/* nag_dspgvd (f08tcc) Example Program. * * Copyright 2011 Numerical Algorithms Group. * * Mark 23, 2011. */ #include #include #include #include #include #include #include #include int main(void) { /* Scalars */ double anorm, bnorm, eps, rcond, rcondb, t1; Integer i, j, n; Integer exit_status = 0; /* Arrays */ double *ap = 0, *bp = 0, *eerbnd = 0, *w = 0; double dummy[1]; char nag_enum_arg[40]; /* Nag Types */ NagError fail; Nag_OrderType order; Nag_UploType uplo; #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 B_UPPER(I, J) bp[J*(J-1)/2 + I - 1] #define B_LOWER(I, J) bp[(2*n-J)*(J-1)/2 + I - 1] order = Nag_ColMajor; #else #define A_UPPER(I, J) ap[(2*n-I)*(I-1)/2 + J - 1] #define A_LOWER(I, J) ap[I*(I-1)/2 + J - 1] #define B_UPPER(I, J) bp[(2*n-I)*(I-1)/2 + J - 1] #define B_LOWER(I, J) bp[I*(I-1)/2 + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); printf("nag_dspgvd (f08tcc) 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); /* Allocate memory */ if (!(ap = NAG_ALLOC(n*(n+1)/2, double)) || !(bp = NAG_ALLOC(n*(n+1)/2, double)) || !(eerbnd = NAG_ALLOC(n, double)) || !(w = NAG_ALLOC(n, double))) { printf("Allocation failure\n"); exit_status = -1; goto END; } /* Read the triangular parts of the matrices A and B from data file. */ if (uplo == Nag_Upper) { for (i = 1; i <= n; ++i) for (j = i; j <= n; ++j) scanf("%lf", &A_UPPER(i, j)); scanf("%*[^\n]"); for (i = 1; i <= n; ++i) for (j = i; j <= n; ++j) scanf("%lf", &B_UPPER(i, j)); } else if (uplo == Nag_Lower) { for (i = 1; i <= n; ++i) for (j = 1; j <= i; ++j) scanf("%lf", &A_LOWER(i, j)); scanf("%*[^\n]"); for (i = 1; i <= n; ++i) for (j = 1; j <= i; ++j) scanf("%lf", &B_LOWER(i, j)); } scanf("%*[^\n]"); /* Compute the one-norms of the symmetric matrices A and B * using nag_dsp_norm (f16rdc). */ nag_dsp_norm(order, Nag_OneNorm, uplo, n, ap, &anorm, &fail); nag_dsp_norm(order, Nag_OneNorm, uplo, n, bp, &bnorm, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dsp_norm (f16rdc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Solve the generalized symmetric eigenvalue problem A*B*x = lambda*x * using nag_dspgvd (f08tcc). * In the following call the 9th argument is set to n rather than 1 to * avoid an incorrect error message in some vendor versions of LAPACK. */ nag_dspgvd(order, 2, Nag_EigVals, uplo, n, ap, bp, w, dummy, n, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dspgvd (f08tcc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print eigensolution */ printf("Eigenvalues\n "); for (j = 0; j < n; ++j) printf(" %11.4f%s", w[j], j%6 == 5?"\n":""); printf("\n"); /* Estimate the reciprocal condition number of the Cholesky factor of B. * nag_dtpcon (f07ugc). * Note that: cond(B) = 1/(rcond*rcond). */ nag_dtpcon(order, Nag_OneNorm, uplo, Nag_NonUnitDiag, n, bp, &rcond, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dtpcon (f07ugc).\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; } t1 = anorm * bnorm; for (i = 0; i < n; ++i) eerbnd[i] = eps * (t1 + fabs(w[i])/rcondb); /* Print the approximate error bounds for the eigenvalues */ 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"); END: if (ap) NAG_FREE(ap); if (bp) NAG_FREE(bp); if (eerbnd) NAG_FREE(eerbnd); if (w) NAG_FREE(w); return exit_status; }