/* nag_dormtr (f08fgc) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. */ #include #include #include #include #include int main(void) { /* Scalars */ Integer i, j, m, n, nsplit, pda, pdz, d_len, e_len, tau_len; Integer exit_status = 0; double vl = 0.0, vu = 0.0; NagError fail; Nag_UploType uplo; Nag_OrderType order; /* Arrays */ char nag_enum_arg[40]; Integer *iblock = 0, *ifailv = 0, *isplit = 0; double *a = 0, *d = 0, *e = 0, *tau = 0, *w = 0, *z = 0; #ifdef NAG_COLUMN_MAJOR #define A(I, J) a[(J - 1) * pda + I - 1] #define Z(I, J) z[(J - 1) * pdz + I - 1] order = Nag_ColMajor; #else #define A(I, J) a[(I - 1) * pda + J - 1] #define Z(I, J) z[(I - 1) * pdz + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); printf("nag_dormtr (f08fgc) Example Program Results\n\n"); /* Skip heading in data file */ scanf("%*[^\n] "); scanf("%ld%*[^\n] ", &n); pda = n; pdz = n; tau_len = n-1; d_len = n; e_len = n-1; /* Allocate memory */ if (!(a = NAG_ALLOC(n * n, double)) || !(d = NAG_ALLOC(d_len, double)) || !(e = NAG_ALLOC(e_len, double)) || !(iblock = NAG_ALLOC(n, Integer)) || !(ifailv = NAG_ALLOC(n, Integer)) || !(isplit = NAG_ALLOC(n, Integer)) || !(w = NAG_ALLOC(n, double)) || !(tau = NAG_ALLOC(tau_len, double)) || !(z = NAG_ALLOC(n * n, double))) { 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", &A(i, j)); } scanf("%*[^\n] "); } else { for (i = 1; i <= n; ++i) { for (j = 1; j <= i; ++j) scanf("%lf", &A(i, j)); } scanf("%*[^\n] "); } /* Reduce A to tridiagonal form T = (Q**T)*A*Q */ /* nag_dsytrd (f08fec). * Orthogonal reduction of real symmetric matrix to * symmetric tridiagonal form */ nag_dsytrd(order, uplo, n, a, pda, d, e, tau, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dsytrd (f08fec).\n%s\n", fail.message); exit_status = 1; goto END; } /* Calculate the two smallest eigenvalues of T (same as A) */ /* nag_dstebz (f08jjc). * Selected eigenvalues of real symmetric tridiagonal matrix * by bisection */ nag_dstebz(Nag_Indices, Nag_ByBlock, n, vl, vu, 1, 2, 0.0, d, e, &m, &nsplit, w, iblock, isplit, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dstebz (f08jjc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print eigenvalues */ printf("Eigenvalues\n"); for (i = 0; i < m; ++i) printf("%8.4f%s", w[i], (i+1)%8 == 0?"\n":" "); printf("\n\n"); /* Calculate the eigenvectors of T storing the result in Z */ /* nag_dstein (f08jkc). * Selected eigenvectors of real symmetric tridiagonal * matrix by inverse iteration, storing eigenvectors in real * array */ nag_dstein(order, n, d, e, m, w, iblock, isplit, z, pdz, ifailv, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dstein (f08jkc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Calculate all the eigenvectors of A = Q*(eigenvectors of T) */ /* nag_dormtr (f08fgc). * Apply orthogonal transformation determined by nag_dsytrd * (f08fec) */ nag_dormtr(order, Nag_LeftSide, uplo, Nag_NoTrans, n, m, a, pda, tau, z, pdz, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dormtr (f08fgc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Normalize the eigenvectors */ for(j=1; j<=m; j++) { for(i=n; i>=1; i--) { Z(i, j) = Z(i, j) / Z(1,j); } } /* Print eigenvectors */ /* nag_gen_real_mat_print (x04cac). * Print real general matrix (easy-to-use) */ fflush(stdout); nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, m, z, pdz, "Eigenvectors", 0, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n", fail.message); exit_status = 1; goto END; } END: if (a) NAG_FREE(a); if (d) NAG_FREE(d); if (e) NAG_FREE(e); if (iblock) NAG_FREE(iblock); if (ifailv) NAG_FREE(ifailv); if (isplit) NAG_FREE(isplit); if (tau) NAG_FREE(tau); if (w) NAG_FREE(w); if (z) NAG_FREE(z); return exit_status; }