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/*
-- MAGMA (version 2.9.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
@date January 2025
@author Raffaele Solca
@author Azzam Haidar
@author Mark Gates
@precisions normal z -> c d s
*/
// includes, system
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <math.h>
// includes, project
#include "magma_v2.h"
#include "magma_lapack.h"
#include "testings.h"
#define COMPLEX
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zhegvd
*/
int main( int argc, char** argv)
{
TESTING_CHECK( magma_init() );
magma_print_environment();
/* Constants */
const magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
const magmaDoubleComplex c_one = MAGMA_Z_ONE;
const magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
const double d_one = 1.;
const double d_neg_one = -1.;
magma_int_t ione = 1;
/* Local variables */
real_Double_t gpu_time, cpu_time;
magmaDoubleComplex *h_A, *h_R, *h_B, *h_S, *h_work;
double *w1, *w2;
double Anorm, result[4] = {0, 0, 0, 0};
magma_int_t *iwork;
magma_int_t N, n2, info, nb, lwork, liwork, lda;
#ifdef COMPLEX
double *rwork;
magma_int_t lrwork;
#endif
int status = 0;
magma_opts opts;
opts.matrix = "rand_dominant"; // default
opts.parse_opts( argc, argv );
double tol = opts.tolerance * lapackf77_dlamch("E");
double tolulp = opts.tolerance * lapackf77_dlamch("P");
// checking NoVec requires LAPACK
opts.lapack |= (opts.check && opts.jobz == MagmaNoVec);
// pass ngpu = -1 to test multi-GPU code using 1 gpu
magma_int_t abs_ngpu = abs( opts.ngpu );
printf("%% itype = %lld, jobz = %s, uplo = %s, ngpu %lld\n",
(long long) opts.itype, lapack_vec_const(opts.jobz), lapack_uplo_const(opts.uplo),
(long long) abs_ngpu );
if (opts.version == 1) {
printf("%% N CPU Time (sec) GPU Time (sec) |D-D_magma| |AZ-BZD| |I-ZZ^H B|\n");
}
else if ( opts.version == 2) {
printf("%% N CPU Time (sec) GPU Time (sec) |D-D_magma| |ABZ-ZD| |I-ZZ^H B|\n");
}
else if ( opts.version == 3) {
printf("%% N CPU Time (sec) GPU Time (sec) |D-D_magma| |BAZ-ZD| |B-ZZ^H|\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_zhetrd_nb(N);
#ifdef COMPLEX
lwork = max( N + N*nb, 2*N + N*N );
lrwork = 1 + 5*N +2*N*N;
#else
lwork = max( 2*N + N*nb, 1 + 6*N + 2*N*N );
#endif
liwork = 3 + 5*N;
TESTING_CHECK( magma_zmalloc_cpu( &h_A, n2 ));
TESTING_CHECK( magma_zmalloc_cpu( &h_B, n2 ));
TESTING_CHECK( magma_dmalloc_cpu( &w1, N ));
TESTING_CHECK( magma_dmalloc_cpu( &w2, N ));
#ifdef COMPLEX
TESTING_CHECK( magma_dmalloc_cpu( &rwork, lrwork ));
#endif
TESTING_CHECK( magma_imalloc_cpu( &iwork, liwork ));
TESTING_CHECK( magma_zmalloc_pinned( &h_R, n2 ));
TESTING_CHECK( magma_zmalloc_pinned( &h_S, n2 ));
TESTING_CHECK( magma_zmalloc_pinned( &h_work, lwork ));
/* Initialize the matrix */
magma_generate_matrix( opts, N, N, h_A, lda );
magma_generate_matrix( opts, N, N, h_B, lda );
lapackf77_zlacpy( MagmaFullStr, &N, &N, h_A, &lda, h_R, &lda );
lapackf77_zlacpy( MagmaFullStr, &N, &N, h_B, &lda, h_S, &lda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
if (opts.ngpu == 1) {
magma_zhegvd( opts.itype, opts.jobz, opts.uplo,
N, h_R, lda, h_S, lda, w1,
h_work, lwork,
#ifdef COMPLEX
rwork, lrwork,
#endif
iwork, liwork,
&info );
}
else {
magma_zhegvd_m( abs_ngpu, opts.itype, opts.jobz, opts.uplo,
N, h_R, lda, h_S, lda, w1,
h_work, lwork,
#ifdef COMPLEX
rwork, lrwork,
#endif
iwork, liwork,
&info );
}
gpu_time = magma_wtime() - gpu_time;
if (info != 0) {
printf("magma_zhegvd returned error %lld: %s.\n",
(long long) info, magma_strerror( info ));
}
bool okay = true;
if ( opts.check && opts.jobz != MagmaNoVec ) {
/* =====================================================================
Check the results following the LAPACK's [zc]hegvd 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) | I - V V^H B | / ( N ) (itype = 1,2)
| B - V V^H | / ( |B| N ) (itype = 3)
(3) | D(with V) - D(w/o V) | / | D |
=================================================================== */
//magmaDoubleComplex *tau;
#ifdef REAL
double *rwork = h_work + N*N;
#endif
if ( opts.itype == 1 || opts.itype == 2 ) {
lapackf77_zlaset( "A", &N, &N, &c_zero, &c_one, h_S, &lda);
blasf77_zgemm("N", "C", &N, &N, &N, &c_one, h_R, &lda, h_R, &lda, &c_zero, h_work, &N);
blasf77_zhemm("R", lapack_uplo_const(opts.uplo), &N, &N, &c_neg_one, h_B, &lda, h_work, &N, &c_one, h_S, &lda);
result[1] = lapackf77_zlange("1", &N, &N, h_S, &lda, rwork) / N;
}
else if ( opts.itype == 3 ) {
lapackf77_zlacpy( MagmaFullStr, &N, &N, h_B, &lda, h_S, &lda);
blasf77_zherk(lapack_uplo_const(opts.uplo), "N", &N, &N, &d_neg_one, h_R, &lda, &d_one, h_S, &lda);
Anorm = safe_lapackf77_zlanhe("1", lapack_uplo_const(opts.uplo), &N, h_B, &lda, rwork);
result[1] = safe_lapackf77_zlanhe("1", lapack_uplo_const(opts.uplo), &N, h_S, &lda, rwork)
/ (N*Anorm);
}
result[0] = 1.;
result[0] /= safe_lapackf77_zlanhe("1", lapack_uplo_const(opts.uplo), &N, h_A, &lda, rwork);
result[0] /= lapackf77_zlange("1", &N, &N, h_R, &lda, rwork);
if ( opts.itype == 1 ) {
blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_A, &lda, h_R, &lda, &c_zero, h_work, &N);
for (int i=0; i < N; ++i)
blasf77_zdscal(&N, &w1[i], &h_R[i*N], &ione);
blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_neg_one, h_B, &lda, h_R, &lda, &c_one, h_work, &N);
result[0] *= lapackf77_zlange("1", &N, &N, h_work, &lda, rwork)/N;
}
else if ( opts.itype == 2 ) {
blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_B, &lda, h_R, &lda, &c_zero, h_work, &N);
for (int i=0; i < N; ++i)
blasf77_zdscal(&N, &w1[i], &h_R[i*N], &ione);
blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_A, &lda, h_work, &N, &c_neg_one, h_R, &lda);
result[0] *= lapackf77_zlange("1", &N, &N, h_R, &lda, rwork)/N;
}
else if ( opts.itype == 3 ) {
blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_A, &lda, h_R, &lda, &c_zero, h_work, &N);
for (int i=0; i < N; ++i)
blasf77_zdscal(&N, &w1[i], &h_R[i*N], &ione);
blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_B, &lda, h_work, &N, &c_neg_one, h_R, &lda);
result[0] *= lapackf77_zlange("1", &N, &N, h_R, &lda, rwork)/N;
}
/*
assert( lwork >= 2*N*N );
lapackf77_zhet21( &ione, lapack_uplo_const(opts.uplo), &N, &izero,
h_A, &lda,
w1, w1,
h_R, &lda,
h_R, &lda,
tau, h_work, rwork, &result[0] );
*/
// Disable eigenvalue check which calls routine again --
// it obscures whether error occurs in first call above or in this call.
// But see comparison to LAPACK below.
//
//lapackf77_zlacpy( MagmaFullStr, &N, &N, h_A, &lda, h_R, &lda );
//lapackf77_zlacpy( MagmaFullStr, &N, &N, h_B, &lda, h_S, &lda );
//
//magma_zhegvd( opts.itype, MagmaNoVec, opts.uplo,
// N, h_R, lda, h_S, lda, w2,
// h_work, lwork,
// #ifdef COMPLEX
// rwork, lrwork,
// #endif
// iwork, liwork,
// &info );
//if (info != 0) {
// printf("magma_zhegvd returned error %lld: %s.\n",
// (long long) info, magma_strerror( info ));
//}
//
//double 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();
lapackf77_zhegvd( &opts.itype, lapack_vec_const(opts.jobz), lapack_uplo_const(opts.uplo),
&N, h_A, &lda, h_B, &lda, w2,
h_work, &lwork,
#ifdef COMPLEX
rwork, &lrwork,
#endif
iwork, &liwork,
&info );
cpu_time = magma_wtime() - cpu_time;
if (info != 0) {
printf("lapackf77_zhegvd returned error %lld: %s.\n",
(long long) info, magma_strerror( info ));
}
// compare eigenvalues
double 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("%5lld %9.4f %9.4f %8.2e ",
(long long) N, cpu_time, gpu_time, result[3] );
}
else {
printf("%5lld --- %9.4f --- ",
(long long) 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;
magma_free_cpu( h_A );
magma_free_cpu( h_B );
magma_free_cpu( w1 );
magma_free_cpu( w2 );
#ifdef COMPLEX
magma_free_cpu( rwork );
#endif
magma_free_cpu( iwork );
magma_free_pinned( h_R );
magma_free_pinned( h_S );
magma_free_pinned( h_work );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
opts.cleanup();
TESTING_CHECK( magma_finalize() );
return status;
}
|
