/* nag_dtgsja (f08yec) Example Program.
*
* Copyright 2014 Numerical Algorithms Group.
*
* Mark 23, 2011.
*/
#include <stdio.h>
#include <nag.h>
#include <nagx04.h>
#include <nag_stdlib.h>
#include <nagx02.h>
#include <nagf08.h>
#include <nagf16.h>
int main(void)
{
/* Scalars */
double norma, normb, eps, tola, tolb;
Integer i, irank, j, k, l, m, n, ncycle, p, pda, pdb, pdq, pdu, pdv;
Integer printq, printr, printu, printv, vsize;
Integer exit_status = 0;
/* Arrays */
double *a = 0, *alpha = 0, *b = 0, *beta = 0, *q = 0, *u = 0,
*v = 0;
char nag_enum_arg[40];
/* Nag Types */
NagError fail;
Nag_OrderType order;
Nag_ComputeUType jobu;
Nag_ComputeVType jobv;
Nag_ComputeQType jobq;
Nag_MatrixType genmat = Nag_GeneralMatrix, upmat = Nag_UpperMatrix;
Nag_DiagType diag = Nag_NonUnitDiag;
Nag_LabelType intlab = Nag_IntegerLabels;
#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_dtgsja (f08yec) Example Program Results\n\n");
/* Skip heading in data file */
scanf("%*[^\n]");
scanf("%ld%ld%ld%*[^\n]", &m, &n, &p);
if (m < 0 || n < 0 || p < 0)
{
printf("Invalid m, n or p\n");
exit_status = 1;
goto END;
}
scanf(" %39s%*[^\n]", nag_enum_arg);
/* nag_enum_name_to_value (x04nac).
* Converts NAG enum member name to value
*/
jobu = (Nag_ComputeUType) nag_enum_name_to_value(nag_enum_arg);
scanf(" %39s%*[^\n]", nag_enum_arg);
jobv = (Nag_ComputeVType) nag_enum_name_to_value(nag_enum_arg);
scanf(" %39s%*[^\n]", nag_enum_arg);
jobq = (Nag_ComputeQType) nag_enum_name_to_value(nag_enum_arg);
pdu = (jobu!=Nag_NotU?m:1);
pdv = (jobv!=Nag_NotV?p:1);
pdq = (jobq!=Nag_NotQ?n:1);
vsize = (jobv!=Nag_NotV?p*m:1);
#ifdef NAG_COLUMN_MAJOR
pda = m;
pdb = p;
#else
pda = n;
pdb = n;
#endif
/* Read in 0s or 1s to determine whether matrices U, V, Q or R are to be
* printed.
*/
scanf("%ld%ld%ld%ld%*[^\n]",
&printu, &printv, &printq, &printr);
/* Allocate memory */
if (!(a = NAG_ALLOC(m*n, double)) ||
!(b = NAG_ALLOC(p*n, double)) ||
!(alpha = NAG_ALLOC(n, double)) ||
!(beta = NAG_ALLOC(n, double)) ||
!(q = NAG_ALLOC(pdq*pdq, double)) ||
!(u = NAG_ALLOC(pdu*pdu, double)) ||
!(v = NAG_ALLOC(vsize, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
/* Read the m by n matrix A and p by n matrix B from data file */
for (i = 1; i <= m; ++i)
for (j = 1; j <= n; ++j) scanf("%lf", &A(i, j));
scanf("%*[^\n]");
for (i = 1; i <= p; ++i)
for (j = 1; j <= n; ++j) scanf("%lf", &B(i, j));
scanf("%*[^\n]");
nag_dge_norm(order, Nag_FrobeniusNorm, m, n, a, pda, &norma, &fail);
nag_dge_norm(order, Nag_FrobeniusNorm, p, n, b, pdb, &normb, &fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_dge_norm (f16rac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Compute tola and tolb using nag_machine_precision (x02ajc) */
eps = nag_machine_precision;
tola = MAX(m, n) * norma * eps;
tolb = MAX(p, n) * normb * eps;
/* Preprocess step:
* compute transformations to reduce (A, B) to upper triangular form
* (A = U1*S*(Q1**T), B = V1*T*(Q1**T))
* using nag_dggsvp (f08vec).
*/
nag_dggsvp(order, jobu, jobv, jobq, m, p, n, a, pda, b, pdb, tola, tolb, &k,
&l, u, pdu, v, pdv, q, pdq, &fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_dggsvp (f08vec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Compute the generalized singular value decomposition of preprocessed (A,B)
* (A = U*D1*(0 R)*(Q**T), B = V*D2*(0 R)*(Q**T))
* using nag_dtgsja (f08yec). */
nag_dtgsja(order, jobu, jobv, jobq, m, p, n, k, l, a, pda, b, pdb, tola,
tolb, alpha, beta, u, pdu, v, pdv, q, pdq, &ncycle, &fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_dtgsja (f08yec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Print the generalized singular value pairs alpha, beta */
irank = MIN(k + l,m);
printf("Number of infinite generalized singular values (k): %5ld\n", k);
printf("Number of finite generalized singular values (l): %5ld\n", l);
printf("Effective Numerical rank of (A**T B**T)**T (k+l): %5ld\n", irank);
printf("\nFinite generalized singular values:\n");
for (j = k; j < irank; ++j) printf("%45s%12.4e\n", "", alpha[j]/beta[j]);
printf("\nNumber of cycles of the Kogbetliantz method: %12ld\n\n", ncycle);
if (printu && jobu!=Nag_NotU) {
fflush(stdout);
nag_gen_real_mat_print_comp(order, genmat, diag, m, m, u, pdu, "%13.4e",
"Orthogonal matrix U", intlab, NULL, intlab,
NULL, 80, 0, NULL, &fail);
if (fail.code != NE_NOERROR) goto PRINTERR;
printf("\n");
}
if (printv && jobv!=Nag_NotV) {
fflush(stdout);
nag_gen_real_mat_print_comp(order, genmat, diag, p, p, v, pdv, "%13.4e",
"Orthogonal matrix V", intlab, NULL, intlab,
NULL, 80, 0, NULL, &fail);
if (fail.code != NE_NOERROR) goto PRINTERR;
printf("\n");
}
if (printq && jobq!=Nag_NotQ) {
fflush(stdout);
nag_gen_real_mat_print_comp(order, genmat, diag, n, n, q, pdq, "%13.4e",
"Orthogonal matrix Q", intlab, NULL, intlab,
NULL, 80, 0, NULL, &fail);
if (fail.code != NE_NOERROR) goto PRINTERR;
printf("\n");
}
if (printr) {
fflush(stdout);
nag_gen_real_mat_print_comp(order, upmat, diag, irank, irank,
&A(1, n - irank + 1), pda, "%13.4e",
"Non singular upper triangular matrix R",
intlab, NULL, intlab, NULL, 80, 0, NULL,
&fail);
}
PRINTERR:
if (fail.code != NE_NOERROR)
{
printf("Error from nag_gen_real_mat_print_comp (x04cbc).\n%s\n",
fail.message);
exit_status = 1;
}
END:
NAG_FREE(a);
NAG_FREE(alpha);
NAG_FREE(b);
NAG_FREE(beta);
NAG_FREE(q);
NAG_FREE(u);
NAG_FREE(v);
return exit_status;
}