/* ////////////////////////////////////////////////////////////////////////////
-- Testing cheevd
*/
int main( int argc, char** argv)
{
TESTING_CUDA_INIT();
cuFloatComplex *h_A, *h_R, *h_work;
float *rwork, *w1, *w2;
magma_int_t *iwork;
float gpu_time, cpu_time;
magma_timestr_t start, end;
/* Matrix size */
magma_int_t N=0, n2;
magma_int_t size[8] = {1024,2048,3072,4032,5184,6016,7040,8064};
magma_int_t i, info;
magma_int_t ione = 1, izero = 0;
magma_int_t ISEED[4] = {0,0,0,1};
const char *uplo = MagmaLowerStr;
const char *jobz = MagmaVectorsStr;
magma_int_t checkres;
float result[3], eps = lapackf77_slamch( "E" );
if (argc != 1){
for(i = 1; i<argc; i++){
if (strcmp("-N", argv[i])==0) {
N = atoi(argv[++i]);
}
else if ( strcmp("-JV", argv[i]) == 0 ) {
jobz = MagmaVectorsStr;
}
else if ( strcmp("-JN", argv[i]) == 0 ) {
jobz = MagmaNoVectorsStr;
}
}
if (N>0)
printf(" testing_cheevd -N %d [-JV] [-JN]\n\n", (int) N);
else {
printf("\nUsage: \n");
printf(" testing_cheevd -N %d [-JV] [-JN]\n\n", (int) N);
exit(1);
}
}
else {
printf("\nUsage: \n");
printf(" testing_cheevd -N %d [-JV] [-JN]\n\n", 1024);
N = size[7];
}
checkres = getenv("MAGMA_TESTINGS_CHECK") != NULL;
if ( checkres && jobz[0] == MagmaNoVectors ) {
printf( "Cannot check results when vectors are not computed (jobz='N')\n" );
checkres = false;
}
/* Query for workspace sizes */
cuFloatComplex aux_work[1];
float aux_rwork[1];
magma_int_t aux_iwork[1];
magma_cheevd( jobz[0], uplo[0],
N, h_R, N, w1,
aux_work, -1,
aux_rwork, -1,
aux_iwork, -1,
&info );
magma_int_t lwork, lrwork, liwork;
lwork = (magma_int_t) MAGMA_C_REAL( aux_work[0] );
lrwork = (magma_int_t) aux_rwork[0];
liwork = aux_iwork[0];
/* Allocate host memory for the matrix */
TESTING_MALLOC( h_A, cuFloatComplex, N*N );
TESTING_MALLOC( w1, float , N );
TESTING_MALLOC( w2, float , N );
TESTING_HOSTALLOC( h_R, cuFloatComplex, N*N );
TESTING_HOSTALLOC( h_work, cuFloatComplex, lwork );
TESTING_MALLOC( rwork, float, lrwork );
TESTING_MALLOC( iwork, magma_int_t, liwork );
printf(" N CPU Time(s) GPU Time(s) \n");
printf("===================================\n");
for(i=0; i<8; i++){
if (argc==1){
N = size[i];
}
n2 = N*N;
/* Initialize the matrix */
lapackf77_clarnv( &ione, ISEED, &n2, h_A );
for( int i=0; i<N; i++) {
MAGMA_C_SET2REAL( h_A[i*N+i], MAGMA_C_REAL(h_A[i*N+i]) );
}
lapackf77_clacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
/* warm up run */
magma_cheevd(jobz[0], uplo[0],
N, h_R, N, w1,
h_work, lwork,
rwork, lrwork,
iwork, liwork,
&info);
lapackf77_clacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
/* query for optimal workspace sizes */
magma_cheevd(jobz[0], uplo[0],
N, h_R, N, w1,
h_work, -1,
rwork, -1,
iwork, -1,
&info);
int lwork_save = lwork;
int lrwork_save = lrwork;
int liwork_save = liwork;
lwork = min( lwork, (magma_int_t) MAGMA_C_REAL( h_work[0] ));
lrwork = min( lrwork, (magma_int_t) rwork[0] );
liwork = min( liwork, iwork[0] );
//printf( "lwork %d, query %d, used %d; liwork %d, query %d, used %d\n",
// lwork_save, (magma_int_t) h_work[0], lwork,
// liwork_save, iwork[0], liwork );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
start = get_current_time();
magma_cheevd(jobz[0], uplo[0],
N, h_R, N, w1,
h_work, lwork,
rwork, lrwork,
iwork, liwork,
&info);
end = get_current_time();
gpu_time = GetTimerValue(start,end)/1000.;
lwork = lwork_save;
lrwork = lrwork_save;
liwork = liwork_save;
if ( checkres ) {
/* =====================================================================
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 |
=================================================================== */
float temp1, temp2;
cuFloatComplex *tau;
lapackf77_chet21(&ione, uplo, &N, &izero,
h_A, &N,
w1, w1,
h_R, &N,
h_R, &N,
tau, h_work, rwork, &result[0]);
lapackf77_clacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
magma_cheevd('N', uplo[0],
N, h_R, N, w2,
h_work, lwork,
rwork, lrwork,
iwork, liwork,
&info);
temp1 = temp2 = 0;
for(int j=0; j<N; j++){
temp1 = max(temp1, absv(w1[j]));
temp1 = max(temp1, absv(w2[j]));
temp2 = max(temp2, absv(w1[j]-w2[j]));
}
result[2] = temp2 / temp1;
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
start = get_current_time();
lapackf77_cheevd(jobz, uplo,
&N, h_A, &N, w2,
h_work, &lwork,
rwork, &lrwork,
iwork, &liwork,
&info);
end = get_current_time();
if (info < 0)
printf("Argument %d of cheevd had an illegal value.\n", (int) -info);
cpu_time = GetTimerValue(start,end)/1000.;
/* =====================================================================
Print execution time
=================================================================== */
printf("%5d %6.2f %6.2f\n",
(int) N, cpu_time, gpu_time);
if ( checkres ){
printf("Testing the factorization A = U S U' for correctness:\n");
printf("(1) | A - U S U' | / (|A| N) = %e\n", result[0]*eps);
printf("(2) | I - U'U | / N = %e\n", result[1]*eps);
printf("(3) | S(w/ U)-S(w/o U)|/ |S| = %e\n\n", result[2]);
}
if (argc != 1)
break;
}
/* Memory clean up */
TESTING_FREE( h_A);
TESTING_FREE( w1);
TESTING_FREE( w2);
TESTING_FREE( rwork);
TESTING_FREE( iwork);
TESTING_HOSTFREE(h_work);
TESTING_HOSTFREE( h_R);
/* Shutdown */
TESTING_CUDA_FINALIZE();
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing cheevd
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gpu_time, cpu_time;
magmaFloatComplex *h_A, *h_R, *h_work, aux_work[1];
float *rwork, *w1, *w2, result[3], eps, aux_rwork[1];
magma_int_t *iwork, aux_iwork[1];
magma_int_t N, n2, info, lwork, lrwork, liwork, lda;
magma_int_t izero = 0;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
eps = lapackf77_slamch( "E" );
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
float tol = opts.tolerance * lapackf77_slamch("E");
float tolulp = opts.tolerance * lapackf77_slamch("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_cheevd( opts.jobz, opts.uplo,
N, NULL, lda, NULL,
aux_work, -1,
aux_rwork, -1,
aux_iwork, -1,
&info );
lwork = (magma_int_t) MAGMA_C_REAL( aux_work[0] );
lrwork = (magma_int_t) aux_rwork[0];
liwork = aux_iwork[0];
/* Allocate host memory for the matrix */
TESTING_MALLOC_CPU( h_A, magmaFloatComplex, N*lda );
TESTING_MALLOC_CPU( w1, float, N );
TESTING_MALLOC_CPU( w2, float, N );
TESTING_MALLOC_CPU( rwork, float, lrwork );
TESTING_MALLOC_CPU( iwork, magma_int_t, liwork );
TESTING_MALLOC_PIN( h_R, magmaFloatComplex, N*lda );
TESTING_MALLOC_PIN( h_work, magmaFloatComplex, lwork );
/* Initialize the matrix */
lapackf77_clarnv( &ione, ISEED, &n2, h_A );
magma_cmake_hermitian( N, h_A, N );
lapackf77_clacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
/* warm up run */
if ( opts.warmup ) {
magma_cheevd( opts.jobz, opts.uplo,
N, h_R, lda, w1,
h_work, lwork,
rwork, lrwork,
iwork, liwork,
&info );
if (info != 0)
printf("magma_cheevd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
lapackf77_clacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
magma_cheevd( opts.jobz, opts.uplo,
N, h_R, lda, w1,
h_work, lwork,
rwork, lrwork,
iwork, liwork,
&info );
gpu_time = magma_wtime() - gpu_time;
if (info != 0)
printf("magma_cheevd 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 |
=================================================================== */
float temp1, temp2;
// tau=NULL is unused since itype=1
lapackf77_chet21( &ione, lapack_uplo_const(opts.uplo), &N, &izero,
h_A, &lda,
w1, w1,
h_R, &lda,
h_R, &lda,
NULL, h_work, rwork, &result[0] );
lapackf77_clacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
magma_cheevd( MagmaNoVec, opts.uplo,
N, h_R, lda, w2,
h_work, lwork,
rwork, lrwork,
iwork, liwork,
&info );
if (info != 0)
printf("magma_cheevd 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 / (((float)N)*temp1);
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
lapackf77_cheevd( lapack_vec_const(opts.jobz), lapack_uplo_const(opts.uplo),
&N, h_A, &lda, w2,
h_work, &lwork,
rwork, &lrwork,
iwork, &liwork,
&info );
cpu_time = magma_wtime() - cpu_time;
if (info != 0)
printf("lapackf77_cheevd 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( rwork );
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;
}
extern "C" int calc_numerical_range(magmaFloatComplex *M, magma_int_t M_lead_dim, float _from, float _step, magma_int_t _steps, magmaFloatComplex *pts)
{
magma_int_t idx = 0, rslt = 0;
magmaFloatComplex p, scalar;
std::complex<float> vtmp;
float j;
magmaFloatComplex *dA = nullptr;
magmaFloatComplex *dAth = NULL, *dAthT = NULL,
*dX = NULL, *dY = NULL;
float *dE = NULL;
//float *hE = NULL;
//magma_int_t *ipiv = NULL;
magma_int_t lda = M_lead_dim;
//magma_int_t ldx = lda;
magma_int_t info = 0;
magma_int_t nb = 0;
//magma_vec_t jobvl;
//magma_vec_t jobvr;
magmaFloatComplex *work = nullptr;
magma_int_t lwork = 0;
float *rwork = nullptr;
magma_int_t lrwork = 0;
magma_int_t *iwork = nullptr;
magma_int_t liwork = 0;
nb = magma_get_cgehrd_nb( M_lead_dim );
lwork = 2 * max(M_lead_dim + M_lead_dim*nb, 2 * M_lead_dim + M_lead_dim*M_lead_dim); // MagmaVec
lrwork = 1 + 5 * M_lead_dim + 2 * M_lead_dim*M_lead_dim; // MagmaVec
liwork = (3 + 5 * M_lead_dim); // MagmaVec
magma_imalloc_cpu(&iwork, liwork);
magma_smalloc_cpu(&rwork, lrwork);
magma_cmalloc_pinned(&work, lwork);
magma_cmalloc_pinned(&dA, lda*M_lead_dim);
magma_cmalloc_pinned(&dAth, lda*M_lead_dim);
magma_cmalloc_pinned(&dAthT, lda*M_lead_dim);
magma_smalloc_pinned(&dE, M_lead_dim);
//magma_smalloc_cpu(&hE, M_lead_dim);
magma_cmalloc_pinned(&dX, M_lead_dim);
magma_cmalloc_pinned(&dY, M_lead_dim);
magma_csetmatrix(M_lead_dim, M_lead_dim, M, lda, dA, M_lead_dim, queue);
// th=[0:resolution:2*pi]
j = _from;
for (idx = 0; idx < _steps; idx++)
{
//scalar = exp( 1im * -j);
vtmp.real( 0.0f );
vtmp.imag( -j );
//vtmp = _FCbuild(0.0f, -j);
//printf("vtmp = %f + i%f\n", vtmp._Val[0], vtmp._Val[1]);
vtmp = exp(vtmp);
scalar.x = vtmp.real();
scalar.y = vtmp.imag();
//printf("scalar = %f + i%f\n", scalar.x, scalar.y);
magma_ccopy(lda * M_lead_dim, dA, 1, dAth, 1, queue);
// Ath = exp(1im * -j) * As
magma_cscal(lda * M_lead_dim, scalar, dAth, 1, queue);
//magma_cprint_gpu(N, N, dA, lda);
//magma_cprint_gpu(N, N, dAth, lda);
// AthT = (Ath + Ath')
magmablas_ctranspose_conj(M_lead_dim, M_lead_dim, dAth, M_lead_dim, dAthT, M_lead_dim, queue);
magmablas_cgeadd(M_lead_dim, M_lead_dim, MAGMA_C_MAKE(1.0f, 0.0f), dAth, M_lead_dim, dAthT, M_lead_dim, queue);
// AthT = AthT / 2
magma_cscal(lda*M_lead_dim, MAGMA_C_MAKE(0.5f, 0.0f), dAthT, 1, queue);
magma_sync_wtime(queue);
//magma_cprint_gpu(M_lead_dim, M_lead_dim, dAthT, lda);
// e, r = eig(AthT)
rslt = magma_cheevd(MagmaVec, MagmaLower,
M_lead_dim,
dAthT, lda,
dE,
work, lwork,
rwork, lrwork,
iwork, liwork,
&info);
magma_sync_wtime(queue);
//printf("magma_cheevd info=%d\n", info);
//magma_cprint_gpu(M_lead_dim, M_lead_dim, dAthT, lda);
//magma_sprint_gpu(M_lead_dim, 1, dE, M_lead_dim);
//magma_sgetvector(M_lead_dim, dE, 1, hE, 1, queue);
//printf("%f %f\n", hE[0], hE[1]);
// p = r[:,s]' * A * r[:,s]
// r = r[:,s]
magma_ccopy(
M_lead_dim,
dAthT + (M_lead_dim*(M_lead_dim-1)), 1, // dAthT + (N), where (N) is a column offset
dX, 1,
queue);
magma_sync_wtime(queue);
//magma_cprint_gpu(M_lead_dim, 1, dX, M_lead_dim);
// pp = A * r[:,s]
magma_cgemv(MagmaNoTrans,
M_lead_dim, M_lead_dim,
MAGMA_C_MAKE(1.0f, 0.0f),
dA, lda,
dX, 1,
MAGMA_C_MAKE(0.0f, 0.0f),
dY, 1, queue);
magma_sync_wtime(queue);
//magma_cprint_gpu(M_lead_dim, 1, dY, M_lead_dim);
// p = r' * pp
p = magma_cdotc(M_lead_dim, dX, 1, dY, 1, queue);
magma_sync_wtime(queue);
pts[idx] = p;
//printf("p = %f %fi\n", p.x, p.y);
j += _step;
} // end of for (idx = 0; idx < _steps; idx++)
magma_free_pinned(dY);
magma_free_pinned(dX);
//magma_free_cpu(hE);
magma_free_pinned(dE);
magma_free_pinned(dAthT);
magma_free_pinned(dAth);
magma_free_pinned(dA);
magma_free_pinned(work);
magma_free_cpu(rwork);
magma_free_cpu(iwork);
//magma_free_cpu(w);
//magma_free_cpu(A);
return rslt;
}
extern "C" int calc_bounding_box(magmaFloatComplex *M, magma_int_t M_lead_dim, float *wReEig, float *wImEig)
{
magma_int_t rslt = 0;
//magmaFloatComplex *AT = nullptr;
magmaFloatComplex *dA = nullptr, *dAT = nullptr,
*dreA = nullptr, *dimA = nullptr;
float *dreEig = nullptr;
float *dimEig = nullptr;
//magma_int_t *ipiv = NULL;
magma_int_t lda = M_lead_dim;
//magma_int_t ldx = lda;
magma_int_t info = 0;
magma_int_t nb = 0;
//magma_vec_t jobvl;
//magma_vec_t jobvr;
magmaFloatComplex *work = nullptr;
magma_int_t lwork = 0;
float *rwork = nullptr;
magma_int_t lrwork = 0;
magma_int_t *iwork = nullptr;
magma_int_t liwork = 0;
nb = magma_get_cgehrd_nb( M_lead_dim );
lwork = 2 * (M_lead_dim + M_lead_dim*nb); // MagmaNoVec
//lwork = 2 * max(M_lead_dim + M_lead_dim*nb, 2*M_lead_dim + M_lead_dim*M_lead_dim); // MagmaVec
lrwork = M_lead_dim; // MagmaNoVec
//lrwork = 1 + 5 * M_lead_dim + 2*M_lead_dim*M_lead_dim; // MagmaVec
liwork = 1; // MagmaNoVec
//liwork = 3 + 5*M_lead_dim; // MagmaVec
magma_imalloc_cpu(&iwork, liwork);
magma_smalloc_cpu(&rwork, lrwork);
//magma_cmalloc_cpu(&A, lda*M_lead_dim);
//magma_cmalloc_cpu(&AT, lda*M_lead_dim);
//magma_smalloc_cpu(&reEig, M_lead_dim);
//magma_smalloc_cpu(&imEig, M_lead_dim);
magma_cmalloc_pinned(&dA, lda*M_lead_dim);
magma_cmalloc_pinned(&dAT, lda*M_lead_dim);
magma_cmalloc_pinned(&dreA, lda*M_lead_dim);
magma_cmalloc_pinned(&dimA, lda*M_lead_dim);
//magma_cmalloc_pinned(&VL, lda*M_lead_dim);
//magma_cmalloc_pinned(&VR, lda*M_lead_dim);
magma_cmalloc_pinned(&work, lwork);
magma_smalloc_pinned(&dreEig, M_lead_dim);
magma_smalloc_pinned(&dimEig, M_lead_dim);
//matrix_fillzero(AT, M_lead_dim);
//vector_fillzero(reEig, M_lead_dim);
//vector_fillzero(imEig, M_lead_dim);
//prepare_matrix_2(M);
magma_csetmatrix(M_lead_dim, M_lead_dim, M, lda, dA, M_lead_dim, queue);
//magma_csetmatrix(M_lead_dim, M_lead_dim, AT, lda, dAT, M_lead_dim, queue);
//magma_ssetvector(M_lead_dim, wReEig, 1, dreEig, 1, queue);
//magma_ssetvector(M_lead_dim, wImEig, 1, dimEig, 1, queue);
//magma_cprint_gpu(M_lead_dim, M_lead_dim, dA, lda);
// reA = ( (A + A')/2.0 )
// A'
magmablas_ctranspose(M_lead_dim, M_lead_dim, dA, M_lead_dim, dAT, M_lead_dim, queue);
//magma_cprint_gpu(M_lead_dim, M_lead_dim, dAT, lda);
// AT = A + A'
magmablas_cgeadd(M_lead_dim, M_lead_dim, MAGMA_C_MAKE(1.0f, 0.0f), dA, M_lead_dim, dAT, M_lead_dim, queue);
//magma_cprint_gpu(M_lead_dim, M_lead_dim, dAT, lda);
// AT=AT*0.5
magma_cscal(lda*M_lead_dim, MAGMA_C_MAKE(0.5f, 0.0f), dAT, 1, queue);
//magma_cprint_gpu(M_lead_dim, M_lead_dim, dAT, lda);
// reA = AT
magma_ccopy(lda*M_lead_dim, dAT, 1, dreA, 1, queue);
//magma_cprint_gpu(M_lead_dim, M_lead_dim, dreA, lda);
magma_sync_wtime(queue);
// imA = ( -1im*(A - A')/2.0 )
// A'
magmablas_ctranspose(M_lead_dim, M_lead_dim, dA, M_lead_dim, dAT, M_lead_dim, queue);
//magma_cprint_gpu(M_lead_dim, M_lead_dim, dAT, lda);
// AT = A + A'
magmablas_cgeadd(M_lead_dim, M_lead_dim, MAGMA_C_MAKE(-1.0f, 0.0f), dAT, M_lead_dim, dA, M_lead_dim, queue);
// A=A*-1j*0.5
magma_cscal(lda*M_lead_dim, MAGMA_C_MAKE(0.0f, -0.5f), dA, 1, queue);
// imA = A
magma_ccopy(lda*M_lead_dim, dA, 1, dimA, 1, queue);
magma_sync_wtime(queue);
//magma_cprint_gpu(M_lead_dim, M_lead_dim, dreA, lda);
//magma_cprint_gpu(M_lead_dim, M_lead_dim, dimA, lda);
// reEig::Vector=eigvals(reA)
rslt = magma_cheevd(MagmaNoVec, MagmaLower,
M_lead_dim,
dreA, lda,
dreEig,
work, lwork,
rwork, lrwork,
iwork, liwork,
&info);
// imEig::Vector=eigvals(imA)
rslt = magma_cheevd(MagmaNoVec, MagmaLower,
M_lead_dim,
dimA, lda,
dimEig,
work, lwork,
rwork, lrwork,
iwork, liwork,
&info);
//magma_sprint_gpu(M_lead_dim, 1, dreEig, M_lead_dim);
//magma_sprint_gpu(M_lead_dim, 1, dimEig, M_lead_dim);
magma_sgetvector(M_lead_dim, dreEig, 1, wReEig, 1, queue);
//magma_sync_wtime(queue);
magma_sgetvector(M_lead_dim, dimEig, 1, wImEig, 1, queue);
//magma_sync_wtime(queue);
/*
maxReIdx = magma_isamax(M_lead_dim, dreEig, 1, queue) - 1;
minReIdx = magma_isamin(M_lead_dim, dreEig, 1, queue) - 1;
maxImIdx = magma_isamax(M_lead_dim, dimEig, 1, queue) - 1;
minImIdx = magma_isamin(M_lead_dim, dimEig, 1, queue) - 1;
printf("max re idx = %d\nmin re idx = %d\n", maxReIdx, minReIdx);
printf("%f %f\n", wReEig[maxReIdx], wReEig[minReIdx]);
printf("max im idx = %d\nmin im idx = %d\n", maxImIdx, minImIdx);
printf("%f %f\n", wImEig[maxImIdx], wImEig[minImIdx]);
*/
//printf("test wReEig: %f %f\n", wReEig[0], wReEig[1]);
//printf("test wImEig: %f %f\n", wImEig[0], wImEig[1]);
magma_free_cpu(iwork);
magma_free_cpu(rwork);
//magma_free_cpu(AT);
magma_free_pinned(dA);
magma_free_pinned(dAT);
magma_free_pinned(dreA);
magma_free_pinned(dimA);
magma_free_pinned(work);
magma_free_pinned(dreEig);
magma_free_pinned(dimEig);
return rslt;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing cheevd
*/
int main( int argc, char** argv)
{
TESTING_INIT();
/* Constants */
const float d_zero = 0;
const magma_int_t izero = 0;
const magma_int_t ione = 1;
/* Local variables */
real_Double_t gpu_time, cpu_time;
magmaFloatComplex *h_A, *h_R, *h_Z, *h_work, aux_work[1];
#ifdef COMPLEX
float *rwork, aux_rwork[1];
magma_int_t lrwork;
#endif
float *w1, *w2, result[4]={0, 0, 0, 0}, eps, abstol;
magma_int_t *iwork, *isuppz, *ifail, aux_iwork[1];
magma_int_t N, n2, info, lwork, liwork, lda;
magma_int_t ISEED[4] = {0,0,0,1};
eps = lapackf77_slamch( "E" );
magma_int_t status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
// checking NoVec requires LAPACK
opts.lapack |= (opts.check && opts.jobz == MagmaNoVec);
magma_range_t range = MagmaRangeAll;
if (opts.fraction != 1)
range = MagmaRangeI;
#ifdef REAL
if (opts.version == 3 || opts.version == 4) {
printf("%% magma_cheevr and magma_cheevx are not available for real precisions (single, float).\n");
return status;
}
#endif
float tol = opts.tolerance * lapackf77_slamch("E");
float tolulp = opts.tolerance * lapackf77_slamch("P");
// pass ngpu = -1 to test multi-GPU code using 1 gpu
magma_int_t abs_ngpu = abs( opts.ngpu );
printf("%% jobz = %s, range = %s, uplo = %s, fraction = %6.4f, ngpu = %d\n",
lapack_vec_const(opts.jobz), lapack_range_const(range), lapack_uplo_const(opts.uplo),
opts.fraction, int(abs_ngpu) );
printf("%% N CPU Time (sec) GPU Time (sec) |S-S_magma| |A-USU^H| |I-U^H U|\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;
abstol = 0; // auto, in cheevr
// TODO: test vl-vu range
magma_int_t m1 = 0;
float vl = 0;
float vu = 0;
magma_int_t il = 0;
magma_int_t iu = 0;
if (opts.fraction == 0) {
il = max( 1, magma_int_t(0.1*N) );
iu = max( 1, magma_int_t(0.3*N) );
}
else {
il = 1;
iu = max( 1, magma_int_t(opts.fraction*N) );
}
// query for workspace sizes
if ( opts.version == 1 || opts.version == 2 ) {
magma_cheevd( opts.jobz, opts.uplo,
N, NULL, lda, NULL, // A, w
aux_work, -1,
#ifdef COMPLEX
aux_rwork, -1,
#endif
aux_iwork, -1,
&info );
}
else if ( opts.version == 3 ) {
#ifdef COMPLEX
magma_cheevr( opts.jobz, range, opts.uplo,
N, NULL, lda, // A
vl, vu, il, iu, abstol,
&m1, NULL, // w
NULL, lda, NULL, // Z, isuppz
aux_work, -1,
#ifdef COMPLEX
aux_rwork, -1,
#endif
aux_iwork, -1,
&info );
#endif
}
else if ( opts.version == 4 ) {
#ifdef COMPLEX
magma_cheevx( opts.jobz, range, opts.uplo,
N, NULL, lda, // A
vl, vu, il, iu, abstol,
&m1, NULL, // w
NULL, lda, // Z
aux_work, -1,
#ifdef COMPLEX
aux_rwork,
#endif
aux_iwork,
NULL, // ifail
&info );
// cheevx doesn't query rwork, iwork; set them for consistency
aux_rwork[0] = float(7*N);
aux_iwork[0] = float(5*N);
#endif
}
lwork = (magma_int_t) MAGMA_C_REAL( aux_work[0] );
#ifdef COMPLEX
lrwork = (magma_int_t) aux_rwork[0];
#endif
liwork = aux_iwork[0];
/* Allocate host memory for the matrix */
TESTING_MALLOC_CPU( h_A, magmaFloatComplex, N*lda );
TESTING_MALLOC_CPU( w1, float, N );
TESTING_MALLOC_CPU( w2, float, N );
#ifdef COMPLEX
TESTING_MALLOC_CPU( rwork, float, lrwork );
#endif
TESTING_MALLOC_CPU( iwork, magma_int_t, liwork );
TESTING_MALLOC_PIN( h_R, magmaFloatComplex, N*lda );
TESTING_MALLOC_PIN( h_work, magmaFloatComplex, lwork );
if (opts.version == 3) {
TESTING_MALLOC_CPU( h_Z, magmaFloatComplex, N*lda );
TESTING_MALLOC_CPU( isuppz, magma_int_t, 2*max(1,N) );
}
if (opts.version == 4) {
TESTING_MALLOC_CPU( h_Z, magmaFloatComplex, N*lda );
TESTING_MALLOC_CPU( ifail, magma_int_t, N );
}
/* Clear eigenvalues, for |S-S_magma| check when fraction < 1. */
lapackf77_slaset( "Full", &N, &ione, &d_zero, &d_zero, w1, &N );
lapackf77_slaset( "Full", &N, &ione, &d_zero, &d_zero, w2, &N );
/* Initialize the matrix */
lapackf77_clarnv( &ione, ISEED, &n2, h_A );
magma_cmake_hermitian( N, h_A, lda );
lapackf77_clacpy( MagmaFullStr, &N, &N, h_A, &lda, h_R, &lda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
if (opts.version == 1) {
if (opts.ngpu == 1) {
magma_cheevd( opts.jobz, opts.uplo,
N, h_R, lda, w1,
h_work, lwork,
#ifdef COMPLEX
rwork, lrwork,
#endif
iwork, liwork,
&info );
}
else {
//printf( "magma_cheevd_m, ngpu %d (%d)\n", opts.ngpu, abs_ngpu );
magma_cheevd_m( abs_ngpu, opts.jobz, opts.uplo,
N, h_R, lda, w1,
h_work, lwork,
#ifdef COMPLEX
rwork, lrwork,
#endif
iwork, liwork,
&info );
}
}
else if ( opts.version == 2 ) { // version 2: cheevdx computes selected eigenvalues/vectors
if (opts.ngpu == 1) {
magma_cheevdx( opts.jobz, range, opts.uplo,
N, h_R, lda,
vl, vu, il, iu,
&m1, w1,
h_work, lwork,
#ifdef COMPLEX
rwork, lrwork,
#endif
iwork, liwork,
&info );
}
else {
//printf( "magma_cheevdx_m, ngpu %d (%d)\n", opts.ngpu, abs_ngpu );
magma_cheevdx_m( abs_ngpu, opts.jobz, range, opts.uplo,
N, h_R, lda,
vl, vu, il, iu,
&m1, w1,
h_work, lwork,
#ifdef COMPLEX
rwork, lrwork,
#endif
iwork, liwork,
&info );
}
//printf( "il %d, iu %d, m1 %d\n", il, iu, m1 );
}
else if ( opts.version == 3 ) { // version 3: MRRR, computes selected eigenvalues/vectors
// only complex version available
#ifdef COMPLEX
magma_cheevr( opts.jobz, range, opts.uplo,
N, h_R, lda,
vl, vu, il, iu, abstol,
&m1, w1,
h_Z, lda, isuppz,
h_work, lwork,
#ifdef COMPLEX
rwork, lrwork,
#endif
iwork, liwork,
&info );
lapackf77_clacpy( "Full", &N, &N, h_Z, &lda, h_R, &lda );
#endif
}
else if ( opts.version == 4 ) { // version 3: cheevx (QR iteration), computes selected eigenvalues/vectors
// only complex version available
#ifdef COMPLEX
magma_cheevx( opts.jobz, range, opts.uplo,
N, h_R, lda,
vl, vu, il, iu, abstol,
&m1, w1,
h_Z, lda,
h_work, lwork,
#ifdef COMPLEX
rwork, /*lrwork,*/
#endif
iwork, /*liwork,*/
ifail,
&info );
lapackf77_clacpy( "Full", &N, &N, h_Z, &lda, h_R, &lda );
#endif
}
gpu_time = magma_wtime() - gpu_time;
if (info != 0) {
printf("magma_cheevd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
bool okay = true;
if ( opts.check && opts.jobz != MagmaNoVec ) {
/* =====================================================================
Check the results following the LAPACK's [zcds]drvst routine.
A is factored as A = U S U^H and the following 3 tests computed:
(1) | A - U S U^H | / ( |A| N )
(2) | I - U^H U | / ( N )
(3) | S(with U) - S(w/o U) | / | S | // currently disabled, but compares to LAPACK
=================================================================== */
magmaFloatComplex *work;
TESTING_MALLOC_CPU( work, magmaFloatComplex, 2*N*N );
// e=NULL is unused since kband=0; tau=NULL is unused since itype=1
lapackf77_chet21( &ione, lapack_uplo_const(opts.uplo), &N, &izero,
h_A, &lda,
w1, NULL,
h_R, &lda,
h_R, &lda,
NULL, work,
#ifdef COMPLEX
rwork,
#endif
&result[0] );
result[0] *= eps;
result[1] *= eps;
TESTING_FREE_CPU( work ); work=NULL;
// Disable third eigenvalue check that calls routine again --
// it obscures whether error occurs in first call above or in this call.
// But see comparison to LAPACK below.
//
//lapackf77_clacpy( MagmaFullStr, &N, &N, h_A, &lda, h_R, &lda );
//magma_cheevd( MagmaNoVec, opts.uplo,
// N, h_R, lda, w2,
// h_work, lwork,
// #ifdef COMPLEX
// rwork, lrwork,
// #endif
// iwork, liwork,
// &info );
//if (info != 0) {
// printf("magma_cheevd returned error %d: %s.\n",
// (int) info, magma_strerror( info ));
//}
//
//float maxw=0, diff=0;
//for( int j=0; j < N; j++ ) {
// maxw = max(maxw, fabs(w1[j]));
// maxw = max(maxw, fabs(w2[j]));
// diff = max(diff, fabs(w1[j]-w2[j]));
//}
//result[2] = diff / (N*maxw);
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
if ( opts.version == 1 || opts.version == 2 ) {
lapackf77_cheevd( lapack_vec_const(opts.jobz), lapack_uplo_const(opts.uplo),
&N, h_A, &lda, w2,
h_work, &lwork,
#ifdef COMPLEX
rwork, &lrwork,
#endif
iwork, &liwork,
&info );
}
else if ( opts.version == 3 ) {
lapackf77_cheevr( lapack_vec_const(opts.jobz),
lapack_range_const(range),
lapack_uplo_const(opts.uplo),
&N, h_A, &lda,
&vl, &vu, &il, &iu, &abstol,
&m1, w2,
h_Z, &lda, isuppz,
h_work, &lwork,
#ifdef COMPLEX
rwork, &lrwork,
#endif
iwork, &liwork,
&info );
lapackf77_clacpy( "Full", &N, &N, h_Z, &lda, h_A, &lda );
}
else if ( opts.version == 4 ) {
lapackf77_cheevx( lapack_vec_const(opts.jobz),
lapack_range_const(range),
lapack_uplo_const(opts.uplo),
&N, h_A, &lda,
&vl, &vu, &il, &iu, &abstol,
&m1, w2,
h_Z, &lda,
h_work, &lwork,
#ifdef COMPLEX
rwork,
#endif
iwork,
ifail,
&info );
lapackf77_clacpy( "Full", &N, &N, h_Z, &lda, h_A, &lda );
}
cpu_time = magma_wtime() - cpu_time;
if (info != 0) {
printf("lapackf77_cheevd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
// compare eigenvalues
float maxw=0, diff=0;
for( int j=0; j < N; j++ ) {
maxw = max(maxw, fabs(w1[j]));
maxw = max(maxw, fabs(w2[j]));
diff = max(diff, fabs(w1[j] - w2[j]));
}
result[3] = diff / (N*maxw);
okay = okay && (result[3] < tolulp);
printf("%5d %9.4f %9.4f %8.2e ",
(int) N, cpu_time, gpu_time, result[3] );
}
else {
printf("%5d --- %9.4f --- ",
(int) N, gpu_time);
}
// print error checks
if ( opts.check && opts.jobz != MagmaNoVec ) {
okay = okay && (result[0] < tol) && (result[1] < tol);
printf(" %8.2e %8.2e", result[0], result[1] );
}
else {
printf(" --- --- ");
}
printf(" %s\n", (okay ? "ok" : "failed"));
status += ! okay;
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( w1 );
TESTING_FREE_CPU( w2 );
#ifdef COMPLEX
TESTING_FREE_CPU( rwork );
#endif
TESTING_FREE_CPU( iwork );
TESTING_FREE_PIN( h_R );
TESTING_FREE_PIN( h_work );
if ( opts.version == 3 ) {
TESTING_FREE_CPU( h_Z );
TESTING_FREE_CPU( isuppz );
}
if ( opts.version == 4 ) {
TESTING_FREE_CPU( h_Z );
TESTING_FREE_CPU( ifail );
}
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
