NAG Library Manual, Mark 27.2
Interfaces:  FL   CL   CPP   AD
```/* nag_lapackeig_dtrsna (f08qlc) Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
*
* Mark 27.2, 2021.
*/

#include <nag.h>
#include <stdio.h>

int main(void) {
/* Scalars */
Integer i, j, m, n, pdt, pdvl, pdvr;
Integer s_len;
Integer exit_status = 0;
double eps, tnorm;
NagError fail;
Nag_OrderType order;
/* Arrays */
double *s = 0, *sep = 0, *t = 0, *vl = 0, *vr = 0;

#ifdef NAG_COLUMN_MAJOR
#define T(I, J) t[(J - 1) * pdt + I - 1]
order = Nag_ColMajor;
#else
#define T(I, J) t[(I - 1) * pdt + J - 1]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

printf("nag_lapackeig_dtrsna (f08qlc) Example Program Results\n");

/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%*[^\n] ", &n);
#ifdef NAG_COLUMN_MAJOR
pdt = n;
pdvl = n;
pdvr = n;
#else
pdt = n;
pdvl = n;
pdvr = n;
#endif
s_len = n;

/* Allocate memory */
if (!(t = NAG_ALLOC(n * n, double)) || !(vl = NAG_ALLOC(n * n, double)) ||
!(vr = NAG_ALLOC(n * n, double)) || !(s = NAG_ALLOC(s_len, double)) ||
!(sep = NAG_ALLOC(s_len, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Read T from data file */
for (i = 1; i <= n; ++i) {
for (j = 1; j <= n; ++j)
scanf("%lf", &T(i, j));
}
scanf("%*[^\n] ");

/* Calculate right and left eigrnvectors of real upper quasi-triangular
* matrix T using nag_lapackeig_dtrevc (f08qkc).
*/
nag_lapackeig_dtrevc(order, Nag_BothSides, Nag_ComputeAll, NULL, n, t, pdt,
vl, pdvl, vr, pdvr, n, &m, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dtrevc (f08qkc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Estimate condition numbers for all the eigenvalues and
* right eigenvectors of real upper quasi-triangular matrix T using
* nag_lapackeig_dtrsna (f08qlc).
*/
nag_lapackeig_dtrsna(order, Nag_DoBoth, Nag_ComputeAll, NULL, n, t, pdt, vl,
pdvl, vr, pdvr, s, sep, n, &m, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dtrsna (f08qlc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Print condition numbers of eigenvalues and right eigenvectors */
printf("\nS\n");
for (i = 0; i < n; ++i)
printf("%11.1e", s[i]);
printf("\n\nSep\n");
for (i = 0; i < n; ++i)
printf("%11.1e", sep[i]);
printf("\n");
/* Calculate approximate error estimates which depends on the 1-norm)
* of matrix T. The 1-norm of T is calculated using nag_blast_dge_norm
* (f16rac).
*/
nag_blast_dge_norm(order, Nag_OneNorm, n, n, t, pdt, &tnorm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_dge_norm (f16rac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* error estimates also depend on nag_machine_precision (x02ajc). */
eps = nag_machine_precision;
printf("\nApproximate error estimates for eigenvalues"
"of T (machine dependent)\n");
for (i = 0; i < m; ++i)
printf("%11.1e", eps * tnorm / s[i]);
printf("\n\nApproximate error estimates for right eigenvectors"
"of T (machine dependent)\n");
for (i = 0; i < m; ++i)
printf("%11.1e", eps * tnorm / sep[i]);
printf("\n");
END:
NAG_FREE(t);
NAG_FREE(s);
NAG_FREE(sep);
NAG_FREE(vl);
NAG_FREE(vr);

return exit_status;
}
```