/* nag_zhegvd (f08sqc) Example Program. * * Copyright 2011 Numerical Algorithms Group. * * Mark 23, 2011. */ #include #include #include #include #include #include #include #include #include int main(void) { /* Scalars */ double anorm, bnorm, eps, rcond, rcondb, t1, t2, t3; Integer i, j, n, pda, pdb; Integer exit_status = 0; /* Arrays */ Complex *a = 0, *b = 0; double *eerbnd = 0, *rcondz = 0, *w = 0, *zerbnd = 0; char nag_enum_arg[40]; /* Nag Types */ NagError fail; Nag_OrderType order; Nag_UploType uplo; #ifdef NAG_COLUMN_MAJOR #define A(I, J) a[(J-1)*pda + I - 1] #define B(I, J) b[(J-1)*pdb + I - 1] order = Nag_ColMajor; #else #define A(I, J) a[(I-1)*pda + J - 1] #define B(I, J) b[(I-1)*pdb + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); printf("nag_zhegvd (f08sqc) Example Program Results\n\n"); /* Skip heading in data file */ scanf("%*[^\n]"); scanf("%ld%*[^\n]", &n); if (n < 0) { printf("Invalid n\n"); exit_status = 1; goto END;; } 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); pda = n; pdb = n; /* Allocate memory */ if (!(a = NAG_ALLOC(n * n, Complex)) || !(b = NAG_ALLOC(n * n, Complex)) || !(eerbnd = NAG_ALLOC(n, double)) || !(rcondz = NAG_ALLOC(n, double)) || !(w = NAG_ALLOC(n, double)) || !(zerbnd = NAG_ALLOC(n, double))) { printf("Allocation failure\n"); exit_status = -1; goto END; } /* Read the triangular parts of the matrices A and B */ if (uplo == Nag_Upper) { for (i = 1; i <= n; ++i) for (j = i; j <= n; ++j) scanf(" ( %lf , %lf ) ", &A(i, j).re, &A(i, j).im); scanf("%*[^\n]"); for (i = 1; i <= n; ++i) for (j = i; j <= n; ++j) scanf(" ( %lf , %lf ) ", &B(i, j).re, &B(i, j).im); } else { for (i = 1; i <= n; ++i) for (j = 1; j <= i; ++j) scanf(" ( %lf , %lf ) ", &A(i, j).re, &A(i, j).im); scanf("%*[^\n]"); for (i = 1; i <= n; ++i) for (j = 1; j <= i; ++j) scanf(" ( %lf , %lf ) ", &B(i, j).re, &B(i, j).im); } scanf("%*[^\n]"); /* Compute the one-norms of the symmetric matrices A and B * using nag_zhe_norm (f16ucc). */ nag_zhe_norm(order, Nag_OneNorm, uplo, n, a, pda, &anorm, &fail); nag_zhe_norm(order, Nag_OneNorm, uplo, n, b, pdb, &bnorm, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zhe_norm (f16ucc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Solve the generalized Hermitian eigenvalue problem A*B*x = lambda*x * using nag_zhegvd (f08sqc). */ nag_zhegvd(order, 2, Nag_DoBoth, uplo, n, a, pda, b, pdb, w, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zhegvd (f08sqc).\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--) A(i, j) = nag_complex_divide(A(i, j),A(1, j)); /* Print eigensolution */ printf(" Eigenvalues\n "); for (j = 0; j < n; ++j) printf(" %11.4f%s", w[j], j%6 == 5?"\n":""); printf("\n"); /* Prnit normalized vectors using nag_gen_complx_mat_print (x04dac). */ fflush(stdout); nag_gen_complx_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, a, pda, "Eigenvectors", 0, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_gen_complx_mat_print (x04dac).\n%s\n", fail.message); exit_status = 1; goto END; } /* Estimate the reciprocal condition number of the Cholesky factor of B. * to estimate the reciprocal condition. * nag_ztrcon (f07tuc) * Note that: cond(B) = 1/rcond**2 */ nag_ztrcon(order, Nag_OneNorm, uplo, Nag_NonUnitDiag, n, b, pdb, &rcond, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_ztrcon (f07tuc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print the reciprocal condition number of B */ rcondb = rcond * rcond; printf("\nEstimate of reciprocal condition number for B\n %11.1e\n", rcondb); /* Get the machine precision, using nag_machine_precision (x02ajc) */ eps = nag_machine_precision; if (rcond < eps) { printf("\nB is very ill-conditioned, error estimates have not been " "computed\n"); goto END; } /* Estimate reciprocal condition numbers for the eigenvectors of A*B-lambda*I * nag_ddisna (f08flc) */ nag_ddisna(Nag_EigVecs, n, n, w, rcondz, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_ddisna (f08flc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Compute the error estimates for the eigenvalues and eigenvectors. */ t1 = 1.0 / rcond; t2 = eps * t1; t3 = anorm * bnorm; for (i = 0; i < n; ++i) { eerbnd[i] = eps * (t3 + abs(w[i])/rcondb); zerbnd[i] = t2 * (t3/rcondz[i] + t1); } /* Print the approximate error bounds for the eigenvalues and vectors. */ printf("\nError estimates for the eigenvalues\n "); for (i = 0; i < n; ++i) printf(" %11.1e%s", eerbnd[i], i%6 == 5?"\n":""); printf("\n\nError estimates for the eigenvectors\n "); for (i = 0; i < n; ++i) printf(" %11.1e%s", zerbnd[i], i%6 == 5?"\n":""); printf("\n"); END: if (a) NAG_FREE(a); if (b) NAG_FREE(b); if (eerbnd) NAG_FREE(eerbnd); if (rcondz) NAG_FREE(rcondz); if (w) NAG_FREE(w); if (zerbnd) NAG_FREE(zerbnd); return exit_status; }