NAG Library Manual, Mark 27.2
```/* nag_lapackeig_zhseqr (f08psc) Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
*
* Mark 27.2, 2021.
*/

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

int main(void) {
/* Scalars */
Complex alpha, beta;
double norm;
Integer i, j, n, pdc, pdd, pdh, pdz, w_len;
Integer exit_status = 0;
NagError fail;
Nag_OrderType order;
/* Arrays */
Complex *c = 0, *d = 0, *h = 0, *w = 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_lapackeig_zhseqr (f08psc) 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
w_len = n;

/* Allocate memory */
if (!(c = NAG_ALLOC(n * n, Complex)) || !(d = NAG_ALLOC(n * n, Complex)) ||
!(h = NAG_ALLOC(n * n, Complex)) || !(w = NAG_ALLOC(w_len, Complex)) ||
!(z = NAG_ALLOC(n * n, Complex))) {
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 , %lf )", &H(i, j).re, &H(i, j).im);
}
scanf("%*[^\n] ");

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

/* nag_file_print_matrix_complex_gen_comp (x04dbc): Print matrix H */
fflush(stdout);
nag_file_print_matrix_complex_gen_comp(
order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, h, pdh, Nag_BracketForm,
"%7.4f", "Matrix H", Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0,
&fail);
printf("\n");
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_complex_gen_comp (x04dbc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

/* Calculate the eigenvalues and Schur factorization of H */
/* nag_lapackeig_zhseqr (f08psc).
* Eigenvalues and Schur factorization of complex upper
* Hessenberg matrix reduced from complex general matrix
*/
nag_lapackeig_zhseqr(order, Nag_Schur, Nag_InitZ, n, 1, n, h, pdh, w, z, pdz,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zhseqr (f08psc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* nag_blast_zgemm (f16zac): Compute A - Z*T*Z^H from the factorization of */
/* A and store in matrix D */
alpha.re = 1.0;
alpha.im = 0.0;
beta.re = 0.0;
beta.im = 0.0;
nag_blast_zgemm(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_blast_zgemm (f16zac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
alpha.re = -1.0;
beta.re = 1.0;
nag_blast_zgemm(order, Nag_NoTrans, Nag_ConjTrans, n, n, n, alpha, c, pdc, z,
pdz, beta, d, pdd, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_zgemm (f16zac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_blast_zge_norm (f16uac): Find norm of matrix D and print warning if */
/* it is too large */
nag_blast_zge_norm(order, Nag_OneNorm, n, n, d, pdd, &norm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_zge_norm (f16uac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
if (norm > pow(x02ajc(), 0.8)) {
printf("%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("(%7.4f,%7.4f) ", w[i - 1].re, w[i - 1].im);
printf("\n\n");
}

END:
NAG_FREE(c);
NAG_FREE(d);
NAG_FREE(h);
NAG_FREE(w);
NAG_FREE(z);

return exit_status;
}
```