```/* nag_dormhr (f08ngc) Example Program.
*
* Copyright 2014 Numerical Algorithms Group.
*
* Mark 7, 2001.
* Mark 7b revised, 2004.
*/

#include <stdio.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <naga02.h>
#include <nagf08.h>
#include <nagx04.h>

int main(void)
{
/* Scalars */
Integer       i, j, k, m, n, pda, pdh, pdvl, pdvr, pdz;
Integer       tau_len, ifaill_len, select_len, w_len;
Integer       exit_status = 0;
double        thresh;
Complex       eig, eig1;
/* Arrays */
double        *a = 0, *h = 0, *vl = 0, *vr = 0, *z = 0, *wi = 0, *wr = 0;
double        *tau = 0;
Integer       *ifaill = 0, *ifailr = 0;

/* Nag Types */
NagError      fail;
Nag_OrderType order;
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_dormhr (f08ngc) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%ld%*[^\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, double)) ||
!(h = NAG_ALLOC(n * n, double)) ||
!(vl = NAG_ALLOC(n * n, double)) ||
!(vr = NAG_ALLOC(n * n, double)) ||
!(z = NAG_ALLOC(1 * 1, double)) ||
!(wi = NAG_ALLOC(w_len, double)) ||
!(wr = NAG_ALLOC(w_len, double)) ||
!(ifaill = NAG_ALLOC(ifaill_len, Integer)) ||
!(ifailr = NAG_ALLOC(ifaill_len, Integer)) ||
!(select = NAG_ALLOC(select_len, Nag_Boolean)) ||
!(tau = NAG_ALLOC(tau_len, double)))
{
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", &A(i, j));
scanf("%*[^\n]");
scanf("%lf%*[^\n]", &thresh);

/* Reduce A to upper Hessenberg form */
/* nag_dgehrd (f08nec).
* Orthogonal reduction of real general matrix to upper
* Hessenberg form
*/
nag_dgehrd(order, n, 1, n, a, pda, tau, &fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_dgehrd (f08nec).\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) = A(i, j);

/* Calculate the eigenvalues of H (same as A) */
/* nag_dhseqr (f08pec).
* Eigenvalues and Schur factorization of real upper
* Hessenberg matrix reduced from real general matrix
*/
nag_dhseqr(order, Nag_EigVals, Nag_NotZ, 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;
}

/* Print eigenvalues */
printf(" Eigenvalues\n");
for (i = 0; i < n; ++i)
printf(" (%8.4f,%8.4f)\n", wr[i], wi[i]);
printf("\n");
for (i = 0; i < n; ++i)
select[i] = wr[i] < thresh?Nag_TRUE:Nag_FALSE;
/* Calculate the eigenvectors of H (as specified by SELECT), */
/* storing the result in VR */
/* nag_dhsein (f08pkc).
* Selected right and/or left eigenvectors of real upper
* Hessenberg matrix by inverse iteration
*/
nag_dhsein(order, Nag_RightSide, Nag_HSEQRSource, Nag_NoVec, select,
n, a, pda, wr, wi, vl, pdvl, vr, pdvr, n, &m, ifaill,
ifailr, &fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_dhsein (f08pkc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Calculate the eigenvectors of A = Q * VR */
/* nag_dormhr (f08ngc).
* Apply orthogonal transformation matrix from reduction to
* Hessenberg form determined by nag_dgehrd (f08nec)
*/
nag_dormhr(order, Nag_LeftSide, Nag_NoTrans, n, m, 1, n, a, pda,
tau, vr, pdvr, &fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_dormhr (f08ngc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Scale selected eigenvectors */
j = 0;
for(k=0; k<n; k++)
{
if (select[k]) {
j++;
if (wi[k]==0.0) {
for(i=2; i<=n; i++) VR(i, j) = VR(i, j) / VR(1,j);
VR(1,j) = 1.0;
} else {
eig1 = nag_complex(VR(1,j),VR(1,j+1));
for(i=1; i<=n; i++) {
eig = nag_complex(VR(i, j),VR(i, j+1));
eig = nag_complex_divide(eig,eig1);
VR(i,j) = eig.re;
VR(i,j+1) = eig.im;
}
j++;
k++;
}
}
}
/* Print Eigenvectors */
/* nag_gen_real_mat_print (x04cac).
* Print real general matrix (easy-to-use)
*/
fflush(stdout);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, m, vr,
pdvr, "Contents of array VR", 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;
}
END:
NAG_FREE(a);
NAG_FREE(h);
NAG_FREE(vl);
NAG_FREE(vr);
NAG_FREE(z);
NAG_FREE(wi);
NAG_FREE(wr);
NAG_FREE(ifaill);
NAG_FREE(ifailr);
NAG_FREE(select);
NAG_FREE(tau);
return exit_status;
}
```