/* nag_lapackeig_dgejsv (f08khc) Example Program.
*
* Copyright 2019 Numerical Algorithms Group.
*
* Mark 27.0, 2019.
*/
#include <stdio.h>
#include <math.h>
#include <nag.h>
int main(void)
{
/* Scalars */
double eps, serrbd;
Integer exit_status = 0;
Integer pda, pdu, pdv;
Integer i, j, m, n, n_uvecs, n_vvecs;
/* Arrays */
double *a = 0, *rcondu = 0, *rcondv = 0, *s = 0, *u = 0, *v = 0;
double work[7];
Integer iwork[3];
char nag_enum_arg[40];
/* Nag Types */
Nag_OrderType order;
Nag_Preprocess joba;
Nag_LeftVecsType jobu;
Nag_RightVecsType jobv;
Nag_ZeroCols jobr;
Nag_TransType jobt;
Nag_Perturb jobp;
NagError fail;
#ifdef NAG_COLUMN_MAJOR
#define A(I, J) a[(J-1)*pda + I-1]
order = Nag_ColMajor;
#else
#define A(I, J) a[(I-1)*pda + J-1]
order = Nag_RowMajor;
#endif
INIT_FAIL(fail);
printf("nag_lapackeig_dgejsv (f08khc) Example Program Results\n\n");
/* Skip heading in data file */
scanf("%*[^\n]");
scanf("%" NAG_IFMT "%" NAG_IFMT "%*[^\n]", &m, &n);
if (n < 0 || m < n) {
printf("Invalid n or nrhs\n");
exit_status = 1;
goto END;;
}
/* Read Nag type arguments by name and convert to value */
scanf(" %39s%*[^\n]", nag_enum_arg);
/* nag_enum_name_to_value (x04nac).
* Converts NAG enum member name to value
*/
joba = (Nag_Preprocess) nag_enum_name_to_value(nag_enum_arg);
scanf(" %39s%*[^\n]", nag_enum_arg);
jobu = (Nag_LeftVecsType) nag_enum_name_to_value(nag_enum_arg);
scanf(" %39s%*[^\n]", nag_enum_arg);
jobv = (Nag_RightVecsType) nag_enum_name_to_value(nag_enum_arg);
scanf(" %39s%*[^\n]", nag_enum_arg);
jobr = (Nag_ZeroCols) nag_enum_name_to_value(nag_enum_arg);
scanf(" %39s%*[^\n]", nag_enum_arg);
jobt = (Nag_TransType) nag_enum_name_to_value(nag_enum_arg);
scanf(" %39s%*[^\n]", nag_enum_arg);
jobp = (Nag_Perturb) nag_enum_name_to_value(nag_enum_arg);
/* Size of u and v depends on some of the above Nag type arguments. */
n_uvecs = 1;
if (jobu == Nag_LeftVecs) {
n_uvecs = m;
}
else if (jobu == Nag_LeftSpan) {
n_uvecs = n;
}
else if (jobu == Nag_NotLeftWork && jobv == Nag_RightVecs &&
jobt == Nag_Trans && m == n) {
n_uvecs = m;
}
if (jobv == Nag_NotRightVecs) {
n_vvecs = 1;
}
else {
n_vvecs = n;
}
#ifdef NAG_COLUMN_MAJOR
pda = m;
pdu = m;
pdv = n;
#else
pda = n;
pdu = n_uvecs;
pdv = n_vvecs;
#endif
if (!(a = NAG_ALLOC(m * n, double)) ||
!(rcondu = NAG_ALLOC(m, double)) ||
!(rcondv = NAG_ALLOC(m, double)) ||
!(s = NAG_ALLOC(n, double)) ||
!(u = NAG_ALLOC(m * n_uvecs, double)) ||
!(v = NAG_ALLOC(n_vvecs * n_vvecs, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
/* Read the m by n matrix A from data file */
for (i = 1; i <= m; i++)
for (j = 1; j <= n; j++)
scanf("%lf", &A(i, j));
scanf("%*[^\n]");
/* nag_lapackeig_dgejsv (f08khc)
* Compute the singular values and left and right singular vectors
* of A (A = U*S*V^T, m>=n).
*/
nag_lapackeig_dgejsv(order, joba, jobu, jobv, jobr, jobt, jobp, m, n, a, pda, s, u,
pdu, v, pdv, work, iwork, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dgejsv (f08khc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Get the machine precision, eps and compute the approximate
* error bound for the computed singular values. Note that for
* the 2-norm, s[0] = norm(A).
*/
eps = nag_machine_precision;
serrbd = eps * s[0];
/* Print (possibly scaled) singular values. */
if (fabs(work[0] - work[1]) < 2.0 * eps) {
/* No scaling required */
printf("Singular values\n");
for (j = 0; j < n; j++)
printf("%8.4f", s[j]);
}
else {
printf("Scaled singular values\n");
for (j = 0; j < n; j++)
printf("%8.4f", s[j]);
printf("\nFor true singular values, multiply by a/b,\n");
printf("where a = %f and b = %f", work[0], work[1]);
}
printf("\n\n");
/* Print left and right (spanning) singular vectors, if requested. using
* nag_file_print_matrix_real_gen (x04cac)
* Print real general matrix (easy-to-use)
*/
if (jobu == Nag_LeftVecs || jobu == Nag_LeftSpan) {
fflush(stdout);
nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, m, n, u,
pdu, "Left singular vectors", 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_real_gen (x04cac).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
}
if (jobv == Nag_RightVecs || jobv == Nag_RightVecsJRots) {
printf("\n");
fflush(stdout);
nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, v,
pdv, "Right singular vectors", 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_real_gen (x04cac).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
}
/* nag_lapackeig_ddisna (f08flc)
* Estimate reciprocal condition numbers for the singular vectors.
*/
nag_lapackeig_ddisna(Nag_LeftSingVecs, m, n, s, rcondu, &fail);
if (fail.code == NE_NOERROR)
nag_lapackeig_ddisna(Nag_RightSingVecs, m, n, s, rcondv, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_ddisna (f08flc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
if (joba == Nag_ColpivRrankCond || joba == Nag_FullpivRrankCond) {
printf("\n\nEstimate of the condition number of column equilibrated A\n");
printf("%11.1e", work[2]);
}
/* Print the approximate error bounds for the singular values and vectors. */
printf("\n\nError estimate for the singular values\n%11.1e", serrbd);
printf("\n\nError estimates for left singular vectors\n");
for (i = 0; i < n; i++)
printf("%11.1e", serrbd / rcondu[i]);
printf("\n\nError estimates for right singular vectors\n");
for (i = 0; i < n; i++)
printf("%11.1e", serrbd / rcondv[i]);
printf("\n");
END:
NAG_FREE(a);
NAG_FREE(rcondu);
NAG_FREE(rcondv);
NAG_FREE(s);
NAG_FREE(u);
NAG_FREE(v);
return exit_status;
}