int main(void) { /* Local scalars */ lapack_int m, m_i; lapack_int n, n_i; lapack_int lda, lda_i; lapack_int lda_r; lapack_int lwork, lwork_i; lapack_int info, info_i; lapack_int i; int failed; /* Local arrays */ double *a = NULL, *a_i = NULL; double *tau = NULL, *tau_i = NULL; double *work = NULL, *work_i = NULL; double *a_save = NULL; double *tau_save = NULL; double *a_r = NULL; /* Iniitialize the scalar parameters */ init_scalars_dgeqrf( &m, &n, &lda, &lwork ); lda_r = n+2; m_i = m; n_i = n; lda_i = lda; lwork_i = lwork; /* Allocate memory for the LAPACK routine arrays */ a = (double *)LAPACKE_malloc( lda*n * sizeof(double) ); tau = (double *)LAPACKE_malloc( MIN(m,n) * sizeof(double) ); work = (double *)LAPACKE_malloc( lwork * sizeof(double) ); /* Allocate memory for the C interface function arrays */ a_i = (double *)LAPACKE_malloc( lda*n * sizeof(double) ); tau_i = (double *)LAPACKE_malloc( MIN(m,n) * sizeof(double) ); work_i = (double *)LAPACKE_malloc( lwork * sizeof(double) ); /* Allocate memory for the backup arrays */ a_save = (double *)LAPACKE_malloc( lda*n * sizeof(double) ); tau_save = (double *)LAPACKE_malloc( MIN(m,n) * sizeof(double) ); /* Allocate memory for the row-major arrays */ a_r = (double *)LAPACKE_malloc( m*(n+2) * sizeof(double) ); /* Initialize input arrays */ init_a( lda*n, a ); init_tau( (MIN(m,n)), tau ); init_work( lwork, work ); /* Backup the ouptut arrays */ for( i = 0; i < lda*n; i++ ) { a_save[i] = a[i]; } for( i = 0; i < (MIN(m,n)); i++ ) { tau_save[i] = tau[i]; } /* Call the LAPACK routine */ dgeqrf_( &m, &n, a, &lda, tau, work, &lwork, &info ); /* Initialize input data, call the column-major middle-level * interface to LAPACK routine and check the results */ for( i = 0; i < lda*n; i++ ) { a_i[i] = a_save[i]; } for( i = 0; i < (MIN(m,n)); i++ ) { tau_i[i] = tau_save[i]; } for( i = 0; i < lwork; i++ ) { work_i[i] = work[i]; } info_i = LAPACKE_dgeqrf_work( LAPACK_COL_MAJOR, m_i, n_i, a_i, lda_i, tau_i, work_i, lwork_i ); failed = compare_dgeqrf( a, a_i, tau, tau_i, info, info_i, lda, m, n ); if( failed == 0 ) { printf( "PASSED: column-major middle-level interface to dgeqrf\n" ); } else { printf( "FAILED: column-major middle-level interface to dgeqrf\n" ); } /* Initialize input data, call the column-major high-level * interface to LAPACK routine and check the results */ for( i = 0; i < lda*n; i++ ) { a_i[i] = a_save[i]; } for( i = 0; i < (MIN(m,n)); i++ ) { tau_i[i] = tau_save[i]; } for( i = 0; i < lwork; i++ ) { work_i[i] = work[i]; } info_i = LAPACKE_dgeqrf( LAPACK_COL_MAJOR, m_i, n_i, a_i, lda_i, tau_i ); failed = compare_dgeqrf( a, a_i, tau, tau_i, info, info_i, lda, m, n ); if( failed == 0 ) { printf( "PASSED: column-major high-level interface to dgeqrf\n" ); } else { printf( "FAILED: column-major high-level interface to dgeqrf\n" ); } /* Initialize input data, call the row-major middle-level * interface to LAPACK routine and check the results */ for( i = 0; i < lda*n; i++ ) { a_i[i] = a_save[i]; } for( i = 0; i < (MIN(m,n)); i++ ) { tau_i[i] = tau_save[i]; } for( i = 0; i < lwork; i++ ) { work_i[i] = work[i]; } LAPACKE_dge_trans( LAPACK_COL_MAJOR, m, n, a_i, lda, a_r, n+2 ); info_i = LAPACKE_dgeqrf_work( LAPACK_ROW_MAJOR, m_i, n_i, a_r, lda_r, tau_i, work_i, lwork_i ); LAPACKE_dge_trans( LAPACK_ROW_MAJOR, m, n, a_r, n+2, a_i, lda ); failed = compare_dgeqrf( a, a_i, tau, tau_i, info, info_i, lda, m, n ); if( failed == 0 ) { printf( "PASSED: row-major middle-level interface to dgeqrf\n" ); } else { printf( "FAILED: row-major middle-level interface to dgeqrf\n" ); } /* Initialize input data, call the row-major high-level * interface to LAPACK routine and check the results */ for( i = 0; i < lda*n; i++ ) { a_i[i] = a_save[i]; } for( i = 0; i < (MIN(m,n)); i++ ) { tau_i[i] = tau_save[i]; } for( i = 0; i < lwork; i++ ) { work_i[i] = work[i]; } /* Init row_major arrays */ LAPACKE_dge_trans( LAPACK_COL_MAJOR, m, n, a_i, lda, a_r, n+2 ); info_i = LAPACKE_dgeqrf( LAPACK_ROW_MAJOR, m_i, n_i, a_r, lda_r, tau_i ); LAPACKE_dge_trans( LAPACK_ROW_MAJOR, m, n, a_r, n+2, a_i, lda ); failed = compare_dgeqrf( a, a_i, tau, tau_i, info, info_i, lda, m, n ); if( failed == 0 ) { printf( "PASSED: row-major high-level interface to dgeqrf\n" ); } else { printf( "FAILED: row-major high-level interface to dgeqrf\n" ); } /* Release memory */ if( a != NULL ) { LAPACKE_free( a ); } if( a_i != NULL ) { LAPACKE_free( a_i ); } if( a_r != NULL ) { LAPACKE_free( a_r ); } if( a_save != NULL ) { LAPACKE_free( a_save ); } if( tau != NULL ) { LAPACKE_free( tau ); } if( tau_i != NULL ) { LAPACKE_free( tau_i ); } if( tau_save != NULL ) { LAPACKE_free( tau_save ); } if( work != NULL ) { LAPACKE_free( work ); } if( work_i != NULL ) { LAPACKE_free( work_i ); } return 0; }
/* * NAME : simultaneous_iteration * DESCRIPTION : permet d'effectuer la methode des iterations simultanees * IN : nombre de ligne, nombre de colonne, nombre de valeurs propres à calculer, matrice * OUT : / * DEBUG : affichage de la matrice Q à chaque itération */ void simultaneous_iteration(int ligne, int colonne, int nb_eigen, double *A) { double *W = calloc(ligne * colonne, sizeof(double)); double *Q = calloc(ligne * colonne, sizeof(double)); double *Q_old = calloc(ligne * colonne, sizeof(double)); double *lambda = calloc(nb_eigen, sizeof(double)); double *med = calloc(ligne, sizeof(double)); double *err = calloc(nb_eigen, sizeof(double)); double tau[ligne]; for(int i = 0; i < nb_eigen; i++) Q[i * nb_eigen + colonne] = 1.; // DGEQRF computes a QR factorization of a real M-by-N matrix A = Q * R LAPACKE_dgeqrf(LAPACK_ROW_MAJOR, ligne, nb_eigen, Q, nb_eigen, tau); // DORGQR generates an M-by-N real matrix Q with orthonormal columns LAPACKE_dorgqr(LAPACK_ROW_MAJOR, ligne, nb_eigen, nb_eigen, Q, nb_eigen, tau); int k = 0; do { // copie de Q dans Q_old copy(ligne, nb_eigen, Q_old, Q); // W = A * Q^k-1 matMat(ligne, nb_eigen, colonne, A, Q, W); // Q * R = W LAPACKE_dgeqrf(LAPACK_ROW_MAJOR, ligne, nb_eigen, W, nb_eigen, tau); // W = Q LAPACKE_dorgqr(LAPACK_ROW_MAJOR, ligne, nb_eigen, nb_eigen, W, nb_eigen, tau);; #ifdef DEBUG fprintf(stdout, "\nMatrice Q\n"); affichage(ligne, nb_eigen, W); #endif // copie de W dans Q copy(ligne, nb_eigen, Q, W); k++; } while(norme_Frobeinius(ligne, nb_eigen, Q_old, Q) > 1E-6); fprintf(stdout, "\nIterations %d - Norme = %e \n", k - 1, norme_Frobeinius(ligne, nb_eigen, Q_old, Q)); // W = AQ matMat(ligne, nb_eigen, colonne, A, Q, W); // calcul des valeurs propres for(int j = 0; j < nb_eigen; j++) { for(int i = 0; i < ligne; i++) med[i] = fabs(W[i * nb_eigen + j] / Q[i * nb_eigen + j]); lambda[j] = mediane(ligne, med); } fprintf(stdout, "\nValeurs propres issues de la méthode\n"); affichage(nb_eigen, 1, lambda); #ifdef DEBUG fprintf(stdout, "\nMatrice Q\n"); affichage(ligne, nb_eigen, Q); #endif free(err); free(lambda); free(med); free(W); free(Q); free(Q_old); }