NAG Library Manual, Mark 27.2
Interfaces:  FL   CL   CPP   AD
```/* nag_lapackeig_ztrsyl (f08qvc) 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;
Integer i, j, m, n, pda, pdb, pdc, pdd, pde, pdf;
Integer exit_status = 0;
double norm, scale;
NagError fail;
Nag_OrderType order;
Nag_SignType sign = Nag_Minus;
/* Arrays */
Complex *a = 0, *b = 0, *c = 0, *d = 0, *e = 0, *f = 0;

#ifdef NAG_COLUMN_MAJOR
#define A(I, J) a[(J - 1) * pda + I - 1]
#define B(I, J) b[(J - 1) * pdb + I - 1]
#define C(I, J) c[(J - 1) * pdc + I - 1]
#define D(I, J) d[(J - 1) * pdd + I - 1]
#define E(I, J) e[(J - 1) * pde + I - 1]
#define F(I, J) f[(J - 1) * pdf + I - 1]
order = Nag_ColMajor;
#else
#define A(I, J) a[(I - 1) * pda + J - 1]
#define B(I, J) b[(I - 1) * pdb + J - 1]
#define C(I, J) c[(I - 1) * pdc + J - 1]
#define D(I, J) d[(I - 1) * pdd + J - 1]
#define E(I, J) e[(I - 1) * pde + J - 1]
#define F(I, J) f[(I - 1) * pdf + J - 1]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

printf("nag_lapackeig_ztrsyl (f08qvc) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &m, &n);
pda = m;
pdb = n;
#ifdef NAG_COLUMN_MAJOR
pdc = m;
pdd = m;
pde = m;
pdf = m;
#else
pdc = n;
pdd = n;
pde = n;
pdf = n;
#endif

/* Allocate memory */
if (!(a = NAG_ALLOC(m * m, Complex)) || !(b = NAG_ALLOC(n * m, Complex)) ||
!(c = NAG_ALLOC(m * n, Complex)) || !(d = NAG_ALLOC(m * n, Complex)) ||
!(e = NAG_ALLOC(m * n, Complex)) || !(f = NAG_ALLOC(m * n, Complex))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Read A, B and C from data file */
for (i = 1; i <= m; ++i) {
for (j = 1; j <= m; ++j)
scanf(" ( %lf , %lf ) ", &A(i, j).re, &A(i, j).im);
}
scanf("%*[^\n] ");
for (i = 1; i <= n; ++i) {
for (j = 1; j <= n; ++j)
scanf(" ( %lf , %lf ) ", &B(i, j).re, &B(i, j).im);
}
scanf("%*[^\n] ");
for (i = 1; i <= m; ++i) {
for (j = 1; j <= n; ++j)
scanf(" ( %lf , %lf ) ", &C(i, j).re, &C(i, j).im);
}
scanf("%*[^\n] ");

/* Copy C into F */
for (i = 1; i <= m; i++) {
for (j = 1; j <= m; j++) {
F(i, j).re = C(i, j).re;
F(i, j).im = C(i, j).im;
}
}

/* nag_file_print_matrix_complex_gen_comp (x04dbc): Print matrix C */
fflush(stdout);
nag_file_print_matrix_complex_gen_comp(
order, Nag_GeneralMatrix, Nag_NonUnitDiag, m, n, c, pdc, Nag_BracketForm,
"%7.4f", "Matrix C", 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;
}

/* Reorder the Schur factorization T */
/* nag_lapackeig_ztrsyl (f08qvc).
* Solve complex Sylvester matrix equation AX + XB = C, A
* and B are upper triangular or conjugate-transposes
*/
nag_lapackeig_ztrsyl(order, Nag_NoTrans, Nag_NoTrans, sign, m, n, a, pda, b,
pdb, c, pdc, &scale, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_ztrsyl (f08qvc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_blast_zgemm (f16zac): Compute aC - (A*X + X*B*sign) from the solution
*/
/* and store in matrix E */
alpha.re = 1.0;
alpha.im = 0.0;
beta.re = 0.0;
beta.im = 0.0;
nag_blast_zgemm(order, Nag_NoTrans, Nag_NoTrans, m, n, m, alpha, a, pda, c,
pdc, 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;
}
if (sign == Nag_Minus)
alpha.re = -1.0;
else
alpha.re = 1.0;
beta.re = 1.0;
nag_blast_zgemm(order, Nag_NoTrans, Nag_NoTrans, m, n, n, alpha, c, pdc, b,
pdb, 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;
}
for (i = 1; i <= m; i++) {
for (j = 1; j <= n; j++) {
E(i, j).re = scale * F(i, j).re - D(i, j).re;
E(i, j).im = scale * F(i, j).im - D(i, j).im;
}
}

/* nag_blast_zge_norm (f16uac): Find norm of matrix E and print warning if */
/* it is too large */
nag_blast_zge_norm(order, Nag_OneNorm, m, n, e, pde, &norm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_dge_norm (f16rac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
if (norm > pow(x02ajc(), 0.8)) {
printf("%s\n%s\n", "Norm of aC - (A*X + X*B*sign) is much greater than 0.",
"Schur factorization has failed.");
} else {
printf(" SCALE = %11.2e\n", scale);
}

END:
NAG_FREE(a);
NAG_FREE(b);
NAG_FREE(c);
NAG_FREE(d);
NAG_FREE(e);
NAG_FREE(f);

return exit_status;
}
```