```/* nag_dtrsen (f08qgc) Example Program.
*
* Copyright 2017 Numerical Algorithms Group.
*
* Mark 26.1, 2017.
*/

#include <stdio.h>
#include <math.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagf08.h>
#include <nagf16.h>
#include <nagx02.h>
#include <nagx04.h>

int main(void)
{
/* Scalars */
Integer i, j, m, n, pda, pdc, pdq, pdt, select_len, w_len;
Integer exit_status = 0;
double alpha, beta, norm, s, sep;
NagError fail;
Nag_OrderType order;
/* Arrays */
double *a = 0, *c = 0, *q = 0, *t = 0, *wi = 0, *wr = 0;
char nag_enum_arg;
Nag_Boolean *select = 0;

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

INIT_FAIL(fail);

printf("nag_dtrsen (f08qgc) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%*[^\n] ", &n);
#ifdef NAG_COLUMN_MAJOR
pda = n;
pdc = n;
pdq = n;
pdt = n;
#else
pda = n;
pdc = n;
pdq = n;
pdt = n;
#endif
w_len = n;
select_len = n;

/* Allocate memory */
if (!(a = NAG_ALLOC(n * n, double)) ||
!(c = NAG_ALLOC(n * n, double)) ||
!(q = NAG_ALLOC(n * n, double)) ||
!(wi = NAG_ALLOC(w_len, double)) ||
!(wr = NAG_ALLOC(w_len, double)) ||
!(select = NAG_ALLOC(select_len, Nag_Boolean)) ||
!(t = NAG_ALLOC(n * n, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Read T and Q from data file */
for (i = 1; i <= n; ++i) {
for (j = 1; j <= n; ++j)
scanf("%lf", &T(i, j));
}
scanf("%*[^\n] ");
for (i = 1; i <= n; ++i) {
for (j = 1; j <= n; ++j)
scanf("%lf", &Q(i, j));
}
scanf("%*[^\n] ");
for (i = 0; i < n; ++i) {
scanf("%39s", nag_enum_arg);
/* nag_enum_name_to_value (x04nac).
* Converts NAG enum member name to value
*/
select[i] = (Nag_Boolean) nag_enum_name_to_value(nag_enum_arg);
}
scanf("%*[^\n] ");

/* nag_dgemm (f16yac): Compute Q*T*QT and store in matrix A */
alpha = 1.0;
beta = 0.0;
nag_dgemm(order, Nag_NoTrans, Nag_NoTrans, n, n, n, alpha, q, pdq,
t, pdt, beta, c, pdc, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dgemm (f16yac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
nag_dgemm(order, Nag_NoTrans, Nag_Trans, n, n, n, alpha, c, pdc, q,
pdq, beta, a, pda, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dgemm (f16yac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_gen_real_mat_print (x04cac): Print Matrix A. */
fflush(stdout);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n,
a, pda, "Matrix A", 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;
}
printf("\n");

/* Reorder the Schur factorization T */
/* nag_dtrsen (f08qgc).
* Reorder Schur factorization of real matrix, form
* orthonormal basis of right invariant subspace for
* selected eigenvalues, with estimates of sensitivities
*/
nag_dtrsen(order, Nag_DoBoth, Nag_UpdateSchur, select, n, t, pdt,
q, pdq, wr, wi, &m, &s, &sep, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dtrsen (f08qgc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_dgemm (f16yac): Compute A = Q*T*Q^T - Qt*Tt*Qt^T */
alpha = 1.0;
beta = 0.0;
nag_dgemm(order, Nag_NoTrans, Nag_NoTrans, n, n, n, alpha, q, pdq,
t, pdt, beta, c, pdc, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dgemm (f16yac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
alpha = -1.0;
beta = 1.0;
nag_dgemm(order, Nag_NoTrans, Nag_Trans, n, n, n, alpha, c, pdc, q,
pdq, beta, a, pda, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dgemm (f16yac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_dge_norm (f16rac): Find norm of matrix A and print warning if */
/* it is too large */
nag_dge_norm(order, Nag_OneNorm, n, n, a, pda, &norm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dge_norm (f16rac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
if (norm > pow(x02ajc(), 0.8)) {
printf("%s\n%s\n",
"Norm of Q*T*Q^H - (Qt*Tt*Qt^H) is much greater than 0.",
"Schur factorization has failed.");
}
else {
/* Print condition number estimates */
printf(" Condition number estimate of the selected cluster of"
" eigenvalues = %11.2e\n", 1.0 / s);
printf("\n Condition number estimate of the specified invariant"
" subspace = %11.2e\n", 1.0 / sep);
}
END:
NAG_FREE(a);
NAG_FREE(c);
NAG_FREE(q);
NAG_FREE(t);
NAG_FREE(wi);
NAG_FREE(wr);
NAG_FREE(select);

return exit_status;
}
```