```/* nag_dhseqr (f08pec) Example Program.
*
* NAGPRODCODE Version.
*
* Copyright 2016 Numerical Algorithms Group.
*
* Mark 26, 2016.
*/

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

int main(void)
{
/* Scalars */
double alpha, beta, norm;
Integer i, j, n, pdc, pdd, pdh, pdz, wi_len, wr_len;
Integer exit_status = 0;
NagError fail;
Nag_OrderType order;
/* Arrays */
double *c = 0, *d = 0, *h = 0, *wi = 0, *wr = 0, *z = 0;

#ifdef NAG_COLUMN_MAJOR
#define H(I, J) h[(J-1)*pdh + I - 1]
#define D(I, J) d[(J-1)*pdd + I - 1]
order = Nag_ColMajor;
#else
#define H(I, J) h[(I-1)*pdh + J - 1]
#define D(I, J) d[(I-1)*pdd + J - 1]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

printf("nag_dhseqr (f08pec) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%*[^\n] ", &n);
#ifdef NAG_COLUMN_MAJOR
pdc = n;
pdd = n;
pdh = n;
pdz = n;
#else
pdc = n;
pdd = n;
pdh = n;
pdz = n;
#endif
wr_len = n;
wi_len = n;

/* Allocate memory */
if (!(c = NAG_ALLOC(n * n, double)) ||
!(d = NAG_ALLOC(n * n, double)) ||
!(h = NAG_ALLOC(n * n, double)) ||
!(wi = NAG_ALLOC(wi_len, double)) ||
!(wr = NAG_ALLOC(wr_len, double)) || !(z = NAG_ALLOC(n * n, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

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

/* Copy H into D */
for (i = 1; i <= n; ++i) {
for (j = 1; j <= n; ++j)
D(i, j) = H(i, j);
}

/* nag_gen_real_mat_print (x04cac): Print Matrix H. */
fflush(stdout);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n,
h, pdh, "Matrix A", 0, &fail);
printf("\n");
if (fail.code != NE_NOERROR) {
printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Calculate the eigenvalues and Schur factorization of H */
/* nag_dhseqr (f08pec).
* Eigenvalues and Schur factorization of real upper
* Hessenberg matrix reduced from real general matrix
*/
nag_dhseqr(order, Nag_Schur, Nag_InitZ, n, 1, n, h, pdh, wr,
wi, z, pdz, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dhseqr (f08pec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_dgemm (f16yac): Compute H - Z*T*Z^T from the factorization of */
/* H and store in matrix D */
alpha = 1.0;
beta = 0.0;
nag_dgemm(order, Nag_NoTrans, Nag_NoTrans, n, n, n, alpha, z, pdz,
h, pdh, 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, z,
pdz, beta, d, pdd, &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 D and print warning if */
/* it is too large */
nag_dge_norm(order, Nag_OneNorm, n, n, d, pdd, &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("\n%s\n%s\n", "Norm of H-(Z*T*Z^H) is much greater than 0.",
"Schur factorization has failed.");
}
else {
printf(" Eigenvalues\n");
for (i = 1; i <= n; ++i)
printf(" (%8.4f,%8.4f)", wr[i - 1], wi[i - 1]);
printf("\n");
}

END:
NAG_FREE(c);
NAG_FREE(d);
NAG_FREE(h);
NAG_FREE(wi);
NAG_FREE(wr);
NAG_FREE(z);

return exit_status;
}
```