```/* nag_dormbr (f08kgc) Example Program.
*
* NAGPRODCODE Version.
*
* Copyright 2016 Numerical Algorithms Group.
*
* Mark 26, 2016.
*/

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

int main(void)
{
/* Scalars */
Integer i, ic, j, m, n, pda, pdpt, pdu;
Integer d_len, e_len, tau_len, tauq_len, taup_len;
Integer exit_status = 0;
NagError fail;
Nag_OrderType order;
/* Arrays */
double *a = 0, *d = 0, *e = 0, *pt = 0, *tau = 0, *taup = 0, *tauq = 0;
double *u = 0;

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

INIT_FAIL(fail);

printf("nag_dormbr (f08kgc) Example Program Results\n");

/* Skip heading in data file */
scanf("%*[^\n] ");
for (ic = 1; ic <= 2; ++ic) {
scanf("%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &m, &n);

#ifdef NAG_COLUMN_MAJOR
pda = m;
#else
pda = n;
#endif
pdu = m;
pdpt = n;
taup_len = n;
tauq_len = n;
tau_len = n;
d_len = n;
e_len = n - 1;

/* Allocate memory */
if (!(a = NAG_ALLOC(m * n, double)) ||
!(d = NAG_ALLOC(d_len, double)) ||
!(e = NAG_ALLOC(e_len, double)) ||
!(pt = NAG_ALLOC(n * n, double)) ||
!(tau = NAG_ALLOC(tau_len, double)) ||
!(taup = NAG_ALLOC(taup_len, double)) ||
!(tauq = NAG_ALLOC(tauq_len, double)) ||
!(u = NAG_ALLOC(m * m, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
/* Read A from data file */
for (i = 1; i <= m; ++i) {
for (j = 1; j <= n; ++j)
scanf("%lf", &A(i, j));
}
scanf("%*[^\n] ");
if (m >= n) {
/* Example 1. */

/* nag_dgeqrf (f08aec): Compute the QR factorization of A */
nag_dgeqrf(order, m, n, a, pda, tau, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dgeqrf (f08aec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Copy A to U */
for (i = 1; i <= m; ++i) {
for (j = 1; j <= MIN(i, n); ++j)
U(i, j) = A(i, j);
}
/* nag_dorgqr (f08afc):                              */
/*        Form Q explicitly, storing the result in U */
nag_dorgqr(order, m, m, n, u, pdu, tau, &fail);
if (fail.code != NE_NOERROR) {
printf("order=%d\n", order);
printf("Error from nag_dorgqr (f08afc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Copy R to PT (used as workspace) */
nag_dtr_copy(order, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, n, a,
pda, pt, pdpt, &fail);
/* Set the strictly lower triangular part of R to zero */
for (i = 2; i <= n; ++i) {
for (j = 1; j <= MIN(i - 1, n - 1); ++j)
PT(i, j) = 0.0;
}
/* nag_dgebrd (f08kec): Bidiagonalize R. */
nag_dgebrd(order, n, n, pt, pdpt, d, e, tauq, taup, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dgebrd (f08kec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* nag_dormbr (f08kgc): Update Q, storing the result in U. */
nag_dormbr(order, Nag_ApplyQ, Nag_RightSide, Nag_NoTrans,
m, n, n, pt, pdpt, tauq, u, pdu, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dormbr (f08kgc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Print bidiagonal form and matrix Q */
printf("\nExample 1: bidiagonal matrix B\nDiagonal\n");
for (i = 1; i <= n; ++i)
printf("%8.4f%s", d[i - 1], i % 8 == 0 ? "\n" : " ");
printf("\nSuperdiagonal\n");
for (i = 1; i <= n - 1; ++i)
printf("%8.4f%s", e[i - 1], i % 8 == 0 ? "\n" : " ");
printf("\n\n");
/* nag_gen_real_mat_print (x04cac): Print Q as stored in u. */
fflush(stdout);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
m, n, u, pdu, "Example 1: matrix Q", 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;
}
}
else {
/* Example 2. */

/* nag_dgelqf (f08ahc): Compute the LQ factorization of A. */
nag_dgelqf(order, m, n, a, pda, tau, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dgelqf (f08ahc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Copy A to PT */
for (i = 1; i <= m; ++i) {
for (j = i; j <= n; ++j)
PT(i, j) = A(i, j);
}
/* nag_dorglq (f08ajc):                               */
/*       Form Q explicitly, storing the result in PT. */
nag_dorglq(order, n, n, m, pt, pdpt, tau, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dorglq (f08ajc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Copy L to U (used as workspace) */
nag_dtr_copy(order, Nag_Lower, Nag_NoTrans, Nag_NonUnitDiag, m, a,
pda, u, pdu, &fail);
/* Set the strictly upper triangular part of L to zero */
for (i = 1; i <= m - 1; ++i) {
for (j = i + 1; j <= m; ++j)
U(i, j) = 0.0;
}
/* nag_dgebrd (f08kec): Bidiagonalize L. */
nag_dgebrd(order, m, m, u, pdu, d, e, tauq, taup, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dgebrd (f08kec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* nag_dormbr (f08kgc):Update P^T, storing the result in PT. */
nag_dormbr(order, Nag_ApplyP, Nag_LeftSide, Nag_Trans, m, n, m, u,
pdu, taup, pt, pdpt, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dormbr (f08kgc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Print bidiagonal form and matrix P^T */
printf("\nExample 2: bidiagonal matrix B\n%s\n", "Diagonal\n");
for (i = 1; i <= m; ++i)
printf("%8.4f%s", d[i - 1], i % 8 == 0 ? "\n" : " ");
printf("\nSuperdiagonal\n");
for (i = 1; i <= m - 1; ++i)
printf("%8.4f%s", e[i - 1], i % 8 == 0 ? "\n" : " ");
printf("\n\n");

/* nag_gen_real_mat_print (x04cac), Print pt. */
fflush(stdout);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
m, n, pt, pdpt, "Example 2: matrix P^T",
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(d);
NAG_FREE(e);
NAG_FREE(pt);
NAG_FREE(tau);
NAG_FREE(taup);
NAG_FREE(tauq);
NAG_FREE(u);
}
return exit_status;
}

#undef A
#undef U
#undef PT
```