/* nag_lapackeig_zunmbr (f08kuc) Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
*
* Mark 30.1, 2024.
*/
#include <nag.h>
#include <stdio.h>
int main(void) {
/* Scalars */
Integer i, ic, j, m, n, pda, pdph, pdu;
Integer d_len, e_len, tau_len, tauq_len, taup_len;
Integer exit_status = 0;
NagError fail;
Nag_OrderType order;
/* Arrays */
Complex *a = 0, *ph = 0, *tau = 0, *taup = 0, *tauq = 0, *u = 0;
double *d = 0, *e = 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 PH(I, J) ph[(J - 1) * pdph + 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 PH(I, J) ph[(I - 1) * pdph + J - 1]
order = Nag_RowMajor;
#endif
INIT_FAIL(fail);
printf("nag_lapackeig_zunmbr (f08kuc) 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;
pdph = n;
pdu = m;
#else
pda = n;
pdph = n;
pdu = m;
#endif
tau_len = n;
taup_len = n;
tauq_len = n;
d_len = n;
e_len = n - 1;
/* Allocate memory */
if (!(a = NAG_ALLOC(m * n, Complex)) || !(ph = NAG_ALLOC(n * n, Complex)) ||
!(tau = NAG_ALLOC(tau_len, Complex)) ||
!(taup = NAG_ALLOC(taup_len, Complex)) ||
!(tauq = NAG_ALLOC(tauq_len, Complex)) ||
!(u = NAG_ALLOC(m * m, Complex)) || !(d = NAG_ALLOC(d_len, double)) ||
!(e = NAG_ALLOC(e_len, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto ENDL;
}
/* Read A 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] ");
if (m >= n) {
/* Compute the QR factorization of A */
/* nag_lapackeig_zgeqrf (f08asc).
* QR factorization of complex general rectangular matrix
*/
nag_lapackeig_zgeqrf(order, m, n, a, pda, tau, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zgeqrf (f08asc).\n%s\n", fail.message);
exit_status = 1;
goto ENDL;
}
/* Copy A to U */
for (i = 1; i <= m; ++i) {
for (j = 1; j <= n; ++j) {
U(i, j).re = A(i, j).re;
U(i, j).im = A(i, j).im;
}
}
/* Form Q explicitly, storing the result in U */
/* nag_lapackeig_zungqr (f08atc).
* Form all or part of unitary Q from QR factorization
* determined by nag_lapackeig_zgeqrf (f08asc) or nag_lapackeig_zgeqpf
* (f08bsc)
*/
nag_lapackeig_zungqr(order, m, n, n, u, pdu, tau, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zungqr (f08atc).\n%s\n", fail.message);
exit_status = 1;
goto ENDL;
}
/* Copy R to PH (used as workspace) */
for (i = 1; i <= n; ++i) {
for (j = i; j <= n; ++j) {
PH(i, j).re = A(i, j).re;
PH(i, j).im = A(i, j).im;
}
}
/* 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) {
PH(i, j).re = 0.0;
PH(i, j).im = 0.0;
}
}
/* Bidiagonalize R */
/* nag_lapackeig_zgebrd (f08ksc).
* Unitary reduction of complex general rectangular matrix
* to bidiagonal form
*/
nag_lapackeig_zgebrd(order, n, n, ph, pdph, d, e, tauq, taup, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zgebrd (f08ksc).\n%s\n", fail.message);
exit_status = 1;
goto ENDL;
}
/* Update Q, storing the result in U */
/* nag_lapackeig_zunmbr (f08kuc).
* Apply unitary transformations from reduction to
* bidiagonal form determined by nag_lapackeig_zgebrd (f08ksc)
*/
nag_lapackeig_zunmbr(order, Nag_ApplyQ, Nag_RightSide, Nag_NoTrans, m, n,
n, ph, pdph, tauq, u, pdu, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zunmbr (f08kuc).\n%s\n", fail.message);
exit_status = 1;
goto ENDL;
}
/* 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_file_print_matrix_complex_gen_comp (x04dbc).
* Print complex general matrix (comprehensive)
*/
fflush(stdout);
nag_file_print_matrix_complex_gen_comp(
order, Nag_GeneralMatrix, Nag_NonUnitDiag, m, n, u, pdu,
Nag_BracketForm, "%7.4f", "Example 1: matrix Q", 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 ENDL;
}
} else {
/* Compute the LQ factorization of A */
/* nag_lapackeig_zgelqf (f08avc).
* LQ factorization of complex general rectangular matrix
*/
nag_lapackeig_zgelqf(order, m, n, a, pda, tau, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zgelqf (f08avc).\n%s\n", fail.message);
exit_status = 1;
goto ENDL;
}
/* Copy A to PH */
for (i = 1; i <= m; ++i) {
for (j = 1; j <= n; ++j) {
PH(i, j).re = A(i, j).re;
PH(i, j).im = A(i, j).im;
}
}
/* Form Q explicitly, storing the result in PH */
/* nag_lapackeig_zunglq (f08awc).
* Form all or part of unitary Q from LQ factorization
* determined by nag_lapackeig_zgelqf (f08avc)
*/
nag_lapackeig_zunglq(order, m, n, m, ph, pdph, tau, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zunglq (f08awc).\n%s\n", fail.message);
exit_status = 1;
goto ENDL;
}
/* Copy L to U (used as workspace) */
for (i = 1; i <= m; ++i) {
for (j = 1; j <= i; ++j) {
U(i, j).re = A(i, j).re;
U(i, j).im = A(i, j).im;
}
}
/* 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).re = 0.0;
U(i, j).im = 0.0;
}
}
/* Bidiagonalize L */
/* nag_lapackeig_zgebrd (f08ksc), see above. */
nag_lapackeig_zgebrd(order, m, m, u, pdu, d, e, tauq, taup, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zgebrd (f08ksc).\n%s\n", fail.message);
exit_status = 1;
goto ENDL;
}
/* Update P^H, storing the result in PH */
/* nag_lapackeig_zunmbr (f08kuc), see above. */
nag_lapackeig_zunmbr(order, Nag_ApplyP, Nag_LeftSide, Nag_ConjTrans, m, n,
m, u, pdu, taup, ph, pdph, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zunmbr (f08kuc).\n%s\n", fail.message);
exit_status = 1;
goto ENDL;
}
/* Print bidiagonal form and matrix P^H */
printf("\nExample 2: bidiagonal matrix B\n%s\n", "Diagonal");
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_file_print_matrix_complex_gen_comp (x04dbc), see above. */
fflush(stdout);
nag_file_print_matrix_complex_gen_comp(
order, Nag_GeneralMatrix, Nag_NonUnitDiag, m, n, ph, pdph,
Nag_BracketForm, "%7.4f", "Example 2: matrix P^H", 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 ENDL;
}
}
ENDL:
NAG_FREE(a);
NAG_FREE(ph);
NAG_FREE(tau);
NAG_FREE(taup);
NAG_FREE(tauq);
NAG_FREE(u);
NAG_FREE(d);
NAG_FREE(e);
}
NAG_FREE(a);
NAG_FREE(ph);
NAG_FREE(tau);
NAG_FREE(taup);
NAG_FREE(tauq);
NAG_FREE(u);
NAG_FREE(d);
NAG_FREE(e);
return exit_status;
}