/* nag_zhptrd (f08gsc) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. */ #include #include #include #include #include #include int main(void) { /* Scalars */ Integer ap_len, i, j, n, pdz, d_len, e_len, tau_len; Integer exit_status = 0; NagError fail; Nag_UploType uplo; Nag_OrderType order; /* Arrays */ char nag_enum_arg[40]; Complex *ap = 0, *tau = 0, *z = 0; double *d = 0, *e = 0; #ifdef NAG_COLUMN_MAJOR #define A_UPPER(I, J) ap[J * (J - 1) / 2 + I - 1] #define A_LOWER(I, J) ap[(2 * n - J) * (J - 1) / 2 + I - 1] #define Z(I, J) z[(J - 1) * pdz + I - 1] order = Nag_ColMajor; #else #define A_LOWER(I, J) ap[I * (I - 1) / 2 + J - 1] #define A_UPPER(I, J) ap[(2 * n - I) * (I - 1) / 2 + J - 1] #define Z(I, J) z[(I - 1) * pdz + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); printf("nag_zhptrd (f08gsc) Example Program Results\n\n"); /* Skip heading in data file */ scanf("%*[^\n] "); scanf("%ld%*[^\n] ", &n); #ifdef NAG_COLUMN_MAJOR pdz = n; #else pdz = n; #endif ap_len = n*(n+1)/2; tau_len = n-1; d_len = n; e_len = n-1; /* Allocate memory */ if (!(ap = NAG_ALLOC(ap_len, Complex)) || !(d = NAG_ALLOC(d_len, double)) || !(e = NAG_ALLOC(e_len, double)) || !(tau = NAG_ALLOC(tau_len, Complex)) || !(z = NAG_ALLOC(n * n, Complex))) { printf("Allocation failure\n"); exit_status = -1; goto END; } /* Read A from data file */ scanf("%s%*[^\n] ", nag_enum_arg); /* nag_enum_name_to_value(x04nac). * Converts NAG enum member name to value */ uplo = (Nag_UploType) nag_enum_name_to_value(nag_enum_arg); if (uplo == Nag_Upper) { for (i = 1; i <= n; ++i) { for (j = i; j <= n; ++j) { scanf(" ( %lf , %lf )", &A_UPPER(i, j).re, &A_UPPER(i, j).im); } } scanf("%*[^\n] "); } else { for (i = 1; i <= n; ++i) { for (j = 1; j <= i; ++j) { scanf(" ( %lf , %lf )", &A_LOWER(i, j).re, &A_LOWER(i, j).im); } } scanf("%*[^\n] "); } /* Reduce A to tridiagonal form T = (Q**H)*A*Q */ /* nag_zhptrd (f08gsc). * Unitary reduction of complex Hermitian matrix to real * symmetric tridiagonal form, packed storage */ nag_zhptrd(order, uplo, n, ap, d, e, tau, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zhptrd (f08gsc).\n%s\n", fail.message); exit_status = 1; } /* Form Q explicitly, storing the result in Z */ /* nag_zupgtr (f08gtc). * Generate unitary transformation matrix from reduction to * tridiagonal form determined by nag_zhptrd (f08gsc) */ nag_zupgtr(order, uplo, n, ap, tau, z, pdz, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zupgtr (f08gtc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Calculate all the eigenvalues and eigenvectors of A */ /* nag_zsteqr (f08jsc). * All eigenvalues and eigenvectors of real symmetric * tridiagonal matrix, reduced from complex Hermitian * matrix, using implicit QL or QR */ nag_zsteqr(order, Nag_UpdateZ, n, d, e, z, pdz, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zsteqr (f08jsc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Normalize the eigenvectors */ for(j=1; j<=n; j++) { for(i=n; i>=1; i--) { Z(i, j) = nag_complex_divide(Z(i, j), Z(1,j)); } } /* Print eigenvalues and eigenvectors */ printf("Eigenvalues\n"); for (i = 1; i <= n; ++i) printf("%8.4f%s", d[i-1], i%8 == 0?"\n":" "); printf("\n\n"); /* nag_gen_complx_mat_print_comp (x04dbc). * Print complex general matrix (comprehensive) */ fflush(stdout); nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, z, pdz, Nag_BracketForm, "%7.4f", "Eigenvectors", Nag_NoLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0, &fail); if (fail.code != NE_NOERROR) { printf( "Error from nag_gen_complx_mat_print_comp (x04dbc).\n%s\n", fail.message); exit_status = 1; goto END; } END: if (ap) NAG_FREE(ap); if (d) NAG_FREE(d); if (e) NAG_FREE(e); if (tau) NAG_FREE(tau); if (z) NAG_FREE(z); return exit_status; }