NAG Library Manual, Mark 30.1
```/* nag_lapackeig_ztpqrt (f08bpc) Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
*
* Mark 30.1, 2024.
*/

#include <nag.h>

int main(void) {
/* Scalars */
double rnorm;
Integer exit_status = 0;
Integer pda, pdb, pdt;
Integer i, j, m, n, nb, nrhs;
/* Arrays */
Complex *a = 0, *b = 0, *c = 0, *t = 0;
/* Nag Types */
Nag_OrderType order;
NagError fail;

#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) * pdb + 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) * pdb + J - 1]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

printf("nag_lapackeig_ztpqrt (f08bpc) Example Program Results\n\n");
fflush(stdout);

/* Skip heading in data file */
scanf("%*[^\n]");
scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\n]", &m, &n, &nrhs);
nb = MIN(m, n);
if (!(a = NAG_ALLOC(m * n, Complex)) || !(b = NAG_ALLOC(m * nrhs, Complex)) ||
!(c = NAG_ALLOC(m * nrhs, Complex)) ||
!(t = NAG_ALLOC(nb * MIN(m, n), Complex))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
#ifdef NAG_COLUMN_MAJOR
pda = m;
pdb = m;
pdt = nb;
#else
pda = n;
pdb = nrhs;
pdt = MIN(m, n);
#endif

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

for (i = 1; i <= m; ++i)
for (j = 1; j <= nrhs; ++j)
scanf(" ( %lf , %lf )", &B(i, j).re, &B(i, j).im);
scanf("%*[^\n]");

for (i = 1; i <= m; ++i)
for (j = 1; j <= nrhs; ++j)
C(i, j) = B(i, j);

/* nag_lapackeig_zgeqrt (f08apc).
* Compute the QR factorization of first n rows of A by recursive algorithm.
*/
nag_lapackeig_zgeqrt(order, n, n, nb, a, pda, t, pdt, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zgeqrt (f08apc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_lapackeig_zgemqrt (f08aqc).
* Compute C = (C1) = (Q^H)*B, storing the result in C
*             (C2)
* by applying Q^H from left.
*/
nag_lapackeig_zgemqrt(order, Nag_LeftSide, Nag_ConjTrans, n, nrhs, n, nb, a,
pda, t, pdt, c, pdb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zgemqrt (f08aqc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

for (i = 1; i <= n; ++i)
for (j = 1; j <= nrhs; ++j)
B(i, j) = C(i, j);

/* nag_lapacklin_ztrtrs (f07tsc).
* Compute least squares solutions for first n rows
* by back-substitution in R*X = C1.
*/
nag_lapacklin_ztrtrs(order, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, n, nrhs,
a, pda, c, pdb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapacklin_ztrtrs (f07tsc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_file_print_matrix_complex_gen_comp (x04dbc).
* Print least squares solutions using first n rows.
*/
nag_file_print_matrix_complex_gen_comp(
order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, c, pdb,
Nag_BracketForm, "%7.4f", "Solution(s) for n rows", 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;
}

/* nag_lapackeig_ztpqrt (f08bpc).
* Now add the remaining rows and perform QR update.
*/
nag_lapackeig_ztpqrt(order, m - n, n, 0, nb, a, pda, &A(n + 1, 1), pda, t,
pdt, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_ztpqrt (f08bpc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_lapackeig_ztpmqrt (f08bqc).
* Apply orthogonal transformations to C.
*/
nag_lapackeig_ztpmqrt(order, Nag_LeftSide, Nag_ConjTrans, m - n, nrhs, n, 0,
nb, &A(n + 1, 1), pda, t, pdt, b, pdb, &B(5, 1), pdb,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_ztpmqrt (f08bqc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_lapacklin_ztrtrs (f07tsc).
* Compute least squares solutions for first n rows
* by back-substitution in R*X = C1.
*/
nag_lapacklin_ztrtrs(order, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, n, nrhs,
a, pda, b, pdb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapacklin_ztrtrs (f07tsc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_file_print_matrix_complex_gen_comp (x04dbc).
* Print least squares solutions.
*/
printf("\n");
fflush(stdout);
nag_file_print_matrix_complex_gen_comp(
order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, b, pdb,
Nag_BracketForm, "%7.4f", "Least squares solution(s) for all rows",
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;
}

printf("\n Square root(s) of the residual sum(s) of squares\n");
for (j = 1; j <= nrhs; j++) {
/* nag_blast_zge_norm (f16uac).
* Compute and print estimate of the square root of the residual
* sum of squares.
*/
nag_blast_zge_norm(order, Nag_FrobeniusNorm, m - n, 1, &B(n + 1, j), pdb,
&rnorm, &fail);
if (fail.code != NE_NOERROR) {
printf("\nError from nag_blast_zge_norm (f16uac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
printf("  %11.2e ", rnorm);
}
printf("\n");

END:
NAG_FREE(a);
NAG_FREE(b);
NAG_FREE(c);
NAG_FREE(t);

return exit_status;
}
```