```/* nag_lapackeig_zgebal (f08nvc) Example Program.
*
* Copyright 2019 Numerical Algorithms Group.
*
* Mark 27.0, 2019.
*/

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

int main(void)
{
/* Scalars */
Integer firstnz, i, ihi, ilo, j, m, n, pda, pdh, pdvr;
Integer scale_len, tau_len, w_len;
Integer exit_status = 0;
NagError fail;
Nag_OrderType order;
/* Arrays */
Complex *a = 0, *h = 0, *tau = 0, *vl = 0, *vr = 0, *w = 0;
double *scale = 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_zgebal (f08nvc) Example Program Results\n\n");

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

pda = n;
pdh = n;
pdvr = n;
scale_len = n;
tau_len = n;
w_len = n;

/* Allocate memory */
if (!(a = NAG_ALLOC(n * n, Complex)) ||
!(h = NAG_ALLOC(n * n, Complex)) ||
!(scale = NAG_ALLOC(scale_len, double)) ||
!(tau = NAG_ALLOC(tau_len, Complex)) ||
!(vl = NAG_ALLOC(1 * 1, Complex)) ||
!(vr = NAG_ALLOC(n * n, Complex)) ||
!(w = NAG_ALLOC(w_len, Complex)) ||
!(select = NAG_ALLOC(1, Nag_Boolean)))
{
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] ");

/* Balance A */
/* nag_lapackeig_zgebal (f08nvc).
* Balance complex general matrix
*/
nag_lapackeig_zgebal(order, Nag_DoBoth, n, a, pda, &ilo, &ihi, scale, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zgebal (f08nvc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Reduce A to upper Hessenberg form H = (Q^H)*A*Q */
/* nag_lapackeig_zgehrd (f08nsc).
* Unitary reduction of complex general matrix to upper
* Hessenberg form
*/
nag_lapackeig_zgehrd(order, n, ilo, ihi, 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 and VR */
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;
VR(i, j).re = A(i, j).re;
VR(i, j).im = A(i, j).im;
}
}

/* Form Q explicitly, storing the result in VR */
/* nag_lapackeig_zunghr (f08ntc).
* Generate unitary transformation matrix from reduction to
* Hessenberg form determined by nag_lapackeig_zgehrd (f08nsc)
*/
nag_lapackeig_zunghr(order, n, 1, n, vr, pdvr, tau, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zunghr (f08ntc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Calculate the eigenvalues and Schur factorization of A */
/* 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_UpdateZ, n, ilo, ihi, h, pdh,
w, vr, pdvr, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zhseqr (f08psc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
printf(" Eigenvalues\n");
for (i = 0; i < n; ++i)
printf(" (%7.4f,%7.4f)", w[i].re, w[i].im);
printf("\n");
/* Calculate the eigenvectors of A, storing the result in VR */
/* nag_lapackeig_ztrevc (f08qxc).
* Left and right eigenvectors of complex upper triangular
* matrix
*/
nag_lapackeig_ztrevc(order, Nag_RightSide, Nag_BackTransform, select, n,
h, pdh, vl, 1, vr, pdvr, n, &m, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_ztrevc (f08qxc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* nag_lapackeig_zgebak (f08nwc).
* Transform eigenvectors of complex balanced matrix to
* those of original matrix supplied to nag_lapackeig_zgebal (f08nvc)
*/
nag_lapackeig_zgebak(order, Nag_DoBoth, Nag_RightSide, n, ilo, ihi, scale,
m, vr, pdvr, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zgebak (f08nwc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Normalize the eigenvectors */
for (j = 1; j <= m; j++) {
firstnz = n;
for (i = n; i >= 1; i--) {
if (VR(i, j).re != 0 || VR(i, j).im != 0) {
firstnz = i;
}
}
for (i = n; i >= 1; i--) {
VR(i, j) = nag_complex_divide(VR(i, j), VR(firstnz, 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(scale);
NAG_FREE(tau);
NAG_FREE(vl);
NAG_FREE(vr);
NAG_FREE(w);
NAG_FREE(select);

return exit_status;
}
```