```/* nag_ztzrzf (f08bvc) Example Program.
*
* NAGPRODCODE Version.
*
* Copyright 2016 Numerical Algorithms Group.
*
* Mark 26, 2016.
*/

#include <stdio.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <naga02.h>
#include <nagf08.h>
#include <nagf16.h>
#include <nagx04.h>

int main(void)
{
/* Scalars */
Complex one = { 1.0, 0.0 };
Complex zero = { 0.0, 0.0 };
double tol;
Integer i, j, k, m, n, nrhs, pda, pdb, pdw;
Integer exit_status = 0;
/* Arrays */
Complex *a = 0, *b = 0, *tau = 0, *work = 0;
double *rnorm = 0;
Integer *jpvt = 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]
order = Nag_ColMajor;
#else
#define A(I, J) a[(I - 1) * pda + J - 1]
#define B(I, J) b[(I - 1) * pdb + J - 1]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

printf("nag_ztzrzf (f08bvc) Example Program Results\n\n");

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

#ifdef NAG_COLUMN_MAJOR
pda = m;
pdb = m;
pdw = m;
#else
pda = n;
pdb = nrhs;
pdw = 1;
#endif

/* Allocate memory */
if (!(a = NAG_ALLOC(m * n, Complex)) ||
!(b = NAG_ALLOC(m * nrhs, Complex)) ||
!(tau = NAG_ALLOC(n, Complex)) ||
!(work = NAG_ALLOC(n, Complex)) ||
!(rnorm = NAG_ALLOC(nrhs, double)) || !(jpvt = NAG_ALLOC(n, Integer)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* 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]");

/* nag_iload (f16dbc).
* Initialize jpvt to be zero so that all columns are free.
*/
nag_iload(n, 0, jpvt, 1, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_iload (f16dbc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_zgeqp3 (f08btc).
* Compute the QR factorization of A with column pivoting as
* A = Q*(R11 R12)*(P^T)
*       ( 0  R22)
*/
nag_zgeqp3(order, m, n, a, pda, jpvt, tau, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_zgeqp3 (f08btc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_zunmqr (f08auc).
* Compute C = (C1) = (Q^H)*B, storing the result in b.
*             (C2)
*/
nag_zunmqr(order, Nag_LeftSide, Nag_ConjTrans, m, nrhs, n, a, pda, tau,
b, pdb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_zunmqr (f08auc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Choose tol to reflect the relative accuracy of the input data */
tol = 0.01;

/* nag_complex_abs (a02dbc).
* Determine and print the rank, k, of R relative to tol.
*/
for (k = 1; k <= n; ++k)
if (nag_complex_abs(A(k, k)) <= tol * nag_complex_abs(A(1, 1)))
break;
--k;

printf("Tolerance used to estimate the rank of A\n");
printf("%11.2e\n", tol);
printf("Estimated rank of A\n");
printf("%6" NAG_IFMT "\n\n", k);

/* nag_ztzrzf (f08bvc).
* Compute the RZ factorization of the k by k part of R as
* (R1 R2) = (T 0)*Z.
*/
nag_ztzrzf(order, k, n, a, pda, tau, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_ztzrzf (f08bvc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_ztrsm (f16zjc).
* Compute least squares solutions of triangular problems by
* back substitution in T*Y1 = C1, storing the result in b.
*/
nag_ztrsm(order, Nag_LeftSide, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, k,
nrhs, one, a, pda, b, pdb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_ztrsm (f16zjc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_zge_norm (f16uac).
* Compute estimates of the square roots of the residual sums of
* squares (2-norm of each of the columns of C2).
*/
for (j = 1; j <= nrhs; ++j) {
nag_zge_norm(order, Nag_FrobeniusNorm, m - k, 1, &B(k + 1, j), pdb,
&rnorm[j - 1], &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_zge_norm (f16uac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
}

/* nag_zge_load (f16thc).
* Set the remaining elements of the solutions to zero (to give
* the minimum-norm solutions), Y2 = 0.
*/
nag_zge_load(order, n - k, nrhs, zero, zero, &B(k + 1, 1), pdb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_zge_load (f16thc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_zurmrz (f08bxc).
* Form W = (Z^H)*Y.
*/
nag_zunmrz(order, Nag_LeftSide, Nag_ConjTrans, n, nrhs, k, n - k, a, pda,
tau, b, pdb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_zurmrz (f08bxc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Permute the least squares solutions stored in B to give X = P*W */
for (j = 1; j <= nrhs; ++j) {
for (i = 1; i <= n; ++i) {
work[jpvt[i - 1] - 1].re = B(i, j).re;
work[jpvt[i - 1] - 1].im = B(i, j).im;
}
/* nag_zge_copy (f16tfc).
* Copy matrix.
*/
nag_zge_copy(order, Nag_NoTrans, n, 1, work, pdw, &B(1, j), pdb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_zge_copy (f16tfc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
}

/* nag_gen_complx_mat_print_comp (x04dbc).
* Print least squares solutions.
*/
fflush(stdout);
nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
nrhs, b, pdb, Nag_BracketForm, "%7.4f",
"Least squares solution(s)",
Nag_IntegerLabels, 0, Nag_IntegerLabels, 0,
80, 0, 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_gen_complx_mat_print_comp (x04dbc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

/* Print the square roots of the residual sums of squares */
printf("\nSquare root(s) of the residual sum(s) of squares\n");

for (j = 0; j < nrhs; ++j)
printf("%11.2e%s", rnorm[j], j % 7 == 6 ? "\n" : " ");

END:
NAG_FREE(a);
NAG_FREE(b);
NAG_FREE(tau);
NAG_FREE(work);
NAG_FREE(rnorm);
NAG_FREE(jpvt);

return exit_status;
}

#undef A
#undef B
```