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/*
-- MAGMA (version 2.9.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
@date January 2025
@precisions normal z -> s d c
*/
// includes, system
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <math.h>
// includes, project
#include "flops.h"
#include "magma_v2.h"
#include "magma_lapack.h"
#include "testings.h"
#define COMPLEX
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zgebrd
*/
int main( int argc, char** argv)
{
TESTING_CHECK( magma_init() );
magma_print_environment();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
magmaDoubleComplex *h_A, *h_Q, *h_PT, *h_work;
magmaDoubleComplex *taup, *tauq;
double *diag, *offdiag;
double result[3] = {0., 0., 0.};
magma_int_t M, N, lda, lhwork, info, minmn, nb;
magma_int_t ione = 1;
int status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
double tol = opts.tolerance * lapackf77_dlamch("E");
double eps = lapackf77_dlamch( "E" );
printf("%% M N CPU Gflop/s (sec) GPU Gflop/s (sec) |A-QBP^H|/N|A| |I-QQ^H|/N |I-PP^H|/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];
minmn = min(M, N);
nb = magma_get_zgebrd_nb( M, N );
lda = M;
lhwork = (M + N)*nb;
gflops = FLOPS_ZGEBRD( M, N ) / 1e9;
TESTING_CHECK( magma_zmalloc_cpu( &h_A, lda*N ));
TESTING_CHECK( magma_zmalloc_cpu( &tauq, minmn ));
TESTING_CHECK( magma_zmalloc_cpu( &taup, minmn ));
TESTING_CHECK( magma_dmalloc_cpu( &diag, minmn ));
TESTING_CHECK( magma_dmalloc_cpu( &offdiag, minmn-1 ));
TESTING_CHECK( magma_zmalloc_pinned( &h_Q, lda*N ));
TESTING_CHECK( magma_zmalloc_pinned( &h_work, lhwork ));
/* Initialize the matrices */
magma_generate_matrix( opts, M, N, h_A, lda );
lapackf77_zlacpy( MagmaFullStr, &M, &N, h_A, &lda, h_Q, &lda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
magma_zgebrd( M, N, h_Q, lda,
diag, offdiag, tauq, taup,
h_work, lhwork, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0) {
printf("magma_zgebrd returned error %lld: %s.\n",
(long long) info, magma_strerror( info ));
}
/* =====================================================================
Check the factorization
=================================================================== */
if ( opts.check ) {
// zungbr prefers minmn*NB
// zbdt01 needs M+N
// zunt01 prefers minmn*(minmn+1) to check Q and P
magma_int_t lwork_err;
magmaDoubleComplex *h_work_err;
lwork_err = max( minmn * nb, M+N );
lwork_err = max( lwork_err, minmn*(minmn+1) );
TESTING_CHECK( magma_zmalloc_cpu( &h_PT, lda*N ));
TESTING_CHECK( magma_zmalloc_cpu( &h_work_err, lwork_err ));
// zbdt01 needs M
// zunt01 needs minmn
#ifdef COMPLEX
double *rwork_err;
TESTING_CHECK( magma_dmalloc_cpu( &rwork_err, M ));
#endif
lapackf77_zlacpy( MagmaFullStr, &M, &N, h_Q, &lda, h_PT, &lda );
// generate Q & P^H
lapackf77_zungbr("Q", &M, &minmn, &N, h_Q, &lda, tauq, h_work_err, &lwork_err, &info);
if (info != 0) {
printf("lapackf77_zungbr #1 returned error %lld: %s.\n",
(long long) info, magma_strerror( info ));
}
lapackf77_zungbr("P", &minmn, &N, &M, h_PT, &lda, taup, h_work_err, &lwork_err, &info);
if (info != 0) {
printf("lapackf77_zungbr #2 returned error %lld: %s.\n",
(long long) info, magma_strerror( info ));
}
// Test 1: Check the decomposition A := Q * B * PT
// 2: Check the orthogonality of Q
// 3: Check the orthogonality of PT
lapackf77_zbdt01( &M, &N, &ione,
h_A, &lda, h_Q, &lda,
diag, offdiag, h_PT, &lda,
h_work_err,
#ifdef COMPLEX
rwork_err,
#endif
&result[0] );
// LAPACK normalizes by N*|A|, but that fails for very tall matrices,
// so normalize by max(M*N)*|A|. TODO: is there justification for that change?
result[0] = N*result[0] / max(M,N);
lapackf77_zunt01( "Columns", &M, &minmn, h_Q, &lda, h_work_err, &lwork_err,
#ifdef COMPLEX
rwork_err,
#endif
&result[1]);
lapackf77_zunt01( "Rows", &minmn, &N, h_PT, &lda, h_work_err, &lwork_err,
#ifdef COMPLEX
rwork_err,
#endif
&result[2]);
magma_free_cpu( h_PT );
magma_free_cpu( h_work_err );
#ifdef COMPLEX
magma_free_cpu( rwork_err );
#endif
// lapack normalizes by eps
result[0] *= eps;
result[1] *= eps;
result[2] *= eps;
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
lapackf77_zgebrd( &M, &N, h_A, &lda,
diag, offdiag, tauq, taup,
h_work, &lhwork, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0) {
printf("lapackf77_zgebrd returned error %lld: %s.\n",
(long long) info, magma_strerror( info ));
}
}
/* =====================================================================
Print performance and error.
=================================================================== */
if ( opts.lapack ) {
printf("%5lld %5lld %7.2f (%7.2f) %7.2f (%7.2f)",
(long long) M, (long long) N, cpu_perf, cpu_time, gpu_perf, gpu_time );
}
else {
printf("%5lld %5lld --- ( --- ) %7.2f (%7.2f)",
(long long) M, (long long) N, gpu_perf, gpu_time );
}
if ( opts.check ) {
bool okay = (result[0] < tol) && (result[1] < tol) && (result[2] < tol);
status += ! okay;
printf(" %8.2e %8.2e %8.2e %s\n",
result[0], result[1], result[2],
(okay ? "ok" : "failed") );
} else {
printf(" --- --- \n");
}
magma_free_cpu( h_A );
magma_free_cpu( tauq );
magma_free_cpu( taup );
magma_free_cpu( diag );
magma_free_cpu( offdiag );
magma_free_pinned( h_Q );
magma_free_pinned( h_work );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
opts.cleanup();
TESTING_CHECK( magma_finalize() );
return status;
}
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