NAG Library Manual, Mark 29
```/* nag_mv_factor (g03cac) Example Program.
*
* Copyright 2023 Numerical Algorithms Group.
*
* Mark 29.0, 2023.
*
*/

#include <nag.h>
#include <stdio.h>
#include <string.h>

#define FL(I, J) fl[(I)*tdfl + J]
#define X(I, J) x[(I)*tdx + J]
int main(void) {
Integer exit_status = 0, i, *isx = 0, j, l, m, n, nfac, nvar, tdfl, tdx;
double *com = 0, *e = 0, eps, *fl = 0, *psi = 0, *res = 0, *stat = 0;
double *wt = 0, *wtptr = 0, *x = 0;
char nag_enum_arg[40];
Nag_Boolean weight;
Nag_E04_Opt options;
Nag_FacMat matrix;
NagError fail;

INIT_FAIL(fail);

printf("nag_mv_factor (g03cac) Example Program Results\n\n");

/* Skip headings in data file */
scanf("%*[^\n]");
scanf("%39s", nag_enum_arg);
/* nag_enum_name_to_value (x04nac).
* Converts NAG enum member name to value
*/
matrix = (Nag_FacMat)nag_enum_name_to_value(nag_enum_arg);
scanf("%39s", nag_enum_arg);
weight = (Nag_Boolean)nag_enum_name_to_value(nag_enum_arg);
scanf("%" NAG_IFMT "", &n);
scanf("%" NAG_IFMT "", &m);
scanf("%" NAG_IFMT "", &nvar);
scanf("%" NAG_IFMT "", &nfac);

if (nvar >= 2 && m >= nvar && n > nvar) {
if (!(com = NAG_ALLOC(nvar, double)) || !(e = NAG_ALLOC(nvar, double)) ||
!(fl = NAG_ALLOC(nvar * nfac, double)) ||
!(psi = NAG_ALLOC(nvar, double)) ||
!(res = NAG_ALLOC(nvar * (nvar - 1) / 2, double)) ||
!(stat = NAG_ALLOC(4, double)) || !(wt = NAG_ALLOC(n, double)) ||
!(x = NAG_ALLOC((matrix == Nag_MatCorr_Covar ? m : n) * m, double)) ||
!(isx = NAG_ALLOC(m, Integer))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
tdfl = nfac;
tdx = m;
} else {
printf("Invalid nvar or m or n.\n");
exit_status = 1;
return exit_status;
}
if (matrix == Nag_MatCorr_Covar) {
for (i = 0; i < m; ++i) {
for (j = 0; j < m; ++j)
scanf("%lf", &X(i, j));
}
} else {
if (weight) {
for (i = 0; i < n; ++i) {
for (j = 0; j < m; ++j)
scanf("%lf", &X(i, j));
scanf("%lf", &wt[i]);
}
wtptr = wt;
} else {
for (i = 0; i < n; ++i) {
for (j = 0; j < m; ++j)
scanf("%lf", &X(i, j));
}
}
}
for (j = 0; j < m; ++j)
scanf("%" NAG_IFMT "", &isx[j]);

/* nag_opt_init (e04xxc).
* Initialization function for option setting
*/
nag_opt_init(&options);
options.max_iter = 500;
options.optim_tol = 1e-2;
eps = 1e-5;
/* nag_mv_factor (g03cac).
* Maximum likelihood estimates of parameters
*/
fflush(stdout);
nag_mv_factor(matrix, n, m, x, tdx, nvar, isx, nfac, wtptr, e, stat, com, psi,
res, fl, tdfl, &options, eps, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_mv_factor (g03cac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
printf("\nEigenvalues\n\n");
for (j = 0; j < nvar; ++j) {
printf(" %13.4e%s", e[j], (j + 1) % 5 == 0 ? "\n" : "");
}
printf("\n\n%s%6.3f\n", "    Test Statistic = ", stat[1]);
printf("%s%6.3f\n", "                df = ", stat[2]);
printf("%s%6.3f\n\n", "Significance level = ", stat[3]);
printf("Residuals\n\n");
l = 1;
for (i = 1; i <= nvar - 1; ++i) {
for (j = l; j <= l + i - 1; ++j)
printf(" %8.3f", res[j - 1]);
printf("\n");
l += i;
}
for (i = 0; i < nvar; ++i) {
for (j = 0; j < nfac; ++j)
printf(" %8.3f", FL(i, j));
printf("%8.3f%8.3f\n", com[i], psi[i]);
}

END:
NAG_FREE(com);
NAG_FREE(e);
NAG_FREE(fl);
NAG_FREE(psi);
NAG_FREE(res);
NAG_FREE(stat);
NAG_FREE(wt);
NAG_FREE(x);
NAG_FREE(isx);

return exit_status;
}
```