```/* nag_dgeesx (f08pbc) 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 <nagf08.h>
#include <nagf16.h>
#include <nagx02.h>
#include <nagx04.h>

#ifdef __cplusplus
extern "C"
{
#endif
static Nag_Boolean NAG_CALL select_fun(const double wr, const double wi);
#ifdef __cplusplus
}
#endif

int main(void)
{

/* Scalars */
double alpha, anorm, beta, eps, norm, rconde, rcondv;
Integer i, j, n, pda, pdc, pdd, pdvs, sdim;
Integer exit_status = 0;

/* Arrays */
double *a = 0, *c = 0, *d = 0, *vs = 0, *wi = 0, *wr = 0;

/* Nag Types */
NagError fail;
Nag_OrderType order;

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

INIT_FAIL(fail);

printf("nag_dgeesx (f08pbc) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n]");
scanf("%" NAG_IFMT "%*[^\n]", &n);
if (n < 0) {
printf("Invalid n\n");
exit_status = 1;
return exit_status;
}

pda = n;
pdc = n;
pdd = n;
pdvs = n;
/* Allocate memory */
if (!(a = NAG_ALLOC(n * n, double)) ||
!(c = NAG_ALLOC(n * n, double)) ||
!(d = NAG_ALLOC(n * n, double)) ||
!(vs = NAG_ALLOC(n * n, double)) ||
!(wi = NAG_ALLOC(n, double)) || !(wr = NAG_ALLOC(n, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Read in the matrix A */
for (i = 1; i <= n; ++i)
for (j = 1; j <= n; ++j)
scanf("%lf", &A(i, j));
scanf("%*[^\n]");

/* Copy A to D: nag_dge_copy (f16qfc),
* real valued general matrix copy.
*/
nag_dge_copy(order, Nag_NoTrans, n, n, a, pda, d, pdd, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dge_copy (f16qfc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* nag_dge_norm (f16rac): Find norm of matrix A for use later
* in relative error test.
*/
nag_dge_norm(order, Nag_OneNorm, n, n, a, pda, &anorm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dge_norm (f16rac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_gen_real_mat_print (x04cac): Print Matrix A. */
fflush(stdout);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, a,
pda, "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;
}

/* Find the Schur factorization of A using nag_dgeesx (f08pbc). */
nag_dgeesx(order, Nag_Schur, Nag_SortEigVals, select_fun, Nag_RCondBoth, n,
a, pda, &sdim, wr, wi, vs, pdvs, &rconde, &rcondv, &fail);

if (fail.code != NE_NOERROR && fail.code != NE_SCHUR_REORDER_SELECT) {
printf("Error from nag_dgeesx (f08pbc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Reconstruct A from Schur Factorization Z*T*Trans(Z) where T is upper
* triangular and stored in A. This can be done using the following steps:
* i.  C = Z*T (nag_dgemm, f16yac),
* ii. D = D-C*trans(Z) (nag_dgemm, f16yac).
*/
alpha = 1.0;
beta = 0.0;
nag_dgemm(order, Nag_NoTrans, Nag_NoTrans, n, n, n, alpha, vs, pdvs, a, pda,
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;
}

/* nag_dgemm (f16yac):
* Compute D = A - C*Z^T.
*/
alpha = -1.0;
beta = 1.0;
nag_dgemm(order, Nag_NoTrans, Nag_Trans, n, n, n, alpha, c, pdc, vs,
pdvs, 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 difference matrix D and print
* warning if it is too large relative to norm of A.
*/
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;
}

/* Get the machine precision, using nag_machine_precision (x02ajc) */
eps = nag_machine_precision;
if (norm > pow(eps, 0.8) * MAX(anorm, 1.0)) {
printf("||A-(Z*T*Z^T)||/||A|| is larger than expected.\n"
"Schur factorization has failed.\n");
exit_status = 1;
goto END;
}

/* Print details on eigenvalues */
printf("Number of eigenvalues for which select is true = %4" NAG_IFMT
"\n\n", sdim);
if (fail.code == NE_SCHUR_REORDER_SELECT) {
printf(" ** Note that rounding errors mean that leading eigenvalues in the"
" Schur form\n    no longer satisfy select(lambda) = Nag_TRUE\n\n");
} else {
printf("The selected eigenvalues are:\n");
for (i = 0; i < sdim; i++)
printf("%3" NAG_IFMT " (%13.4e, %13.4e)\n", i + 1, wr[i], wi[i]);
}

/* Print out the reciprocal condition numbers */
printf("\nReciprocal of projection norm onto the invariant subspace\n");
printf("%26sfor the selected eigenvalues rconde = %8.1e\n\n", "", rconde);
printf("Reciprocal condition number for the invariant subspace rcondv = "
"%8.1e\n\n", rcondv);

/* Compute the approximate asymptotic error bound on the average absolute
* error of the selected eigenvalues given by  eps*norm(A)/rconde.
*/
printf("Approximate asymptotic error bound for selected eigenvalues   = "
"%8.1e\n\n", eps * anorm / rconde);

/* Compute an approximate asymptotic bound on the maximum angular error in
* the computed invariant subspace given by  eps*norm(A)/rcondv
*/
printf("Approximate asymptotic error bound for the invariant subspace = "
"%8.1e\n", eps * anorm / rcondv);

END:
NAG_FREE(a);
NAG_FREE(c);
NAG_FREE(d);
NAG_FREE(vs);
NAG_FREE(wi);
NAG_FREE(wr);

return exit_status;
}

static Nag_Boolean NAG_CALL select_fun(const double ar, const double ai)
{
/* Boolean function select for use with nag_dgees (f08pac)
* Returns the value Nag_TRUE if the eigenvalue is real and positive
*/

return (ar > 0.0 && ai == 0.0 ? Nag_TRUE : Nag_FALSE);
}
```