight };
magma_trans_t trans[] = { MagmaTrans, MagmaNoTrans };
printf(" M N K side trans CPU GFlop/s (sec) GPU GFlop/s (sec) ||R||_F / ||QC||_F\n");
printf("===============================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iside = 0; iside < 2; ++iside ) {
for( int itran = 0; itran < 2; ++itran ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
m = opts.msize[itest];
n = opts.nsize[itest];
k = opts.ksize[itest];
nb = magma_get_dgelqf_nb( min( m, n ));
ldc = m;
// A is k x m (left) or k x n (right)
mm = (side[iside] == MagmaLeft ? m : n);
lda = k;
gflops = FLOPS_DORMLQ( m, n, k, side[iside] ) / 1e9;
if ( side[iside] == MagmaLeft && m < k ) {
printf( "%5d %5d %5d %4c %5c skipping because side=left and m < k\n",
(int) m, (int) n, (int) k,
lapacke_side_const( side[iside] ),
lapacke_trans_const( trans[itran] ) );
continue;
}
if ( side[iside] == MagmaRight && n < k ) {
printf( "%5d %5d %5d %4c %5c skipping because side=right and n < k\n",
(int) m, (int) n, (int) k,
lapacke_side_const( side[iside] ),
lapacke_trans_const( trans[itran] ) );
continue;
}
// need at least 2*nb*nb for gelqf
lwork_max = max( max( m*nb, n*nb ), 2*nb*nb );
TESTING_MALLOC_CPU( C, double, ldc*n );
TESTING_MALLOC_CPU( R, double, ldc*n );
TESTING_MALLOC_CPU( A, double, lda*mm );
TESTING_MALLOC_CPU( W, double, lwork_max );
TESTING_MALLOC_CPU( tau, double, k );
// C is full, m x n
size = ldc*n;
lapackf77_dlarnv( &ione, ISEED, &size, C );
lapackf77_dlacpy( "Full", &m, &n, C, &ldc, R, &ldc );
size = lda*mm;
lapackf77_dlarnv( &ione, ISEED, &size, A );
// compute LQ factorization to get Householder vectors in A, tau
magma_dgelqf( k, mm, A, lda, tau, W, lwork_max, &info );
if (info != 0)
printf("magma_dgelqf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
lapackf77_dormlq( lapack_side_const( side[iside] ), lapack_trans_const( trans[itran] ),
&m, &n, &k,
A, &lda, tau, C, &ldc, W, &lwork_max, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_dormlq returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
// query for workspace size
lwork = -1;
magma_dormlq( side[iside], trans[itran],
m, n, k,
A, lda, tau, R, ldc, W, lwork, &info );
if (info != 0)
printf("magma_dormlq (lwork query) returned error %d: %s.\n",
(int) info, magma_strerror( info ));
lwork = (magma_int_t) MAGMA_D_REAL( W[0] );
if ( lwork < 0 || lwork > lwork_max ) {
printf("optimal lwork %d > lwork_max %d\n", (int) lwork, (int) lwork_max );
lwork = lwork_max;
}
gpu_time = magma_wtime();
magma_dormlq( side[iside], trans[itran],
m, n, k,
A, lda, tau, R, ldc, W, lwork, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_dormlq returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
compute relative error |QC_magma - QC_lapack| / |QC_lapack|
=================================================================== */
error = lapackf77_dlange( "Fro", &m, &n, C, &ldc, work );
size = ldc*n;
blasf77_daxpy( &size, &c_neg_one, C, &ione, R, &ione );
error = lapackf77_dlange( "Fro", &m, &n, R, &ldc, work ) / error;
printf( "%5d %5d %5d %4c %5c %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %s\n",
(int) m, (int) n, (int) k,
lapacke_side_const( side[iside] ),
lapacke_trans_const( trans[itran] ),
cpu_perf, cpu_time, gpu_perf, gpu_time,
error, (error < tol ? "ok" : "failed") );
status += ! (error < tol);
TESTING_FREE_CPU( C );
TESTING_FREE_CPU( R );
TESTING_FREE_CPU( A );
TESTING_FREE_CPU( W );
TESTING_FREE_CPU( tau );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}} // end iside, itran
printf( "\n" );
}
TESTING_FINALIZE();
return status;
}
int main( int argc, char** argv)
{
real_Double_t gflops, gpu_perf, cpu_perf, gpu_time, cpu_time;
double *h_R = NULL, *h_P = NULL;
magmaDouble_ptr d_lA[MagmaMaxSubs * MagmaMaxGPUs];
magma_int_t N = 0, n2, lda, ldda;
magma_int_t size[10] =
{ 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000 };
magma_int_t i, j, k, check = 0, info;
double mz_one = MAGMA_D_NEG_ONE;
magma_int_t ione = 1;
magma_int_t num_gpus0 = 1, num_gpus, num_subs0 = 1, num_subs, tot_subs, flag = 0;
magma_int_t nb, n_local, nk;
magma_uplo_t uplo = MagmaLower;
if (argc != 1){
for(i = 1; i<argc; i++){
if (strcmp("-N", argv[i]) == 0){
N = atoi(argv[++i]);
if (N > 0) {
size[0] = size[9] = N;
flag = 1;
}
}
if(strcmp("-NGPU", argv[i]) == 0)
num_gpus0 = atoi(argv[++i]);
if(strcmp("-NSUB", argv[i]) == 0)
num_subs0 = atoi(argv[++i]);
if(strcmp("-UPLO", argv[i]) == 0)
uplo = (strcmp("L", argv[++i]) == 0 ? MagmaLower : MagmaUpper);
if(strcmp("-check", argv[i]) == 0)
check = 1;
}
}
/* Initialize */
magma_queue_t queues[2*MagmaMaxGPUs];
magma_device_t devices[ MagmaMaxGPUs ];
magma_int_t num = 0;
magma_int_t err;
magma_init();
err = magma_getdevices( devices, MagmaMaxGPUs, &num );
if ( err != 0 || num < 1 ) {
fprintf( stderr, "magma_getdevices failed: %d\n", (int) err );
exit(-1);
}
for(i=0;i<num_gpus0;i++){
err = magma_queue_create( devices[i], &queues[2*i] );
if ( err != 0 ) {
fprintf( stderr, "magma_queue_create failed: %d\n", (int) err );
exit(-1);
}
err = magma_queue_create( devices[i], &queues[2*i+1] );
if ( err != 0 ) {
fprintf( stderr, "magma_queue_create failed: %d\n", (int) err );
exit(-1);
}
}
printf("\nUsing %d GPUs:\n", num_gpus0);
printf(" testing_dpotrf_msub -N %d -NGPU %d -NSUB %d -UPLO %c %s\n\n", size[0], num_gpus0,num_subs0,
(uplo == MagmaLower ? 'L' : 'U'),(check == 1 ? "-check" : " "));
printf(" N CPU GFlop/s (sec) GPU GFlop/s (sec) ||R_magma-R_lapack||_F / ||R_lapack||_F\n");
printf("========================================================================================\n");
for(i=0; i<10; i++){
N = size[i];
lda = N;
n2 = lda*N;
gflops = FLOPS_DPOTRF( N ) / 1e9;;
nb = magma_get_dpotrf_nb(N);
if (num_subs0*num_gpus0 > N/nb) {
num_gpus = N/nb;
num_subs = 1;
if(N%nb != 0) num_gpus ++;
printf("too many GPUs for the matrix size, using %d GPUs\n", (int)num_gpus);
} else {
num_gpus = num_gpus0;
num_subs = num_subs0;
}
tot_subs = num_subs * num_gpus;
/* Allocate host memory for the matrix */
#ifdef USE_PINNED_CLMEMORY
cl_mem buffer1 = clCreateBuffer(gContext, CL_MEM_READ_WRITE | CL_MEM_ALLOC_HOST_PTR, n2*sizeof(double), NULL, NULL);
cl_mem buffer2 = clCreateBuffer(gContext, CL_MEM_READ_WRITE | CL_MEM_ALLOC_HOST_PTR, lda*nb*sizeof(double), NULL, NULL);
for (k=0; k<num_gpus; k++) {
h_R = (double*)clEnqueueMapBuffer(queues[2*k], buffer1, CL_TRUE, CL_MAP_READ | CL_MAP_WRITE, 0,
n2*sizeof(double), 0, NULL, NULL, NULL);
h_P = (double*)clEnqueueMapBuffer(queues[2*k], buffer2, CL_TRUE, CL_MAP_READ | CL_MAP_WRITE, 0,
lda*nb*sizeof(double), 0, NULL, NULL, NULL);
}
#else
TESTING_MALLOC_PIN( h_P, double, lda*nb );
TESTING_MALLOC_PIN( h_R, double, n2 );
#endif
/* Initialize the matrix */
init_matrix( N, h_R, lda );
/* Allocate GPU memory */
if (uplo == MagmaUpper) {
ldda = ((N+nb-1)/nb)*nb;
n_local = ((N+nb*tot_subs-1)/(nb*tot_subs))*nb;
} else {
ldda = ((N+nb*tot_subs-1)/(nb*tot_subs))*nb;
n_local = ((N+nb-1)/nb)*nb;
}
for (j=0; j<tot_subs; j++) {
TESTING_MALLOC_DEV( d_lA[j], double, n_local*ldda );
}
/* Warm up to measure the performance */
/* distribute matrix to gpus */
if (uplo == MagmaUpper) {
for (j=0; j<N; j+=nb) {
k = (j/nb)%tot_subs;
nk = min(nb, N-j);
magma_dsetmatrix( j+nk, nk,
&h_R[j*lda], lda,
d_lA[k], j/(nb*tot_subs)*nb*ldda, ldda,
queues[2*(k%num_gpus)]);
}
} else {
for (j=0; j<N; j+=nb) {
nk = min(nb, N-j);
for (magma_int_t kk = 0; kk<tot_subs; kk++) {
magma_int_t mk = 0;
for (magma_int_t ii=j+kk*nb; ii<N; ii+=nb*tot_subs) {
magma_int_t mii = min(nb, N-ii);
lapackf77_dlacpy( MagmaFullStr, &mii, &nk, &h_R[ii+j*lda], &lda, &h_P[mk], &lda );
mk += mii;
}
k = ((j+kk*nb)/nb)%tot_subs;
if (mk > 0 && nk > 0) {
magma_dsetmatrix( mk, nk,
h_P, lda,
d_lA[k], j*ldda+(j+kk*nb)/(nb*tot_subs)*nb, ldda,
queues[2*(k%num_gpus)]);
}
}
}
/*for (j=0; j<N; j+=nb) {
k = (j/nb)%tot_subs;
nk = min(nb, N-j);
magma_dsetmatrix( nk, j+nk, &h_R[j], lda,
d_lA[k], j/(nb*tot_subs)*nb, ldda,
queues[2*(k%num_gpus)]);
}*/
}
magma_dpotrf_msub( num_subs, num_gpus, uplo, N, d_lA, 0, ldda, queues, &info );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
/* distribute matrix to gpus */
if (uplo == MagmaUpper) {
for (j=0; j<N; j+=nb) {
k = (j/nb)%tot_subs;
nk = min(nb, N-j);
magma_dsetmatrix( j+nk, nk,
&h_R[j*lda], lda,
d_lA[k], j/(nb*tot_subs)*nb*ldda, ldda,
queues[2*(k%num_gpus)]);
}
} else {
for (j=0; j<N; j+=nb) {
nk = min(nb, N-j);
for (magma_int_t kk = 0; kk<tot_subs; kk++) {
magma_int_t mk = 0;
for (magma_int_t ii=j+kk*nb; ii<N; ii+=nb*tot_subs) {
magma_int_t mii = min(nb, N-ii);
lapackf77_dlacpy( MagmaFullStr, &mii, &nk, &h_R[ii+j*lda], &lda, &h_P[mk], &lda );
mk += mii;
}
k = ((j+kk*nb)/nb)%tot_subs;
if (mk > 0 && nk > 0) {
magma_dsetmatrix( mk, nk,
h_P, lda,
d_lA[k], j*ldda+(j+kk*nb)/(nb*tot_subs)*nb, ldda,
queues[2*(k%num_gpus)]);
}
}
}
/*for (j=0; j<N; j+=nb) {
k = (j/nb)%tot_subs;
nk = min(nb, N-j);
magma_dsetmatrix( nk, j+nk, &h_R[j], lda,
d_lA[k], (j/(nb*tot_subs)*nb), ldda,
queues[2*(k%num_gpus)]);
}*/
}
gpu_time = magma_wtime();
magma_dpotrf_msub( num_subs, num_gpus, uplo, N, d_lA, 0, ldda, queues, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf( "magma_dpotrf had error %d.\n", info );
/* gather matrix from gpus */
if (uplo==MagmaUpper) {
for (j=0; j<N; j+=nb) {
k = (j/nb)%tot_subs;
nk = min(nb, N-j);
magma_dgetmatrix( j+nk, nk,
d_lA[k], j/(nb*tot_subs)*nb*ldda, ldda,
&h_R[j*lda], lda, queues[2*(k%num_gpus)]);
}
} else {
for (j=0; j<N; j+=nb) {
nk = min(nb, N-j);
for (magma_int_t kk = 0; kk<tot_subs; kk++) {
k = ((j+kk*nb)/nb)%tot_subs;
magma_int_t mk = 0;
mk = 0;
for (magma_int_t ii=j+kk*nb; ii<N; ii+=nb*tot_subs) {
mk += min(nb, N-ii);
}
if (mk > 0 && nk > 0) {
magma_dgetmatrix( mk, nk,
d_lA[k], j*ldda+(j+kk*nb)/(nb*tot_subs)*nb, ldda,
h_P, lda,
queues[2*(k%num_gpus)]);
}
mk = 0;
for (magma_int_t ii=j+kk*nb; ii<N; ii+=nb*tot_subs) {
magma_int_t mii = min(nb, N-ii);
lapackf77_dlacpy( MagmaFullStr, &mii, &nk, &h_P[mk], &lda, &h_R[ii+j*lda], &lda );
mk += mii;
}
}
}
/*for (j=0; j<N; j+=nb) {
k = (j/nb)%tot_subs;
nk = min(nb, N-j);
magma_dgetmatrix( nk, j+nk,
d_lA[k], (j/(nb*tot_subs)*nb), ldda,
&h_R[j], lda, queues[2*(k%num_gpus)] );
}*/
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if (check == 1) {
double work[1], matnorm, diffnorm;
double *h_A;
TESTING_MALLOC_PIN( h_A, double, n2 );
init_matrix( N, h_A, lda );
cpu_time = magma_wtime();
if (uplo == MagmaLower) {
lapackf77_dpotrf( MagmaLowerStr, &N, h_A, &lda, &info );
} else {
lapackf77_dpotrf( MagmaUpperStr, &N, h_A, &lda, &info );
}
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf( "lapackf77_dpotrf had error %d.\n", info );
/* =====================================================================
Check the result compared to LAPACK
|R_magma - R_lapack| / |R_lapack|
=================================================================== */
matnorm = lapackf77_dlange("f", &N, &N, h_A, &lda, work);
blasf77_daxpy(&n2, &mz_one, h_A, &ione, h_R, &ione);
diffnorm = lapackf77_dlange("f", &N, &N, h_R, &lda, work);
printf( "%5d %6.2f (%6.2f) %6.2f (%6.2f) %e\n",
N, cpu_perf, cpu_time, gpu_perf, gpu_time, diffnorm / matnorm );
TESTING_FREE_PIN( h_A );
} else {
printf( "%5d - - (- -) %6.2f (%6.2f) - -\n",
N, gpu_perf, gpu_time );
}
// free memory
#ifdef USE_PINNED_CLMEMORY
for (k=0; k<num_gpus; k++) {
clEnqueueUnmapMemObject(queues[2*k], buffer1, h_R, 0, NULL, NULL);
clEnqueueUnmapMemObject(queues[2*k], buffer2, h_P, 0, NULL, NULL);
}
clReleaseMemObject(buffer1);
clReleaseMemObject(buffer2);
#else
TESTING_FREE_PIN( h_P );
TESTING_FREE_PIN( h_R );
#endif
for (j=0; j<tot_subs; j++) {
TESTING_FREE_DEV( d_lA[j] );
}
if (flag != 0)
break;
}
/* clean up */
for (i=0; i<num_gpus; i++) {
magma_queue_destroy( queues[2*i] );
magma_queue_destroy( queues[2*i+1] );
}
magma_finalize();
return 0;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dgehrd_m
*/
int main( int argc, char** argv)
{
TESTING_INIT();
magma_setdevice( 0 ); // without this, T -> dT copy fails
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
double *h_A, *h_R, *h_Q, *h_work, *tau, *twork, *T, *dT;
#if defined(PRECISION_z) || defined(PRECISION_c)
double *rwork;
#endif
double eps, result[2];
magma_int_t N, n2, lda, nb, lwork, ltwork, info;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
eps = lapackf77_dlamch( "E" );
magma_opts opts;
parse_opts( argc, argv, &opts );
double tol = opts.tolerance * lapackf77_dlamch("E");
printf(" N CPU GFlop/s (sec) GPU GFlop/s (sec) |A-QHQ'|/N|A| |I-QQ'|/N\n");
printf("=========================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
lda = N;
n2 = lda*N;
nb = magma_get_dgehrd_nb(N);
// magma needs larger workspace than lapack, esp. multi-gpu verison
lwork = N*(nb + nb*MagmaMaxGPUs);
gflops = FLOPS_DGEHRD( N ) / 1e9;
TESTING_MALLOC_CPU( h_A, double, n2 );
TESTING_MALLOC_CPU( tau, double, N );
TESTING_MALLOC_CPU( T, double, nb*N );
TESTING_MALLOC_PIN( h_R, double, n2 );
TESTING_MALLOC_PIN( h_work, double, lwork );
TESTING_MALLOC_DEV( dT, double, nb*N );
/* Initialize the matrices */
lapackf77_dlarnv( &ione, ISEED, &n2, h_A );
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
magma_dgehrd_m( N, ione, N, h_R, lda, tau, h_work, lwork, T, &info);
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_dgehrd_m returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Check the factorization
=================================================================== */
if ( opts.check ) {
ltwork = 2*(N*N);
TESTING_MALLOC_PIN( h_Q, double, lda*N );
TESTING_MALLOC_CPU( twork, double, ltwork );
#if defined(PRECISION_z) || defined(PRECISION_c)
TESTING_MALLOC_CPU( rwork, double, N );
#endif
lapackf77_dlacpy(MagmaUpperLowerStr, &N, &N, h_R, &lda, h_Q, &lda);
for( int j = 0; j < N-1; ++j )
for( int i = j+2; i < N; ++i )
h_R[i+j*lda] = MAGMA_D_ZERO;
magma_dsetmatrix( nb, N, T, nb, dT, nb );
magma_dorghr(N, ione, N, h_Q, lda, tau, dT, nb, &info);
if ( info != 0 ) {
printf("magma_dorghr returned error %d: %s.\n",
(int) info, magma_strerror( info ));
exit(1);
}
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_dhst01(&N, &ione, &N,
h_A, &lda, h_R, &lda,
h_Q, &lda, twork, <work, rwork, result);
#else
lapackf77_dhst01(&N, &ione, &N,
h_A, &lda, h_R, &lda,
h_Q, &lda, twork, <work, result);
#endif
TESTING_FREE_PIN( h_Q );
TESTING_FREE_CPU( twork );
#if defined(PRECISION_z) || defined(PRECISION_c)
TESTING_FREE_CPU( rwork );
#endif
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
lapackf77_dgehrd(&N, &ione, &N, h_R, &lda, tau, h_work, &lwork, &info);
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_dgehrd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* =====================================================================
Print performance and error.
=================================================================== */
if ( opts.lapack ) {
printf("%5d %7.2f (%7.2f) %7.2f (%7.2f)",
(int) N, cpu_perf, cpu_time, gpu_perf, gpu_time );
}
else {
printf("%5d --- ( --- ) %7.2f (%7.2f)",
(int) N, gpu_perf, gpu_time );
}
if ( opts.check ) {
printf(" %8.2e %8.2e %s\n",
result[0]*eps, result[1]*eps,
( ( (result[0]*eps < tol) && (result[1]*eps < tol) ) ? "ok" : "failed") );
status += ! (result[0]*eps < tol);
status += ! (result[1]*eps < tol);
}
else {
printf(" --- ---\n");
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( tau );
TESTING_FREE_CPU( T );
TESTING_FREE_PIN( h_R );
TESTING_FREE_PIN( h_work );
TESTING_FREE_DEV( dT );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dsysv
*/
int main( int argc, char** argv)
{
TESTING_INIT();
double *h_A, *h_B, *h_X, *work, temp;
real_Double_t gflops, gpu_perf, gpu_time = 0.0, cpu_perf=0, cpu_time=0;
double error, error_lapack = 0.0;
magma_int_t *ipiv;
magma_int_t N, n2, lda, ldb, sizeB, lwork, info;
magma_int_t status = 0, ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_opts opts;
opts.parse_opts( argc, argv );
double tol = opts.tolerance * lapackf77_dlamch("E");
printf("%% M N CPU Gflop/s (sec) GPU Gflop/s (sec) |Ax-b|/(N*|A|*|x|)\n");
printf("%%========================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
ldb = N;
lda = N;
n2 = lda*N;
sizeB = ldb*opts.nrhs;
gflops = ( FLOPS_DPOTRF( N ) + FLOPS_DPOTRS( N, opts.nrhs ) ) / 1e9;
TESTING_MALLOC_CPU( ipiv, magma_int_t, N );
TESTING_MALLOC_PIN( h_A, double, n2 );
TESTING_MALLOC_PIN( h_B, double, sizeB );
TESTING_MALLOC_PIN( h_X, double, sizeB );
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
lwork = -1;
lapackf77_dsysv(lapack_uplo_const(opts.uplo), &N, &opts.nrhs,
h_A, &lda, ipiv, h_X, &ldb, &temp, &lwork, &info);
lwork = (int)MAGMA_D_REAL(temp);
TESTING_MALLOC_CPU( work, double, lwork );
init_matrix( N, N, h_A, lda );
lapackf77_dlarnv( &ione, ISEED, &sizeB, h_B );
lapackf77_dlacpy( MagmaFullStr, &N, &opts.nrhs, h_B, &ldb, h_X, &ldb );
cpu_time = magma_wtime();
lapackf77_dsysv(lapack_uplo_const(opts.uplo), &N, &opts.nrhs,
h_A, &lda, ipiv, h_X, &ldb, work, &lwork, &info);
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0) {
printf("lapackf77_dsysv returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
error_lapack = get_residual( opts.uplo, N, opts.nrhs, h_A, lda, ipiv, h_X, ldb, h_B, ldb );
TESTING_FREE_CPU( work );
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
init_matrix( N, N, h_A, lda );
lapackf77_dlarnv( &ione, ISEED, &sizeB, h_B );
lapackf77_dlacpy( MagmaFullStr, &N, &opts.nrhs, h_B, &ldb, h_X, &ldb );
magma_setdevice(0);
gpu_time = magma_wtime();
magma_dsysv( opts.uplo, N, opts.nrhs, h_A, lda, ipiv, h_X, ldb, &info);
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0) {
printf("magma_dsysv returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* =====================================================================
Check the factorization
=================================================================== */
if ( opts.lapack ) {
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f)",
(int) N, (int) N, cpu_perf, cpu_time, gpu_perf, gpu_time );
}
else {
printf("%5d %5d --- ( --- ) %7.2f (%7.2f)",
(int) N, (int) N, gpu_perf, gpu_time );
}
if ( opts.check == 0 ) {
printf(" --- \n");
} else {
error = get_residual( opts.uplo, N, opts.nrhs, h_A, lda, ipiv, h_X, ldb, h_B, ldb );
printf(" %8.2e %s", error, (error < tol ? "ok" : "failed"));
if (opts.lapack)
printf(" (lapack rel.res. = %8.2e)", error_lapack);
printf("\n");
status += ! (error < tol);
}
TESTING_FREE_CPU( ipiv );
TESTING_FREE_PIN( h_X );
TESTING_FREE_PIN( h_B );
TESTING_FREE_PIN( h_A );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
/**
Purpose
-------
DLAEX3 finds the roots of the secular equation, as defined by the
values in D, W, and RHO, between 1 and K. It makes the
appropriate calls to DLAED4 and then updates the eigenvectors by
multiplying the matrix of eigenvectors of the pair of eigensystems
being combined by the matrix of eigenvectors of the K-by-K system
which is solved here.
It is used in the last step when only a part of the eigenvectors
is required.
It compute only the required part of the eigenvectors and the rest
is not used.
This code 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]
k INTEGER
The number of terms in the rational function to be solved by
DLAED4. K >= 0.
@param[in]
n INTEGER
The number of rows and columns in the Q matrix.
N >= K (deflation may result in N > K).
@param[in]
n1 INTEGER
The location of the last eigenvalue in the leading submatrix.
min(1,N) <= N1 <= N/2.
@param[out]
d DOUBLE PRECISION array, dimension (N)
D(I) contains the updated eigenvalues for
1 <= I <= K.
@param[out]
Q DOUBLE PRECISION array, dimension (LDQ,N)
Initially the first K columns are used as workspace.
On output the columns ??? to ??? contain
the updated eigenvectors.
@param[in]
ldq INTEGER
The leading dimension of the array Q. LDQ >= max(1,N).
@param[in]
rho DOUBLE PRECISION
The value of the parameter in the rank one update equation.
RHO >= 0 required.
@param[in,out]
dlamda DOUBLE PRECISION array, dimension (K)
The first K elements of this array contain the old roots
of the deflated updating problem. These are the poles
of the secular equation. May be changed on output by
having lowest order bit set to zero on Cray X-MP, Cray Y-MP,
Cray-2, or Cray C-90, as described above.
@param[in]
Q2 DOUBLE PRECISION array, dimension (LDQ2, N)
The first K columns of this matrix contain the non-deflated
eigenvectors for the split problem.
TODO what is LDQ2?
@param[in]
indx INTEGER array, dimension (N)
The permutation used to arrange the columns of the deflated
Q matrix into three groups (see DLAED2).
The rows of the eigenvectors found by DLAED4 must be likewise
permuted before the matrix multiply can take place.
@param[in]
ctot INTEGER array, dimension (4)
A count of the total number of the various types of columns
in Q, as described in INDX. The fourth column type is any
column which has been deflated.
@param[in,out]
w DOUBLE PRECISION array, dimension (K)
The first K elements of this array contain the components
of the deflation-adjusted updating vector. Destroyed on
output.
@param
s (workspace) DOUBLE PRECISION array, dimension (N1 + 1)*K
Will contain the eigenvectors of the repaired matrix which
will be multiplied by the previously accumulated eigenvectors
to update the system.
@param[out]
indxq INTEGER array, dimension (N)
On exit, the permutation which will reintegrate the
subproblems back into sorted order,
i.e. D( INDXQ( I = 1, N ) ) will be in ascending order.
@param
dwork (workspace) DOUBLE PRECISION array, dimension (3*N*N/2+3*N)
@param[in]
range magma_range_t
- = MagmaRangeAll: all eigenvalues will be found.
- = MagmaRangeV: all eigenvalues in the half-open interval (VL,VU]
will be found.
- = MagmaRangeI: the IL-th through IU-th eigenvalues will be found.
TODO verify range, vl, vu, il, iu -- copied from dlaex1.
@param[in]
vl DOUBLE PRECISION
@param[in]
vu DOUBLE PRECISION
if RANGE=MagmaRangeV, the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeI.
@param[in]
il INTEGER
@param[in]
iu INTEGER
if RANGE=MagmaRangeI, the indices (in ascending order) of the
smallest and largest eigenvalues to be returned.
1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeV.
@param[out]
info INTEGER
- = 0: successful exit.
- < 0: if INFO = -i, the i-th argument had an illegal value.
- > 0: if INFO = 1, an eigenvalue did not converge
Further Details
---------------
Based on contributions by
Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
Modified by Francoise Tisseur, University of Tennessee.
@ingroup magma_dsyev_aux
********************************************************************/
extern "C" magma_int_t
magma_dlaex3(magma_int_t k, magma_int_t n, magma_int_t n1, double* d,
double* Q, magma_int_t ldq, double rho,
double* dlamda, double* Q2, magma_int_t* indx,
magma_int_t* ctot, double* w, double* s, magma_int_t* indxq,
double* dwork,
magma_range_t range, double vl, double vu, magma_int_t il, magma_int_t iu,
magma_int_t* info )
{
#define Q(i_,j_) (Q + (i_) + (j_)*ldq)
double d_one = 1.;
double d_zero = 0.;
magma_int_t ione = 1;
magma_int_t ineg_one = -1;
magma_int_t iil, iiu, rk;
double* dq2= dwork;
double* ds = dq2 + n*(n/2+1);
double* dq = ds + n*(n/2+1);
magma_int_t lddq = n/2 + 1;
magma_int_t i, iq2, j, n12, n2, n23, tmp, lq2;
double temp;
magma_int_t alleig, valeig, indeig;
alleig = (range == MagmaRangeAll);
valeig = (range == MagmaRangeV);
indeig = (range == MagmaRangeI);
*info = 0;
if (k < 0)
*info=-1;
else if (n < k)
*info=-2;
else if (ldq < max(1,n))
*info=-6;
else if (! (alleig || valeig || indeig))
*info = -15;
else {
if (valeig) {
if (n > 0 && vu <= vl)
*info = -17;
}
else if (indeig) {
if (il < 1 || il > max(1,n))
*info = -18;
else if (iu < min(n,il) || iu > n)
*info = -19;
}
}
if (*info != 0) {
magma_xerbla(__func__, -(*info));
return *info;
}
// Quick return if possible
if (k == 0)
return *info;
/*
Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can
be computed with high relative accuracy (barring over/underflow).
This is a problem on machines without a guard digit in
add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2).
The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I),
which on any of these machines zeros out the bottommost
bit of DLAMDA(I) if it is 1; this makes the subsequent
subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation
occurs. On binary machines with a guard digit (almost all
machines) it does not change DLAMDA(I) at all. On hexadecimal
and decimal machines with a guard digit, it slightly
changes the bottommost bits of DLAMDA(I). It does not account
for hexadecimal or decimal machines without guard digits
(we know of none). We use a subroutine call to compute
2*DLAMBDA(I) to prevent optimizing compilers from eliminating
this code.*/
n2 = n - n1;
n12 = ctot[0] + ctot[1];
n23 = ctot[1] + ctot[2];
iq2 = n1 * n12;
lq2 = iq2 + n2 * n23;
magma_dsetvector_async( lq2, Q2, 1, dq2, 1, NULL );
#ifdef _OPENMP
/////////////////////////////////////////////////////////////////////////////////
//openmp implementation
/////////////////////////////////////////////////////////////////////////////////
magma_timer_t time=0;
timer_start( time );
#pragma omp parallel private(i, j, tmp, temp)
{
magma_int_t id = omp_get_thread_num();
magma_int_t tot = omp_get_num_threads();
magma_int_t ib = ( id * k) / tot; //start index of local loop
magma_int_t ie = ((id+1) * k) / tot; //end index of local loop
magma_int_t ik = ie - ib; //number of local indices
for (i = ib; i < ie; ++i)
dlamda[i]=lapackf77_dlamc3(&dlamda[i], &dlamda[i]) - dlamda[i];
for (j = ib; j < ie; ++j) {
magma_int_t tmpp=j+1;
magma_int_t iinfo = 0;
lapackf77_dlaed4(&k, &tmpp, dlamda, w, Q(0,j), &rho, &d[j], &iinfo);
// If the zero finder fails, the computation is terminated.
if (iinfo != 0) {
#pragma omp critical (info)
*info=iinfo;
break;
}
}
#pragma omp barrier
if (*info == 0) {
#pragma omp single
{
//Prepare the INDXQ sorting permutation.
magma_int_t nk = n - k;
lapackf77_dlamrg( &k, &nk, d, &ione, &ineg_one, indxq);
//compute the lower and upper bound of the non-deflated eigenvectors
if (valeig)
magma_dvrange(k, d, &iil, &iiu, vl, vu);
else if (indeig)
magma_dirange(k, indxq, &iil, &iiu, il, iu);
else {
iil = 1;
iiu = k;
}
rk = iiu - iil + 1;
}
if (k == 2) {
#pragma omp single
{
for (j = 0; j < k; ++j) {
w[0] = *Q(0,j);
w[1] = *Q(1,j);
i = indx[0] - 1;
*Q(0,j) = w[i];
i = indx[1] - 1;
*Q(1,j) = w[i];
}
}
}
else if (k != 1) {
// Compute updated W.
blasf77_dcopy( &ik, &w[ib], &ione, &s[ib], &ione);
// Initialize W(I) = Q(I,I)
tmp = ldq + 1;
blasf77_dcopy( &ik, Q(ib,ib), &tmp, &w[ib], &ione);
for (j = 0; j < k; ++j) {
magma_int_t i_tmp = min(j, ie);
for (i = ib; i < i_tmp; ++i)
w[i] = w[i] * ( *Q(i, j) / ( dlamda[i] - dlamda[j] ) );
i_tmp = max(j+1, ib);
for (i = i_tmp; i < ie; ++i)
w[i] = w[i] * ( *Q(i, j) / ( dlamda[i] - dlamda[j] ) );
}
for (i = ib; i < ie; ++i)
w[i] = copysign( sqrt( -w[i] ), s[i]);
#pragma omp barrier
//reduce the number of used threads to have enough S workspace
tot = min(n1, omp_get_num_threads());
if (id < tot) {
ib = ( id * rk) / tot + iil - 1;
ie = ((id+1) * rk) / tot + iil - 1;
ik = ie - ib;
}
else {
ib = -1;
ie = -1;
ik = -1;
}
// Compute eigenvectors of the modified rank-1 modification.
for (j = ib; j < ie; ++j) {
for (i = 0; i < k; ++i)
s[id*k + i] = w[i] / *Q(i,j);
temp = magma_cblas_dnrm2( k, s+id*k, 1 );
for (i = 0; i < k; ++i) {
magma_int_t iii = indx[i] - 1;
*Q(i,j) = s[id*k + iii] / temp;
}
}
}
}
}
if (*info != 0)
return *info;
timer_stop( time );
timer_printf( "eigenvalues/vector D+zzT = %6.2f\n", time );
#else
/////////////////////////////////////////////////////////////////////////////////
// Non openmp implementation
/////////////////////////////////////////////////////////////////////////////////
magma_timer_t time=0;
timer_start( time );
for (i = 0; i < k; ++i)
dlamda[i]=lapackf77_dlamc3(&dlamda[i], &dlamda[i]) - dlamda[i];
for (j = 0; j < k; ++j) {
magma_int_t tmpp=j+1;
magma_int_t iinfo = 0;
lapackf77_dlaed4(&k, &tmpp, dlamda, w, Q(0,j), &rho, &d[j], &iinfo);
// If the zero finder fails, the computation is terminated.
if (iinfo != 0)
*info=iinfo;
}
if (*info != 0)
return *info;
//Prepare the INDXQ sorting permutation.
magma_int_t nk = n - k;
lapackf77_dlamrg( &k, &nk, d, &ione, &ineg_one, indxq);
//compute the lower and upper bound of the non-deflated eigenvectors
if (valeig)
magma_dvrange(k, d, &iil, &iiu, vl, vu);
else if (indeig)
magma_dirange(k, indxq, &iil, &iiu, il, iu);
else {
iil = 1;
iiu = k;
}
rk = iiu - iil + 1;
if (k == 2) {
for (j = 0; j < k; ++j) {
w[0] = *Q(0,j);
w[1] = *Q(1,j);
i = indx[0] - 1;
*Q(0,j) = w[i];
i = indx[1] - 1;
*Q(1,j) = w[i];
}
}
else if (k != 1) {
// Compute updated W.
blasf77_dcopy( &k, w, &ione, s, &ione);
// Initialize W(I) = Q(I,I)
tmp = ldq + 1;
blasf77_dcopy( &k, Q, &tmp, w, &ione);
for (j = 0; j < k; ++j) {
for (i = 0; i < j; ++i)
w[i] = w[i] * ( *Q(i, j) / ( dlamda[i] - dlamda[j] ) );
for (i = j+1; i < k; ++i)
w[i] = w[i] * ( *Q(i, j) / ( dlamda[i] - dlamda[j] ) );
}
for (i = 0; i < k; ++i)
w[i] = copysign( sqrt( -w[i] ), s[i]);
// Compute eigenvectors of the modified rank-1 modification.
for (j = iil-1; j < iiu; ++j) {
for (i = 0; i < k; ++i)
s[i] = w[i] / *Q(i,j);
temp = magma_cblas_dnrm2( k, s, 1 );
for (i = 0; i < k; ++i) {
magma_int_t iii = indx[i] - 1;
*Q(i,j) = s[iii] / temp;
}
}
}
timer_stop( time );
timer_printf( "eigenvalues/vector D+zzT = %6.2f\n", time );
#endif //_OPENMP
// Compute the updated eigenvectors.
timer_start( time );
magma_queue_sync( NULL );
if (rk != 0) {
if ( n23 != 0 ) {
if (rk < magma_get_dlaed3_k()) {
lapackf77_dlacpy("A", &n23, &rk, Q(ctot[0],iil-1), &ldq, s, &n23);
blasf77_dgemm("N", "N", &n2, &rk, &n23, &d_one, &Q2[iq2], &n2,
s, &n23, &d_zero, Q(n1,iil-1), &ldq );
} else {
magma_dsetmatrix( n23, rk, Q(ctot[0],iil-1), ldq, ds, n23 );
magma_dgemm( MagmaNoTrans, MagmaNoTrans, n2, rk, n23, d_one, &dq2[iq2], n2, ds, n23, d_zero, dq, lddq);
magma_dgetmatrix( n2, rk, dq, lddq, Q(n1,iil-1), ldq );
}
} else
lapackf77_dlaset("A", &n2, &rk, &d_zero, &d_zero, Q(n1,iil-1), &ldq);
if ( n12 != 0 ) {
if (rk < magma_get_dlaed3_k()) {
lapackf77_dlacpy("A", &n12, &rk, Q(0,iil-1), &ldq, s, &n12);
blasf77_dgemm("N", "N", &n1, &rk, &n12, &d_one, Q2, &n1,
s, &n12, &d_zero, Q(0,iil-1), &ldq);
} else {
magma_dsetmatrix( n12, rk, Q(0,iil-1), ldq, ds, n12 );
magma_dgemm( MagmaNoTrans, MagmaNoTrans, n1, rk, n12, d_one, dq2, n1, ds, n12, d_zero, dq, lddq);
magma_dgetmatrix( n1, rk, dq, lddq, Q(0,iil-1), ldq );
}
} else
lapackf77_dlaset("A", &n1, &rk, &d_zero, &d_zero, Q(0,iil-1), &ldq);
}
timer_stop( time );
timer_printf( "gemms = %6.2f\n", time );
return *info;
} /* magma_dlaex3 */
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;
}
extern "C" magma_int_t
magma_dlaex0(magma_int_t n, double* d, double* e, double* q, magma_int_t ldq,
double* work, magma_int_t* iwork, magmaDouble_ptr dwork,
magma_vec_t range, double vl, double vu,
magma_int_t il, magma_int_t iu, magma_int_t* info, magma_queue_t queue)
{
/*
-- MAGMA (version 1.1.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
@date January 2014
.. Scalar Arguments ..
CHARACTER RANGE
INTEGER IL, IU, INFO, LDQ, N
DOUBLE PRECISION VL, VU
..
.. Array Arguments ..
INTEGER IWORK( * )
DOUBLE PRECISION D( * ), E( * ), Q( LDQ, * ),
$ WORK( * ), DWORK( * )
..
Purpose
=======
DLAEX0 computes all eigenvalues and the choosen eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer method.
Arguments
=========
N (input) INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
D (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the main diagonal of the tridiagonal matrix.
On exit, its eigenvalues.
E (input) DOUBLE PRECISION array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix.
On exit, E has been destroyed.
Q (input/output) DOUBLE PRECISION array, dimension (LDQ, N)
On entry, Q will be the identity matrix.
On exit, Q contains the eigenvectors of the
tridiagonal matrix.
LDQ (input) INTEGER
The leading dimension of the array Q. If eigenvectors are
desired, then LDQ >= max(1,N). In any case, LDQ >= 1.
WORK (workspace) DOUBLE PRECISION array,
the dimension of WORK must be at least 4*N + N**2.
IWORK (workspace) INTEGER array,
the dimension of IWORK must be at least 3 + 5*N.
DWORK (device workspace) DOUBLE PRECISION array, dimension (3*N*N/2+3*N)
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.
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'.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: 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
=====================================================================
*/
magma_int_t ione = 1;
magma_vec_t range_ = range;
magma_int_t curlvl, curprb, i, indxq;
magma_int_t j, k, matsiz, msd2, smlsiz;
magma_int_t submat, subpbs, tlvls;
// Test the input parameters.
*info = 0;
if( n < 0 )
*info = -1;
else if( ldq < max(1, n) )
*info = -5;
if( *info != 0 ){
magma_xerbla( __func__, -*info );
return MAGMA_ERR_ILLEGAL_VALUE;
}
// Quick return if possible
if(n == 0)
return MAGMA_SUCCESS;
smlsiz = get_dlaex0_smlsize();
// Determine the size and placement of the submatrices, and save in
// the leading elements of IWORK.
iwork[0] = n;
subpbs= 1;
tlvls = 0;
while (iwork[subpbs - 1] > smlsiz) {
for (j = subpbs; j > 0; --j){
iwork[2*j - 1] = (iwork[j-1]+1)/2;
iwork[2*j - 2] = iwork[j-1]/2;
}
++tlvls;
subpbs *= 2;
}
for (j=1; j<subpbs; ++j)
iwork[j] += iwork[j-1];
// Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1
// using rank-1 modifications (cuts).
for(i=0; i < subpbs-1; ++i){
submat = iwork[i];
d[submat-1] -= MAGMA_D_ABS(e[submat-1]);
d[submat] -= MAGMA_D_ABS(e[submat-1]);
}
indxq = 4*n + 3;
// Solve each submatrix eigenproblem at the bottom of the divide and
// conquer tree.
char char_I[] = {'I', 0};
//#define ENABLE_TIMER
#ifdef ENABLE_TIMER
magma_timestr_t start, end;
start = get_current_time();
#endif
for (i = 0; i < subpbs; ++i){
if(i == 0){
submat = 0;
matsiz = iwork[0];
} else {
submat = iwork[i-1];
matsiz = iwork[i] - iwork[i-1];
}
lapackf77_dsteqr(char_I , &matsiz, &d[submat], &e[submat],
Q(submat, submat), &ldq, work, info); // change to edc?
if(*info != 0){
printf("info: %d\n, submat: %d\n", (int) *info, (int) submat);
*info = (submat+1)*(n+1) + submat + matsiz;
printf("info: %d\n", (int) *info);
return MAGMA_SUCCESS;
}
k = 1;
for(j = submat; j < iwork[i]; ++j){
iwork[indxq+j] = k;
++k;
}
}
#ifdef ENABLE_TIMER
end = get_current_time();
printf("for: dsteqr = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
// Successively merge eigensystems of adjacent submatrices
// into eigensystem for the corresponding larger matrix.
curlvl = 1;
while (subpbs > 1){
#ifdef ENABLE_TIMER
magma_timestr_t start, end;
start = get_current_time();
#endif
for (i=0; i<subpbs-1; i+=2){
if(i == 0){
submat = 0;
matsiz = iwork[1];
msd2 = iwork[0];
} else {
submat = iwork[i-1];
matsiz = iwork[i+1] - iwork[i-1];
msd2 = matsiz / 2;
}
// Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2)
// into an eigensystem of size MATSIZ.
// DLAEX1 is used only for the full eigensystem of a tridiagonal
// matrix.
if (matsiz == n)
range_=range;
else
// We need all the eigenvectors if it is not last step
range_= MagmaAllVec;
magma_dlaex1(matsiz, &d[submat], Q(submat, submat), ldq,
&iwork[indxq+submat], e[submat+msd2-1], msd2,
work, &iwork[subpbs], dwork,
range_, vl, vu, il, iu, info, queue);
if(*info != 0){
*info = (submat+1)*(n+1) + submat + matsiz;
return MAGMA_SUCCESS;
}
iwork[i/2]= iwork[i+1];
}
subpbs /= 2;
++curlvl;
#ifdef ENABLE_TIMER
end = get_current_time();
printf("%d: time: %6.2f\n", curlvl, GetTimerValue(start,end)/1000.);
#endif
}
// Re-merge the eigenvalues/vectors which were deflated at the final
// merge step.
for(i = 0; i<n; ++i){
j = iwork[indxq+i] - 1;
work[i] = d[j];
blasf77_dcopy(&n, Q(0, j), &ione, &work[ n*(i+1) ], &ione);
}
blasf77_dcopy(&n, work, &ione, d, &ione);
char char_A[] = {'A',0};
lapackf77_dlacpy ( char_A, &n, &n, &work[n], &n, q, &ldq );
return MAGMA_SUCCESS;
} /* magma_dlaex0 */
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 */
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dgetrf
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf=0, cpu_time=0;
double error;
double *h_A, *h_R;
magmaDouble_ptr d_A;
magma_int_t *ipiv;
magma_int_t M, N, n2, lda, ldda, info, min_mn;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
double tol = opts.tolerance * lapackf77_dlamch("E");
printf("%% M N CPU Gflop/s (ms) GPU Gflop/s (ms) Copy time (ms) ||PA-LU||/(||A||*N)\n");
printf("%%======================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[itest];
N = opts.nsize[itest];
min_mn = min(M, N);
lda = M;
n2 = lda*N;
ldda = magma_roundup( M, opts.align ); // multiple of 32 by default
gflops = FLOPS_DGETRF( M, N ) / 1e9;
if ( N > 512 ) {
printf( "%5d %5d skipping because dgetf2 does not support N > 512\n", (int) M, (int) N );
continue;
}
TESTING_MALLOC_CPU( ipiv, magma_int_t, min_mn );
TESTING_MALLOC_CPU( h_A, double, n2 );
TESTING_MALLOC_PIN( h_R, double, n2 );
TESTING_MALLOC_DEV( d_A, double, ldda*N );
/* Initialize the matrix */
lapackf77_dlarnv( &ione, ISEED, &n2, h_A );
lapackf77_dlacpy( MagmaFullStr, &M, &N, h_A, &lda, h_R, &lda );
real_Double_t set_time = magma_wtime();
magma_dsetmatrix( M, N, h_R, lda, d_A, ldda, opts.queue );
set_time = magma_wtime() - set_time;
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
lapackf77_dgetrf( &M, &N, h_A, &lda, ipiv, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0) {
printf("lapackf77_dgetrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_sync_wtime( opts.queue );
magma_dgetf2_gpu( M, N, d_A, ldda, ipiv, opts.queue, &info );
gpu_time = magma_sync_wtime( opts.queue ) - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0) {
printf("magma_dgetf2_gpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
real_Double_t get_time = magma_wtime();
magma_dgetmatrix( M, N, d_A, ldda, h_A, lda, opts.queue );
get_time = magma_wtime() - get_time;
/* =====================================================================
Check the factorization
=================================================================== */
if ( opts.lapack ) {
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %7.2f",
(int) M, (int) N, cpu_perf, cpu_time*1000., gpu_perf, gpu_time*1000.,
set_time*1000.+get_time*1000.);
}
else {
printf("%5d %5d --- ( --- ) %7.2f (%7.2f) %7.2f",
(int) M, (int) N, gpu_perf, gpu_time*1000., set_time*1000.+get_time*1000. );
}
if ( opts.check ) {
magma_dgetmatrix( M, N, d_A, ldda, h_A, lda, opts.queue );
error = get_LU_error( M, N, h_R, lda, h_A, ipiv );
printf(" %8.2e %s\n", error, (error < tol ? "ok" : "failed") );
status += ! (error < tol);
}
else {
printf(" --- \n");
}
TESTING_FREE_CPU( ipiv );
TESTING_FREE_CPU( h_A );
TESTING_FREE_PIN( h_R );
TESTING_FREE_DEV( d_A );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
/**
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 */
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dpotrf
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
double *h_A, *h_R;
double *d_A;
double c_neg_one = MAGMA_D_NEG_ONE;
magma_int_t N, n2, lda, ldda, info;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
double work[1], error;
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
opts.lapack |= opts.check; // check (-c) implies lapack (-l)
double tol = opts.tolerance * lapackf77_dlamch("E");
printf(" N CPU GFlop/s (sec) GPU GFlop/s (sec) ||R||_F / ||A||_F\n");
printf("=================================================================\n");
for( int i = 0; i < opts.ntest; ++i ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[i];
lda = N;
n2 = lda*N;
ldda = ((N+31)/32)*32;
gflops = FLOPS_DPOTRI( N ) / 1e9;
TESTING_MALLOC_CPU( h_A, double, n2 );
TESTING_MALLOC_PIN( h_R, double, n2 );
TESTING_MALLOC_DEV( d_A, double, ldda*N );
/* Initialize the matrix */
lapackf77_dlarnv( &ione, ISEED, &n2, h_A );
magma_dmake_hpd( N, h_A, lda );
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
/* factorize matrix */
magma_dsetmatrix( N, N, h_A, lda, d_A, ldda );
magma_dpotrf_gpu( opts.uplo, N, d_A, ldda, &info );
// check for exact singularity
//magma_dgetmatrix( N, N, d_A, ldda, h_R, lda );
//h_R[ 10 + 10*lda ] = MAGMA_D_MAKE( 0.0, 0.0 );
//magma_dsetmatrix( N, N, h_R, lda, d_A, ldda );
gpu_time = magma_wtime();
magma_dpotri_gpu( opts.uplo, N, d_A, ldda, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_dpotri_gpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
lapackf77_dpotrf( &opts.uplo, &N, h_A, &lda, &info );
cpu_time = magma_wtime();
lapackf77_dpotri( &opts.uplo, &N, h_A, &lda, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_dpotri returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Check the result compared to LAPACK
=================================================================== */
magma_dgetmatrix( N, N, d_A, ldda, h_R, lda );
error = lapackf77_dlange("f", &N, &N, h_A, &lda, work);
blasf77_daxpy(&n2, &c_neg_one, h_A, &ione, h_R, &ione);
error = lapackf77_dlange("f", &N, &N, h_R, &lda, work) / error;
printf("%5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e%s\n",
(int) N, cpu_perf, cpu_time, gpu_perf, gpu_time,
error, (error < tol ? "" : " failed") );
status |= ! (error < tol);
}
else {
printf("%5d --- ( --- ) %7.2f (%7.2f) ---\n",
(int) N, gpu_perf, gpu_time );
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_PIN( h_R );
TESTING_FREE_DEV( d_A );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dgeqrf
*/
int main( int argc, char** argv)
{
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
double error, work[1];
double c_neg_one = MAGMA_D_NEG_ONE;
double *h_A, *h_T, *h_R, *tau, *h_work, tmp[1];
magmaDouble_ptr d_A, d_T, ddA, dtau;
magmaDouble_ptr dwork;
/* Matrix size */
magma_int_t M = 0, N = 0, n2, lda, ldda, lwork;
const int MAXTESTS = 10;
magma_int_t msize[MAXTESTS] = { 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 8100, 8192 };
magma_int_t nsize[MAXTESTS] = { 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 8100, 8192 };
magma_int_t i, info, min_mn;
magma_int_t ione = 1;
//magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t checkres;
checkres = getenv("MAGMA_TESTINGS_CHECK") != NULL;
// process command line arguments
printf( "\nUsage: %s -N <m,n> -c\n", argv[0] );
printf( " -N can be repeated up to %d times. If only m is given, then m=n.\n", MAXTESTS );
printf( " -c or setting $MAGMA_TESTINGS_CHECK runs LAPACK and checks result.\n\n" );
int ntest = 0;
for( int i = 1; i < argc; ++i ) {
if ( strcmp("-N", argv[i]) == 0 && i+1 < argc ) {
magma_assert( ntest < MAXTESTS, "error: -N repeated more than maximum %d tests\n", MAXTESTS );
int m, n;
info = sscanf( argv[++i], "%d,%d", &m, &n );
if ( info == 2 && m > 0 && n > 0 ) {
msize[ ntest ] = m;
nsize[ ntest ] = n;
}
else if ( info == 1 && m > 0 ) {
msize[ ntest ] = m;
nsize[ ntest ] = m; // implicitly
}
else {
printf( "error: -N %s is invalid; ensure m > 0, n > 0.\n", argv[i] );
exit(1);
}
M = max( M, msize[ ntest ] );
N = max( N, nsize[ ntest ] );
ntest++;
}
else if ( strcmp("-M", argv[i]) == 0 ) {
printf( "-M has been replaced in favor of -N m,n to allow -N to be repeated.\n\n" );
exit(1);
}
else if ( strcmp("-c", argv[i]) == 0 ) {
checkres = true;
}
else {
printf( "invalid argument: %s\n", argv[i] );
exit(1);
}
}
if ( ntest == 0 ) {
ntest = MAXTESTS;
M = msize[ntest-1];
N = nsize[ntest-1];
}
ldda = ((M+31)/32)*32;
n2 = M * N;
min_mn = min(M, N);
/* Initialize */
magma_queue_t queue;
magma_device_t device[ MagmaMaxGPUs ];
int num = 0;
magma_err_t err;
magma_init();
err = magma_get_devices( device, MagmaMaxGPUs, &num );
if ( err != 0 || num < 1 ) {
fprintf( stderr, "magma_get_devices failed: %d\n", err );
exit(-1);
}
err = magma_queue_create( device[0], &queue );
if ( err != 0 ) {
fprintf( stderr, "magma_queue_create failed: %d\n", err );
exit(-1);
}
/* Allocate memory for the matrix */
TESTING_MALLOC_PIN( tau, double, min_mn );
TESTING_MALLOC_PIN( h_A, double, n2 );
TESTING_MALLOC_PIN( h_T, double, N*N );
TESTING_MALLOC_PIN( h_R, double, n2 );
TESTING_MALLOC_DEV( d_A, double, ldda*N );
TESTING_MALLOC_DEV( d_T, double, N*N );
TESTING_MALLOC_DEV( ddA, double, N*N );
TESTING_MALLOC_DEV( dtau, double, min_mn );
TESTING_MALLOC_DEV( dwork, double, max(5*min_mn, (32*2+2)*min_mn) );
double *h1 = (double*)malloc(sizeof(double)*N*N);
memset(h1, 0, N*N*sizeof(double));
clEnqueueWriteBuffer(queue, ddA, CL_TRUE, 0, sizeof(double)*N*N, h1, 0, NULL, NULL);
clEnqueueWriteBuffer(queue, d_T, CL_TRUE, 0, sizeof(double)*N*N, h1, 0, NULL, NULL);
lwork = -1;
lapackf77_dgeqrf(&M, &N, h_A, &M, tau, tmp, &lwork, &info);
lwork = (magma_int_t)MAGMA_D_REAL( tmp[0] );
lwork = max(lwork, N*N);
TESTING_MALLOC_PIN( h_work, double, lwork );
printf(" M N CPU GFlop/s (ms) GPU GFlop/s (ms) ||R||_F/||A||_F ||R_T||\n");
printf("=============================================================================\n");
for( i = 0; i < ntest; ++i ) {
M = msize[i];
N = nsize[i];
min_mn= min(M, N);
lda = M;
n2 = lda*N;
ldda = ((M+31)/32)*32;
gflops = (FLOPS_DGEQRF( M, N ) + FLOPS_DGEQRT( M, N)) / 1e9;
/* Initialize the matrix */
magma_int_t ISEED[4] = {0,0,0,1};
lapackf77_dlarnv( &ione, ISEED, &n2, h_A );
lapackf77_dlacpy( MagmaUpperLowerStr, &M, &N, h_A, &lda, h_R, &lda );
magma_dsetmatrix( M, N, h_R, 0, lda, d_A, 0, ldda, queue );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
// warm-up
// magma_dgeqr2x3_gpu(&M, &N, d_A, 0, &ldda, dtau, 0, d_T, 0, ddA, 0, dwork, 0, &info, queue);
/*
magma_dsetmatrix( M, N, h_R, 0, lda, d_A, 0, ldda, queue );
clEnqueueWriteBuffer(queue, ddA, CL_TRUE, 0, sizeof(double)*N*N, h1, 0, NULL, NULL);
clEnqueueWriteBuffer(queue, d_T, CL_TRUE, 0, sizeof(double)*N*N, h1, 0, NULL, NULL);
*/
gpu_time = magma_wtime();
magma_dgeqr2x3_gpu(&M, &N, d_A, 0, &ldda, dtau, 0, d_T, 0, ddA, 0, dwork, 0, &info, queue);
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_dgeqrf returned error %d.\n", (int) info);
if ( checkres ) {
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
lapackf77_dgeqrf(&M, &N, h_A, &lda, tau, h_work, &lwork, &info);
lapackf77_dlarft( MagmaForwardStr, MagmaColumnwiseStr,
&M, &N, h_A, &lda, tau, h_work, &N);
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_dgeqrf returned error %d.\n", (int) info);
/* =====================================================================
Check the result compared to LAPACK
=================================================================== */
magma_dgetmatrix( M, N, d_A, 0, ldda, h_R, 0, M, queue );
magma_dgetmatrix( N, N, ddA, 0, N, h_T, 0, N, queue );
// Restore the upper triangular part of A before the check
for(int col=0; col<N; col++){
for(int row=0; row<=col; row++)
h_R[row + col*M] = h_T[row + col*N];
}
error = lapackf77_dlange("M", &M, &N, h_A, &lda, work);
blasf77_daxpy(&n2, &c_neg_one, h_A, &ione, h_R, &ione);
error = lapackf77_dlange("M", &M, &N, h_R, &lda, work) / error;
// Check if T is the same
double terr = 0.;
magma_dgetmatrix( N, N, d_T, 0, N, h_T, 0, N, queue );
for(int col=0; col<N; col++)
for(int row=0; row<=col; row++)
terr += ( MAGMA_D_ABS(h_work[row + col*N] - h_T[row + col*N])*
MAGMA_D_ABS(h_work[row + col*N] - h_T[row + col*N]) );
terr = magma_dsqrt(terr);
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %8.2e\n",
(int) M, (int) N, cpu_perf, 1000.*cpu_time, gpu_perf, 1000.*gpu_time,
error, terr);
}
else {
printf("%5d %5d --- ( --- ) %7.2f (%7.2f) --- \n",
(int) M, (int) N, gpu_perf, 1000.*gpu_time);
}
}
/* Memory clean up */
TESTING_FREE_PIN( tau );
TESTING_FREE_PIN( h_A );
TESTING_FREE_PIN( h_T );
TESTING_FREE_PIN( h_work );
TESTING_FREE_PIN( h_R );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_T );
TESTING_FREE_DEV( ddA );
TESTING_FREE_DEV( dtau );
free(h1);
magma_queue_destroy( queue );
magma_finalize();
}
/***************************************************************************//**
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
---------
@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[in]
T DOUBLE PRECISION array, dimension (NB, min(M,N)).
T contains the T matrices used in blocking the elementary
reflectors H(i), e.g., this can be the 6th argument of
magma_dgeqrf_gpu (except stored on the CPU, not the GPU).
@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 T.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_ungqr
*******************************************************************************/
extern "C" magma_int_t
magma_dorgqr_m(
magma_int_t m, magma_int_t n, magma_int_t k,
double *A, magma_int_t lda,
double *tau,
double *T, magma_int_t nb,
magma_int_t *info)
{
#define A(i,j) ( A + (i) + (j)*lda )
#define dA(d,i,j) (dA[d] + (i) + (j)*ldda)
#define dT(d,i,j) (dT[d] + (i) + (j)*nb)
double c_zero = MAGMA_D_ZERO;
double c_one = MAGMA_D_ONE;
magma_int_t m_kk, n_kk, k_kk, mi;
magma_int_t lwork, ldwork;
magma_int_t d, i, ib, j, jb, ki, kk;
double *work=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;
}
magma_int_t di, dn;
magma_int_t dpanel;
magma_int_t ngpu = magma_num_gpus();
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
// Allocate memory on GPUs for A and workspaces
magma_int_t ldda = magma_roundup( m, 32 );
magma_int_t lddwork = magma_roundup( n, 32 );
magma_int_t min_lblocks = (n / nb) / ngpu; // min. blocks per gpu
magma_int_t last_dev = (n / nb) % ngpu; // device with last block
magma_int_t nlocal[ MagmaMaxGPUs ] = { 0 };
double *dA[ MagmaMaxGPUs ] = { NULL };
double *dT[ MagmaMaxGPUs ] = { NULL };
double *dV[ MagmaMaxGPUs ] = { NULL };
double *dW[ MagmaMaxGPUs ] = { NULL };
magma_queue_t queues[ MagmaMaxGPUs ] = { NULL };
for( d = 0; d < ngpu; ++d ) {
// example with n = 75, nb = 10, ngpu = 3
// min_lblocks = 2
// last_dev = 1
// gpu 0: 2 blocks, cols: 0- 9, 30-39, 60-69
// gpu 1: 1+ blocks, cols: 10-19, 40-49, 70-74 (partial)
// gpu 2: 1 block, cols: 20-29, 50-59
magma_setdevice( d );
nlocal[d] = min_lblocks*nb;
if ( d < last_dev ) {
nlocal[d] += nb;
}
else if ( d == last_dev ) {
nlocal[d] += (n % nb);
}
ldwork = nlocal[d]*ldda // dA
+ nb*m // dT
+ nb*ldda // dV
+ nb*lddwork; // dW
if ( MAGMA_SUCCESS != magma_dmalloc( &dA[d], ldwork )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
goto cleanup;
}
dT[d] = dA[d] + nlocal[d]*ldda;
dV[d] = dT[d] + nb*m;
dW[d] = dV[d] + nb*ldda;
magma_queue_create( d, &queues[d] );
}
trace_init( 1, ngpu, 1, queues );
// 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 CPU work space
// n*nb for larfb work
// m*nb for V
// nb*nb for T
lwork = (n + m + nb) * nb;
magma_dmalloc_cpu( &work, lwork );
if (work == NULL) {
*info = MAGMA_ERR_HOST_ALLOC;
goto cleanup;
}
double *work_T, *work_V;
work_T = work + n*nb;
work_V = work + n*nb + nb*nb;
// Use unblocked code for the last or only block.
if (kk < n) {
trace_cpu_start( 0, "ungqr", "ungqr last block" );
m_kk = m - kk;
n_kk = n - kk;
k_kk = k - kk;
// dorgqr requires less workspace (n*nb), but is slow if k < dorgqr's block size.
// replacing it with the 4 routines below is much faster (e.g., 60x).
//magma_int_t iinfo;
//lapackf77_dorgqr( &m_kk, &n_kk, &k_kk,
// A(kk, kk), &lda,
// &tau[kk], work, &lwork, &iinfo );
lapackf77_dlacpy( MagmaFullStr, &m_kk, &k_kk, A(kk,kk), &lda, work_V, &m_kk);
lapackf77_dlaset( MagmaFullStr, &m_kk, &n_kk, &c_zero, &c_one, A(kk, kk), &lda );
lapackf77_dlarft( MagmaForwardStr, MagmaColumnwiseStr,
&m_kk, &k_kk,
work_V, &m_kk, &tau[kk], work_T, &k_kk);
lapackf77_dlarfb( MagmaLeftStr, MagmaNoTransStr, MagmaForwardStr, MagmaColumnwiseStr,
&m_kk, &n_kk, &k_kk,
work_V, &m_kk, work_T, &k_kk, A(kk, kk), &lda, work, &n_kk );
if (kk > 0) {
for( j=kk; j < n; j += nb ) {
jb = min( n-j, nb );
d = (j / nb) % ngpu;
di = ((j / nb) / ngpu) * nb;
magma_setdevice( d );
magma_dsetmatrix( m_kk, jb,
A(kk, j), lda,
dA(d, kk, di), ldda, queues[d] );
// Set A(1:kk,kk+1:n) to zero.
magmablas_dlaset( MagmaFull, kk, jb, c_zero, c_zero, dA(d, 0, di), ldda, queues[d] );
}
}
trace_cpu_end( 0 );
}
if (kk > 0) {
// Use blocked code
// send T to all GPUs
for( d = 0; d < ngpu; ++d ) {
magma_setdevice( d );
trace_gpu_start( d, 0, "set", "set T" );
magma_dsetmatrix_async( nb, min(m,n), T, nb, dT[d], nb, queues[d] );
trace_gpu_end( d, 0 );
}
// queue: set Aii (V) --> laset --> laset --> larfb --> [next]
// CPU has no computation
for( i = ki; i >= 0; i -= nb ) {
ib = min(nb, k - i);
mi = m - i;
dpanel = (i / nb) % ngpu;
di = ((i / nb) / ngpu) * nb;
// Send current panel to dV on the GPUs
lapackf77_dlaset( "Upper", &ib, &ib, &c_zero, &c_one, A(i, i), &lda );
for( d = 0; d < ngpu; ++d ) {
magma_setdevice( d );
trace_gpu_start( d, 0, "set", "set V" );
magma_dsetmatrix_async( mi, ib,
A(i, i), lda,
dV[d], ldda, queues[d] );
trace_gpu_end( d, 0 );
}
// set panel to identity
magma_setdevice( dpanel );
trace_gpu_start( dpanel, 0, "laset", "laset" );
magmablas_dlaset( MagmaFull, i, ib, c_zero, c_zero, dA(dpanel, 0, di), ldda, queues[dpanel] );
magmablas_dlaset( MagmaFull, mi, ib, c_zero, c_one, dA(dpanel, i, di), ldda, queues[dpanel] );
trace_gpu_end( dpanel, 0 );
if (i < n) {
// Apply H to A(i:m,i:n) from the left
for( d = 0; d < ngpu; ++d ) {
magma_setdevice( d );
magma_indices_1D_bcyclic( nb, ngpu, d, i, n, &di, &dn );
trace_gpu_start( d, 0, "larfb", "larfb" );
magma_dlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise,
mi, dn-di, ib,
dV[d], ldda, dT(d,0,i), nb,
dA(d, i, di), ldda, dW[d], lddwork, queues[d] );
trace_gpu_end( d, 0 );
}
}
}
// copy result back to CPU
trace_cpu_start( 0, "get", "get A" );
magma_dgetmatrix_1D_col_bcyclic( ngpu, m, n, nb, dA, ldda, A, lda, queues );
trace_cpu_end( 0 );
}
#ifdef TRACING
char name[80];
snprintf( name, sizeof(name), "dorgqr-n%lld-ngpu%lld.svg", (long long) m, (long long) ngpu );
trace_finalize( name, "trace.css" );
#endif
cleanup:
for( d = 0; d < ngpu; ++d ) {
magma_setdevice( d );
magma_free( dA[d] );
magma_queue_destroy( queues[d] );
}
magma_free_cpu( work );
magma_setdevice( orig_dev );
return *info;
} /* magma_dorgqr */
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dormbr
*/
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
double Cnorm, error, dwork[1];
double c_neg_one = MAGMA_D_NEG_ONE;
magma_int_t ione = 1;
magma_int_t m, n, k, mi, ni, mm, nn, nq, size, info;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t nb, ldc, lda, lwork, lwork_max;
double *C, *R, *A, *work, *tau, *tauq, *taup;
double *d, *e;
magma_int_t status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
// need slightly looser bound (60*eps instead of 30*eps) for some tests
opts.tolerance = max( 60., opts.tolerance );
double tol = opts.tolerance * lapackf77_dlamch("E");
// test all combinations of input parameters
magma_vect_t vect [] = { MagmaQ, MagmaP };
magma_side_t side [] = { MagmaLeft, MagmaRight };
magma_trans_t trans[] = { MagmaTrans, MagmaNoTrans };
printf("%% M N K vect side trans CPU Gflop/s (sec) GPU Gflop/s (sec) ||R||_F / ||QC||_F\n");
printf("%%==============================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int ivect = 0; ivect < 2; ++ivect ) {
for( int iside = 0; iside < 2; ++iside ) {
for( int itran = 0; itran < 2; ++itran ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
m = opts.msize[itest];
n = opts.nsize[itest];
k = opts.ksize[itest];
nb = magma_get_dgebrd_nb( m, n );
ldc = m;
// A is nq x k (vect=Q) or k x nq (vect=P)
// where nq=m (left) or nq=n (right)
nq = (side[iside] == MagmaLeft ? m : n );
mm = (vect[ivect] == MagmaQ ? nq : k );
nn = (vect[ivect] == MagmaQ ? k : nq);
lda = mm;
// MBR calls either MQR or MLQ in various ways
if ( vect[ivect] == MagmaQ ) {
if ( nq >= k ) {
gflops = FLOPS_DORMQR( m, n, k, side[iside] ) / 1e9;
}
else {
if ( side[iside] == MagmaLeft ) {
mi = m - 1;
ni = n;
}
else {
mi = m;
ni = n - 1;
}
gflops = FLOPS_DORMQR( mi, ni, nq-1, side[iside] ) / 1e9;
}
}
else {
if ( nq > k ) {
gflops = FLOPS_DORMLQ( m, n, k, side[iside] ) / 1e9;
}
else {
if ( side[iside] == MagmaLeft ) {
mi = m - 1;
ni = n;
}
else {
mi = m;
ni = n - 1;
}
gflops = FLOPS_DORMLQ( mi, ni, nq-1, side[iside] ) / 1e9;
}
}
// workspace for gebrd is (mm + nn)*nb
// workspace for unmbr is m*nb or n*nb, depending on side
lwork_max = max( (mm + nn)*nb, max( m*nb, n*nb ));
// this rounds it up slightly if needed to agree with lwork query below
lwork_max = int( real( magma_dmake_lwork( lwork_max )));
TESTING_MALLOC_CPU( C, double, ldc*n );
TESTING_MALLOC_CPU( R, double, ldc*n );
TESTING_MALLOC_CPU( A, double, lda*nn );
TESTING_MALLOC_CPU( work, double, lwork_max );
TESTING_MALLOC_CPU( d, double, min(mm,nn) );
TESTING_MALLOC_CPU( e, double, min(mm,nn) );
TESTING_MALLOC_CPU( tauq, double, min(mm,nn) );
TESTING_MALLOC_CPU( taup, double, min(mm,nn) );
// C is full, m x n
size = ldc*n;
lapackf77_dlarnv( &ione, ISEED, &size, C );
lapackf77_dlacpy( "Full", &m, &n, C, &ldc, R, &ldc );
size = lda*nn;
lapackf77_dlarnv( &ione, ISEED, &size, A );
// compute BRD factorization to get Householder vectors in A, tauq, taup
//lapackf77_dgebrd( &mm, &nn, A, &lda, d, e, tauq, taup, work, &lwork_max, &info );
magma_dgebrd( mm, nn, A, lda, d, e, tauq, taup, work, lwork_max, &info );
if (info != 0) {
printf("magma_dgebrd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
if ( vect[ivect] == MagmaQ ) {
tau = tauq;
} else {
tau = taup;
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
lapackf77_dormbr( lapack_vect_const( vect[ivect] ),
lapack_side_const( side[iside] ),
lapack_trans_const( trans[itran] ),
&m, &n, &k,
A, &lda, tau, C, &ldc, work, &lwork_max, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0) {
printf("lapackf77_dormbr returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
// query for workspace size
lwork = -1;
magma_dormbr( vect[ivect], side[iside], trans[itran],
m, n, k,
A, lda, tau, R, ldc, work, lwork, &info );
if (info != 0) {
printf("magma_dormbr (lwork query) returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
lwork = (magma_int_t) MAGMA_D_REAL( work[0] );
if ( lwork < 0 || lwork > lwork_max ) {
printf("Warning: optimal lwork %d > allocated lwork_max %d\n", (int) lwork, (int) lwork_max );
lwork = lwork_max;
}
gpu_time = magma_wtime();
magma_dormbr( vect[ivect], side[iside], trans[itran],
m, n, k,
A, lda, tau, R, ldc, work, lwork, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0) {
printf("magma_dormbr returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* =====================================================================
compute relative error |QC_magma - QC_lapack| / |QC_lapack|
=================================================================== */
size = ldc*n;
blasf77_daxpy( &size, &c_neg_one, C, &ione, R, &ione );
Cnorm = lapackf77_dlange( "Fro", &m, &n, C, &ldc, dwork );
error = lapackf77_dlange( "Fro", &m, &n, R, &ldc, dwork ) / (magma_dsqrt(m*n) * Cnorm);
printf( "%5d %5d %5d %c %4c %5c %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %s\n",
(int) m, (int) n, (int) k,
lapacke_vect_const( vect[ivect] ),
lapacke_side_const( side[iside] ),
lapacke_trans_const( trans[itran] ),
cpu_perf, cpu_time, gpu_perf, gpu_time,
error, (error < tol ? "ok" : "failed") );
status += ! (error < tol);
TESTING_FREE_CPU( C );
TESTING_FREE_CPU( R );
TESTING_FREE_CPU( A );
TESTING_FREE_CPU( work );
TESTING_FREE_CPU( d );
TESTING_FREE_CPU( e );
TESTING_FREE_CPU( taup );
TESTING_FREE_CPU( tauq );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}}} // end ivect, iside, itran
printf( "\n" );
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
SEXP magmaCholeskyFinal_m(SEXP A, SEXP n, SEXP NB, SEXP zeroTri, SEXP ngpu, SEXP lowerTri)
{
magma_init();
int ndevices;
double *h_R;
ndevices = INTEGER_VALUE(ngpu);
int idevice;
for(idevice=0; idevice < ndevices; idevice++)
{
magma_setdevice(idevice);
if(CUBLAS_STATUS_SUCCESS != cublasInit())
{
printf("Error: gpu %d: cublasInit failed\n", idevice);
magma_finalize();
exit(-1);
}
}
// magma_print_devices();
int In, INB;
In = INTEGER_VALUE(n);
INB = INTEGER_VALUE(NB);
double *PA = NUMERIC_POINTER(A);
int i,j;
//magma_timestr_t start, end;
double gpu_time;
printf("Inside magma_dpotrf_m");
/*for(i = 0; i < 5; i++)
{
for(j = 0; j < 5; j++)
{
printf("%.8f ", PA[i+j*In]);
}
printf("\n");
} */
magma_int_t N, status, info, nGPU, n2, lda;
clock_t t1, t2;
N = In;
status = 0;
int nGPUs = ndevices;
lda = N;
n2 = lda*N;
if ( MAGMA_SUCCESS != magma_malloc_pinned( (void**) &h_R, (n2)*sizeof(double) )) {
fprintf( stderr, "!!!! magma_malloc_pinned failed for: %s\n", h_R );
magma_finalize();
exit(-1);
}
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, PA, &lda, h_R, &lda );
//printf("Modified by Vinay in 2 GPU\n");
//INB = magma_get_dpotrf_nb(N);
// INB = 224;
// printf("INB = %d\n", INB);
//ngpu = ndevices;
// printf("ngpu = %d\n", ngpu);
//max_size = INB*(1+N/(INB*ndevices))*INB*((N+INB-1)/INB);
// printf("max_size = %d\n", max_size);
//int imax_size = max_size;
//double *dA;
//magma_dmalloc_pinned((void**)&dA, In*In*sizeof(double));
//ldda = (1+N/(INB*ndevices))*INB;
// printf("ldda = %d\n", ldda);
//magma_dsetmatrix_1D_row_bcyclic(N, N, PA, N, dA, ldda, ngpu, INB);
//magma_dpotrf_mgpu(ngpu, MagmaLower, N, dA, ldda, &info);
int lTri;
lTri = INTEGER_VALUE(lowerTri);
if(lTri){
t1 = clock();
magma_dpotrf_m(nGPUs, MagmaLower, N, h_R, N, &info);
t2 = clock ();
}
else{
t1 = clock();
magma_dpotrf_m(nGPUs, MagmaUpper, N, h_R, N, &info);
t2 = clock ();
}
gpu_time = (double) (t2-t1)/(CLOCKS_PER_SEC) ; // Magma time
printf (" magma_dpotrf_m time : %f sec. \n", gpu_time );
if(info != 0)
{
printf("magma_dpotrf returned error %d: %s.\n", (int) info, magma_strerror(info));
}
//magma_dgetmatrix_1D_row_bcyclic(N, N, dA, ldda, PA, N, ngpu, INB);
//for(dev = 0; dev < ndevices; dev++)
//{
//magma_setdevice(dev);
//cudaFree(dA[dev]);
//}
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_R, &lda, PA, &lda );
magma_free_pinned(h_R);
magma_finalize();
cublasShutdown();
int IZeroTri;
IZeroTri = INTEGER_VALUE(zeroTri);
if(IZeroTri & lTri) {
for(i = 1; i < In; i++)
{
for(j=0; j< i; j++)
{
PA[i*In+j] = 0.0;
}
}
}
else if(IZeroTri){
for(i = 0; i < In; i++)
{
for(j=i+1; j < In; j++)
{
PA[i*In+j] = 0.0;
}
}
}
return(R_NilValue);
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dgeqrf
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
double error, work[1];
double c_neg_one = MAGMA_D_NEG_ONE;
double *h_A, *h_T, *h_R, *tau, *h_work, tmp[1];
double *d_A, *d_T, *ddA, *dtau;
double *d_A2, *d_T2, *ddA2, *dtau2;
double *dwork, *dwork2;
magma_int_t M, N, lda, ldda, lwork, n2, info, min_mn;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
#define BLOCK_SIZE 64
magma_opts opts;
parse_opts( argc, argv, &opts );
double tol = 10. * opts.tolerance * lapackf77_dlamch("E");
magma_queue_t stream[2];
magma_queue_create( &stream[0] );
magma_queue_create( &stream[1] );
printf("version %d\n", (int) opts.version );
printf(" M N CPU GFlop/s (ms) GPU GFlop/s (ms) ||R||_F/||A||_F ||R_T||\n");
printf("=============================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[itest];
N = opts.nsize[itest];
if (N > 128) {
printf("%5d %5d skipping because dgeqr2x requires N <= 128\n",
(int) M, (int) N);
continue;
}
if (M < N) {
printf("%5d %5d skipping because dgeqr2x requires M >= N\n",
(int) M, (int) N);
continue;
}
min_mn = min(M, N);
lda = M;
n2 = lda*N;
ldda = ((M+31)/32)*32;
gflops = (FLOPS_DGEQRF( M, N ) + FLOPS_DGEQRT( M, N )) / 1e9;
/* Allocate memory for the matrix */
TESTING_MALLOC_CPU( tau, double, min_mn );
TESTING_MALLOC_CPU( h_A, double, n2 );
TESTING_MALLOC_CPU( h_T, double, N*N );
TESTING_MALLOC_PIN( h_R, double, n2 );
TESTING_MALLOC_DEV( d_A, double, ldda*N );
TESTING_MALLOC_DEV( d_T, double, N*N );
TESTING_MALLOC_DEV( ddA, double, N*N );
TESTING_MALLOC_DEV( dtau, double, min_mn );
TESTING_MALLOC_DEV( d_A2, double, ldda*N );
TESTING_MALLOC_DEV( d_T2, double, N*N );
TESTING_MALLOC_DEV( ddA2, double, N*N );
TESTING_MALLOC_DEV( dtau2, double, min_mn );
TESTING_MALLOC_DEV( dwork, double, max(5*min_mn, (BLOCK_SIZE*2+2)*min_mn) );
TESTING_MALLOC_DEV( dwork2, double, max(5*min_mn, (BLOCK_SIZE*2+2)*min_mn) );
// todo replace with magma_dlaset
cudaMemset(ddA, 0, N*N*sizeof(double));
cudaMemset(d_T, 0, N*N*sizeof(double));
cudaMemset(ddA2, 0, N*N*sizeof(double));
cudaMemset(d_T2, 0, N*N*sizeof(double));
lwork = -1;
lapackf77_dgeqrf(&M, &N, NULL, &M, NULL, tmp, &lwork, &info);
lwork = (magma_int_t)MAGMA_D_REAL( tmp[0] );
lwork = max(lwork, N*N);
TESTING_MALLOC_CPU( h_work, double, lwork );
/* Initialize the matrix */
lapackf77_dlarnv( &ione, ISEED, &n2, h_A );
lapackf77_dlacpy( MagmaUpperLowerStr, &M, &N, h_A, &lda, h_R, &lda );
magma_dsetmatrix( M, N, h_R, lda, d_A, ldda );
magma_dsetmatrix( M, N, h_R, lda, d_A2, ldda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_sync_wtime(0);
if (opts.version == 1)
magma_dgeqr2x_gpu(M, N, d_A, ldda, dtau, d_T, ddA, dwork, &info);
else if (opts.version == 2)
magma_dgeqr2x2_gpu(M, N, d_A, ldda, dtau, d_T, ddA, dwork, &info);
else if (opts.version == 3)
magma_dgeqr2x3_gpu(M, N, d_A, ldda, dtau, d_T, ddA, dwork, &info);
else {
printf( "call magma_dgeqr2x4_gpu\n" );
/*
Going through NULL stream is faster
Going through any stream is slower
Doing two streams in parallel is slower than doing them sequentially
Queuing happens on the NULL stream - user defined buffers are smaller?
*/
magma_dgeqr2x4_gpu(M, N, d_A, ldda, dtau, d_T, ddA, dwork, &info, NULL);
//magma_dgeqr2x4_gpu(M, N, d_A, ldda, dtau, d_T, ddA, dwork, &info, stream[1]);
//magma_dgeqr2x4_gpu(M, N, d_A2, ldda, dtau2, d_T2, ddA2, dwork2, &info, stream[0]);
//magma_dgeqr2x4_gpu(M, N, d_A2, ldda, dtau2, d_T2, ddA2, dwork2, &info, NULL);
//gflops *= 2;
}
gpu_time = magma_sync_wtime(0) - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0) {
printf("magma_dgeqr2x_gpu version %d returned error %d: %s.\n",
(int) opts.version, (int) info, magma_strerror( info ));
}
else {
if ( opts.check ) {
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
lapackf77_dgeqrf(&M, &N, h_A, &lda, tau, h_work, &lwork, &info);
lapackf77_dlarft( MagmaForwardStr, MagmaColumnwiseStr,
&M, &N, h_A, &lda, tau, h_work, &N);
//magma_dgeqr2(&M, &N, h_A, &lda, tau, h_work, &info);
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_dgeqrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Check the result compared to LAPACK
=================================================================== */
magma_dgetmatrix( M, N, d_A, ldda, h_R, M );
magma_dgetmatrix( N, N, ddA, N, h_T, N );
// Restore the upper triangular part of A before the check
for(int col=0; col < N; col++){
for(int row=0; row <= col; row++)
h_R[row + col*M] = h_T[row + col*N];
}
error = lapackf77_dlange("M", &M, &N, h_A, &lda, work);
blasf77_daxpy(&n2, &c_neg_one, h_A, &ione, h_R, &ione);
error = lapackf77_dlange("M", &M, &N, h_R, &lda, work) / (N * error);
// Check if T is the same
magma_dgetmatrix( N, N, d_T, N, h_T, N );
double terr = 0.;
for(int col=0; col < N; col++)
for(int row=0; row <= col; row++)
terr += ( MAGMA_D_ABS(h_work[row + col*N] - h_T[row + col*N])*
MAGMA_D_ABS(h_work[row + col*N] - h_T[row + col*N]) );
terr = magma_dsqrt(terr);
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %8.2e %s\n",
(int) M, (int) N, cpu_perf, 1000.*cpu_time, gpu_perf, 1000.*gpu_time,
error, terr, (error < tol ? "ok" : "failed") );
status += ! (error < tol);
}
else {
printf("%5d %5d --- ( --- ) %7.2f (%7.2f) --- \n",
(int) M, (int) N, gpu_perf, 1000.*gpu_time);
}
}
TESTING_FREE_CPU( tau );
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_T );
TESTING_FREE_CPU( h_work );
TESTING_FREE_PIN( h_R );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_T );
TESTING_FREE_DEV( ddA );
TESTING_FREE_DEV( dtau );
TESTING_FREE_DEV( dwork );
TESTING_FREE_DEV( d_A2 );
TESTING_FREE_DEV( d_T2 );
TESTING_FREE_DEV( ddA2 );
TESTING_FREE_DEV( dtau2 );
TESTING_FREE_DEV( dwork2 );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
magma_queue_destroy( stream[0] );
magma_queue_destroy( stream[1] );
TESTING_FINALIZE();
return status;
}
int main( int argc, char** argv)
{
real_Double_t gpu_time, cpu_time;
double *h_A, *h_R, *VL, *VR, *h_work, *w1, *w2;
double *w1i, *w2i;
double c_neg_one = MAGMA_D_NEG_ONE;
double matnorm, tnrm, result[8];
/* Matrix size */
magma_int_t N=0, n2, lda, nb, lwork;
magma_int_t size[8] = {1024,2048,3072,4032,5184,6016,7040,8064};
magma_int_t i, j, info, checkres, once = 0;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_vec_t jobl = MagmaVec;
magma_vec_t jobr = MagmaVec;
if (argc != 1){
for(i = 1; i<argc; i++){
if (strcmp("-N", argv[i])==0) {
N = atoi(argv[++i]);
once = 1;
}
else if (strcmp("-LN", argv[i])==0)
jobl = MagmaNoVec;
else if (strcmp("-LV", argv[i])==0)
jobl = MagmaVec;
else if (strcmp("-RN", argv[i])==0)
jobr = MagmaNoVec;
else if (strcmp("-RV", argv[i])==0)
jobr = MagmaVec;
}
if ( N > 0 )
printf(" testing_dgeev -L[N|V] -R[N|V] -N %d\n\n", (int) N);
else
{
printf("\nUsage: \n");
printf(" testing_dgeev -L[N|V] -R[N|V] -N %d\n\n", 1024);
exit(1);
}
}
else {
printf("\nUsage: \n");
printf(" testing_dgeev -L[N|V] -R[N|V] -N %d\n\n", 1024);
N = size[7];
}
checkres = getenv("MAGMA_TESTINGS_CHECK") != NULL;
lda = N;
n2 = lda * N;
nb = magma_get_dgehrd_nb(N);
lwork = N*(2+nb);
// generous workspace - required by dget22
lwork = max(lwork, N * ( 5 + 2*N));
TESTING_MALLOC_CPU( w1, double, N );
TESTING_MALLOC_CPU( w2, double, N );
TESTING_MALLOC_CPU( w1i, double, N );
TESTING_MALLOC_CPU( w2i, double, N );
TESTING_MALLOC_CPU( h_A, double, n2 );
TESTING_MALLOC_PIN( h_R, double, n2 );
TESTING_MALLOC_PIN( VL, double, n2 );
TESTING_MALLOC_PIN( VR, double, n2 );
TESTING_MALLOC_PIN( h_work, double, lwork );
/* Initialize */
magma_queue_t queue;
magma_device_t device[ MagmaMaxGPUs ];
int num = 0;
magma_err_t err;
magma_init();
err = magma_get_devices( device, MagmaMaxGPUs, &num );
if ( err != 0 || num < 1 ) {
fprintf( stderr, "magma_get_devices failed: %d\n", err );
exit(-1);
}
err = magma_queue_create( device[0], &queue );
if ( err != 0 ) {
fprintf( stderr, "magma_queue_create failed: %d\n", err );
exit(-1);
}
printf(" N CPU Time(s) GPU Time(s) ||R||_F / ||A||_F\n");
printf("==========================================================\n");
for(i=0; i<8; i++){
if ( argc == 1 ){
N = size[i];
}
lda = N;
n2 = lda*N;
/* Initialize the matrix */
lapackf77_dlarnv( &ione, ISEED, &n2, h_A );
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
// warm-up
magma_dgeev(jobl, jobr,
N, h_R, lda, w1, w1i,
VL, lda, VR, lda,
h_work, lwork, &info, queue);
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
gpu_time = magma_wtime();
magma_dgeev(jobl, jobr,
N, h_R, lda, w1, w1i,
VL, lda, VR, lda,
h_work, lwork, &info, queue);
gpu_time = magma_wtime() - gpu_time;
if (info < 0)
printf("Argument %d of magma_dgeev had an illegal value.\n", (int) -info);
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
lapackf77_dgeev(lapack_const(jobl), lapack_const(jobr),
&N, h_A, &lda, w2, w2i,
VL, &lda, VR, &lda,
h_work, &lwork, &info);
cpu_time = magma_wtime() - cpu_time;
if (info < 0)
printf("Argument %d of dgeev had an illegal value.\n", (int) -info);
/* =====================================================================
Check the result compared to LAPACK
=================================================================== */
if ( checkres )
{
/* ===================================================================
Check the result following LAPACK's [zcds]drvev routine.
The following 7 tests are performed:
* (1) | A * VR - VR * W | / ( n |A| )
*
* Here VR is the matrix of unit right eigenvectors.
* W is a diagonal matrix with diagonal entries W(j).
*
* (2) | A**T * VL - VL * W**T | / ( n |A| )
*
* Here VL is the matrix of unit left eigenvectors, A**T is the
* ugate-transpose of A, and W is as above.
*
* (3) | |VR(i)| - 1 | and whether largest component real
*
* VR(i) denotes the i-th column of VR.
*
* (4) | |VL(i)| - 1 | and whether largest component real
*
* VL(i) denotes the i-th column of VL.
*
* (5) W(full) = W(partial)
*
* W(full) denotes the eigenvalues computed when both VR and VL
* are also computed, and W(partial) denotes the eigenvalues
* computed when only W, only W and VR, or only W and VL are
* computed.
*
* (6) VR(full) = VR(partial)
*
* VR(full) denotes the right eigenvectors computed when both VR
* and VL are computed, and VR(partial) denotes the result
* when only VR is computed.
*
* (7) VL(full) = VL(partial)
*
* VL(full) denotes the left eigenvectors computed when both VR
* and VL are also computed, and VL(partial) denotes the result
* when only VL is computed.
================================================================= */
int jj;
double ulp, ulpinv, vmx, vrmx, vtst, res[2];
double *LRE, DUM;
TESTING_MALLOC_PIN( LRE, double, n2 );
ulp = lapackf77_dlamch( "P" );
ulpinv = 1./ulp;
// Initialize RESULT
for (j = 0; j < 8; j++)
result[j] = -1.;
lapackf77_dlarnv( &ione, ISEED, &n2, h_A );
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
magma_dgeev(MagmaVec, MagmaVec,
N, h_R, lda, w1, w1i,
VL, lda, VR, lda,
h_work, lwork, &info, queue);
// Do test 1
lapackf77_dget22("N", "N", "N", &N, h_A, &lda, VR, &lda, w1, w1i,
h_work, res);
result[0] = res[0];
result[0] *= ulp;
// Do test 2
lapackf77_dget22("T", "N", "T", &N, h_A, &lda, VL, &lda, w1, w1i,
h_work, &result[1]);
result[1] *= ulp;
// Do test 3
result[2] = -1.;
for (j = 0; j < N; ++j) {
tnrm = 1.;
if (w1i[j] == 0.)
tnrm = cblas_dnrm2(N, &VR[j * lda], ione);
else if (w1i[j] > 0.)
tnrm = magma_dlapy2( cblas_dnrm2(N, &VR[j * lda], ione),
cblas_dnrm2(N, &VR[(j+1)* lda], ione) );
result[2] = fmax(result[2], fmin(ulpinv, magma_abs(tnrm-1.)/ulp));
if (w1i[j] > 0.)
{
vmx = vrmx = 0.;
for (jj = 0; jj <N; ++jj) {
vtst = magma_dlapy2( VR[jj+j*lda], VR[jj+(j+1)*lda]);
if (vtst > vmx)
vmx = vtst;
if ( (VR[jj + (j+1)*lda])==0. &&
magma_abs( VR[jj+j*lda] ) > vrmx)
vrmx = magma_abs( VR[jj+j*lda] );
}
if (vrmx / vmx < 1. - ulp * 2.)
result[2] = ulpinv;
}
}
result[2] *= ulp;
// Do test 4
result[3] = -1.;
for (j = 0; j < N; ++j) {
tnrm = 1.;
if (w1i[j] == 0.)
tnrm = cblas_dnrm2(N, &VL[j * lda], ione);
else if (w1i[j] > 0.)
tnrm = magma_dlapy2( cblas_dnrm2(N, &VL[j * lda], ione),
cblas_dnrm2(N, &VL[(j+1)* lda], ione) );
result[3] = fmax(result[3], fmin(ulpinv, magma_abs(tnrm-1.)/ulp));
if (w1i[j] > 0.)
{
vmx = vrmx = 0.;
for (jj = 0; jj <N; ++jj) {
vtst = magma_dlapy2( VL[jj+j*lda], VL[jj+(j+1)*lda]);
if (vtst > vmx)
vmx = vtst;
if ( (VL[jj + (j+1)*lda])==0. &&
magma_abs( VL[jj+j*lda]) > vrmx)
vrmx = magma_abs( VL[jj+j*lda] );
}
if (vrmx / vmx < 1. - ulp * 2.)
result[3] = ulpinv;
}
}
result[3] *= ulp;
// Compute eigenvalues only, and test them
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
magma_dgeev(MagmaNoVec, MagmaNoVec,
N, h_R, lda, w2, w2i,
&DUM, 1, &DUM, 1,
h_work, lwork, &info, queue);
if (info != 0) {
result[0] = ulpinv;
info = abs(info);
printf("Info = %d fo case N, N\n", (int) info);
}
// Do test 5
result[4] = 1;
for (j = 0; j < N; ++j)
if ( w1[j] != w2[j] || w1i[j] != w2i[j] )
result[4] = 0;
//if (result[4] == 0) printf("test 5 failed with N N\n");
// Compute eigenvalues and right eigenvectors, and test them
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
magma_dgeev(MagmaNoVec, MagmaVec,
N, h_R, lda, w2, w2i,
&DUM, 1, LRE, lda,
h_work, lwork, &info, queue);
if (info != 0) {
result[0] = ulpinv;
info = abs(info);
printf("Info = %d fo case N, V\n", (int) info);
}
// Do test 5 again
result[4] = 1;
for (j = 0; j < N; ++j)
if ( w1[j] != w2[j] || w1i[j] != w2i[j] )
result[4] = 0;
//if (result[4] == 0) printf("test 5 failed with N V\n");
// Do test 6
result[5] = 1;
for (j = 0; j < N; ++j)
for (jj = 0; jj < N; ++jj)
if ( VR[j+jj*lda] != LRE[j+jj*lda] )
result[5] = 0;
// Compute eigenvalues and left eigenvectors, and test them
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
magma_dgeev(MagmaVec, MagmaNoVec,
N, h_R, lda, w2, w2i,
LRE, lda, &DUM, 1,
h_work, lwork, &info, queue);
if (info != 0) {
result[0] = ulpinv;
info = abs(info);
printf("Info = %d fo case V, N\n", (int) info);
}
// Do test 5 again
result[4] = 1;
for (j = 0; j < N; ++j)
if ( w1[j] != w2[j] || w1i[j] != w2i[j] )
result[4] = 0;
//if (result[4] == 0) printf("test 5 failed with V N\n");
// Do test 7
result[6] = 1;
for (j = 0; j < N; ++j)
for (jj = 0; jj < N; ++jj)
if ( VL[j+jj*lda] != LRE[j+jj*lda] )
result[6] = 0;
printf("Test 1: | A * VR - VR * W | / ( n |A| ) = %e\n", result[0]);
printf("Test 2: | A'* VL - VL * W'| / ( n |A| ) = %e\n", result[1]);
printf("Test 3: | |VR(i)| - 1 | = %e\n", result[2]);
printf("Test 4: | |VL(i)| - 1 | = %e\n", result[3]);
printf("Test 5: W (full) == W (partial) = %f\n", result[4]);
printf("Test 6: VR (full) == VR (partial) = %f\n", result[5]);
printf("Test 7: VL (full) == VL (partial) = %f\n", result[6]);
//====================================================================
matnorm = lapackf77_dlange("f", &N, &ione, w1, &N, h_work);
blasf77_daxpy(&N, &c_neg_one, w1, &ione, w2, &ione);
result[7] = lapackf77_dlange("f", &N, &ione, w2, &N, h_work) / matnorm;
printf("%5d %6.2f %6.2f %e\n",
(int) N, cpu_time, gpu_time, result[7]);
TESTING_FREE_PIN( LRE );
}
else
{
printf("%5d %6.2f %6.2f\n",
(int) N, cpu_time, gpu_time);
}
if (argc != 1)
break;
}
/* Memory clean up */
TESTING_FREE_CPU( w1 );
TESTING_FREE_CPU( w2 );
TESTING_FREE_CPU( w1i );
TESTING_FREE_CPU( w2i );
TESTING_FREE_CPU( h_A );
TESTING_FREE_PIN( h_R );
TESTING_FREE_PIN( VL );
TESTING_FREE_PIN( VR );
TESTING_FREE_PIN( h_work );
/* Shutdown */
magma_queue_destroy( queue );
magma_finalize();
}