NAG Library Manual, Mark 27.3
```/* nag_lapackeig_zunmhr (f08nuc) Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
*
* Mark 27.3, 2021.
*/

#include <nag.h>
#include <stdio.h>
int main(void) {
/* Scalars */
Integer i, j, m, n, pda, pdh, pdvl, pdvr, pdz;
Integer tau_len, ifaill_len, select_len, w_len;
Integer exit_status = 0;
double thresh;
NagError fail;
Nag_OrderType order;
/* Arrays */
Complex *a = 0, *h = 0, *vl = 0, *vr = 0, *z = 0, *w = 0, *tau = 0;
Integer *ifaill = 0, *ifailr = 0;
Nag_Boolean *select = 0;

#ifdef NAG_COLUMN_MAJOR
#define A(I, J) a[(J - 1) * pda + I - 1]
#define H(I, J) h[(J - 1) * pdh + I - 1]
#define VR(I, J) vr[(J - 1) * pdvr + I - 1]
order = Nag_ColMajor;
#else
#define A(I, J) a[(I - 1) * pda + J - 1]
#define H(I, J) h[(I - 1) * pdh + J - 1]
#define VR(I, J) vr[(I - 1) * pdvr + J - 1]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

printf("nag_lapackeig_zunmhr (f08nuc) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%*[^\n] ", &n);

pda = n;
pdh = n;
pdvl = n;
pdvr = n;
pdz = 1;
tau_len = n;
w_len = n;
ifaill_len = n;
select_len = n;

/* Allocate memory */
if (!(a = NAG_ALLOC(n * n, Complex)) || !(h = NAG_ALLOC(n * n, Complex)) ||
!(vl = NAG_ALLOC(n * n, Complex)) || !(vr = NAG_ALLOC(n * n, Complex)) ||
!(z = NAG_ALLOC(1 * 1, Complex)) || !(w = NAG_ALLOC(w_len, Complex)) ||
!(ifaill = NAG_ALLOC(ifaill_len, Integer)) ||
!(ifailr = NAG_ALLOC(ifaill_len, Integer)) ||
!(select = NAG_ALLOC(select_len, Nag_Boolean)) ||
!(tau = NAG_ALLOC(tau_len, Complex))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
/* Read A from data file */
for (i = 1; i <= n; ++i) {
for (j = 1; j <= n; ++j)
scanf(" ( %lf , %lf )", &A(i, j).re, &A(i, j).im);
}
scanf("%*[^\n] ");
scanf("%lf%*[^\n] ", &thresh);

/* Reduce A to upper Hessenberg form */
/* nag_lapackeig_zgehrd (f08nsc).
* Unitary reduction of complex general matrix to upper
* Hessenberg form
*/
nag_lapackeig_zgehrd(order, n, 1, n, a, pda, tau, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zgehrd (f08nsc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

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

/* Calculate the eigenvalues of H (same as A) */
/* nag_lapackeig_zhseqr (f08psc).
* Eigenvalues and Schur factorization of complex upper
* Hessenberg matrix reduced from complex general matrix
*/
nag_lapackeig_zhseqr(order, Nag_EigVals, Nag_NotZ, 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;
}

/* Print eigenvalues */
printf(" Eigenvalues\n");
for (i = 0; i < n; ++i)
printf(" (%7.4f,%7.4f)", w[i].re, w[i].im);
printf("\n");
for (i = 0; i < n; ++i)
select[i] = w[i].re < thresh ? Nag_TRUE : Nag_FALSE;
/* Calculate the eigenvectors of H (as specified by SELECT), */
/* storing the result in VR */
/* nag_lapackeig_zhsein (f08pxc).
* Selected right and/or left eigenvectors of complex upper
* Hessenberg matrix by inverse iteration
*/
nag_lapackeig_zhsein(order, Nag_RightSide, Nag_HSEQRSource, Nag_NoVec, select,
n, a, pda, w, vl, pdvl, vr, pdvr, n, &m, ifaill, ifailr,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zhsein (f08pxc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Calculate the eigenvectors of A = Q * VR */
/* nag_lapackeig_zunmhr (f08nuc).
* Apply unitary transformation matrix from reduction to
* Hessenberg form determined by nag_lapackeig_zgehrd (f08nsc)
*/
nag_lapackeig_zunmhr(order, Nag_LeftSide, Nag_NoTrans, n, m, 1, n, a, pda,
tau, vr, pdvr, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zunmhr (f08nuc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Normalize the eigenvectors */
for (j = 1; j <= m; j++) {
for (i = n; i >= 1; i--) {
VR(i, j) = nag_complex_divide(VR(i, j), VR(1, j));
}
}

/* Print Eigenvectors */
printf("\n");
/* nag_file_print_matrix_complex_gen_comp (x04dbc).
* Print complex general matrix (comprehensive)
*/
fflush(stdout);
nag_file_print_matrix_complex_gen_comp(
order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, m, vr, pdvr,
Nag_BracketForm, "%7.4f", "Contents of array VR", Nag_IntegerLabels, 0,
Nag_IntegerLabels, 0, 80, 0, 0, &fail);
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;
}
END:
NAG_FREE(a);
NAG_FREE(h);
NAG_FREE(vl);
NAG_FREE(vr);
NAG_FREE(z);
NAG_FREE(w);
NAG_FREE(ifaill);
NAG_FREE(ifailr);
NAG_FREE(select);
NAG_FREE(tau);
return exit_status;
}
```