NAG Library Manual, Mark 29.3
Interfaces:  FL   CL   CPP   AD
```/* nag_correg_robustm_corr_user_deriv (g02hlc) Example Program.
*
* Copyright 2023 Numerical Algorithms Group.
*
* Mark 29.3, 2023.
*/

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

#ifdef __cplusplus
extern "C" {
#endif
static void NAG_CALL ucv(double t, double *u, double *ud, double *w, double *wd,
Nag_Comm *comm);
#ifdef __cplusplus
}
#endif

int main(void) {

/* Scalars */
double bd, bl, tol;
Integer exit_status, i__, indm, j, k, l1, l2, m, maxit, mm, n, nit, nitmon;
Integer pdx;
NagError fail;
Nag_OrderType order;
Nag_Comm comm;

/* Arrays */
double *a = 0, *cov = 0, *theta = 0, *userp = 0, *wt = 0, *x = 0;

#ifdef NAG_COLUMN_MAJOR
#define X(I, J) x[(J - 1) * pdx + I - 1]
order = Nag_ColMajor;
#else
#define X(I, J) x[(I - 1) * pdx + J - 1]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

exit_status = 0;
printf(
"nag_correg_robustm_corr_user_deriv (g02hlc) Example Program Results\n");

/* Skip heading in data file */
scanf("%*[^\n] ");

/* Read in the dimensions of X */
scanf("%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &n, &m);

/* Allocate memory */
if (!(a = NAG_ALLOC(m * (m + 1) / 2, double)) ||
!(cov = NAG_ALLOC(m * (m + 1) / 2, double)) ||
!(theta = NAG_ALLOC(m, double)) || !(userp = NAG_ALLOC(2, double)) ||
!(wt = NAG_ALLOC(n, double)) || !(x = NAG_ALLOC(n * m, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
#ifdef NAG_COLUMN_MAJOR
pdx = n;
#else
pdx = m;
#endif

/* Read in the X matrix */
for (i__ = 1; i__ <= n; ++i__) {
for (j = 1; j <= m; ++j)
scanf("%lf", &X(i__, j));
scanf("%*[^\n] ");
}
/* Read in the initial value of A */
mm = (m + 1) * m / 2;
for (j = 1; j <= mm; ++j)
scanf("%lf", &a[j - 1]);
scanf("%*[^\n] ");

/* Read in the initial value of theta */
for (j = 1; j <= m; ++j)
scanf("%lf", &theta[j - 1]);
scanf("%*[^\n] ");

/* Read in the values of the parameters of the ucv functions */
scanf("%lf%lf%*[^\n] ", &userp[0], &userp[1]);
/* Set the values of remaining parameters */
indm = 1;
bl = 0.9;
bd = 0.9;
maxit = 50;
tol = 5e-5;
/* Change nitmon to a positive value if monitoring information
*          is required
*/
nitmon = 0;
comm.p = (void *)userp;

/* nag_correg_robustm_corr_user_deriv (g02hlc).
* Calculates a robust estimation of a correlation matrix,
* user-supplied weight function plus derivatives
*/
nag_correg_robustm_corr_user_deriv(order, ucv, indm, n, m, x, pdx, cov, a, wt,
theta, bl, bd, maxit, nitmon, 0, tol, &nit,
&comm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_correg_robustm_corr_user_deriv (g02hlc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

printf("\n");
printf("nag_correg_robustm_corr_user_deriv (g02hlc) required %4" NAG_IFMT " "
"iterations to converge\n\n",
nit);
printf("Robust covariance matrix\n");
l2 = 0;
for (j = 1; j <= m; ++j) {
l1 = l2 + 1;
l2 += j;
for (k = l1; k <= l2; ++k)
printf("%10.3f%s", cov[k - 1], k % 6 == 0 || k == l2 ? "\n" : " ");
}
printf("\n");

printf("Robust estimates of theta\n");
for (j = 1; j <= m; ++j)
printf(" %10.3f\n", theta[j - 1]);

END:
NAG_FREE(a);
NAG_FREE(cov);
NAG_FREE(theta);
NAG_FREE(userp);
NAG_FREE(wt);
NAG_FREE(x);

return exit_status;
}

void NAG_CALL ucv(double t, double *u, double *ud, double *w, double *wd,
Nag_Comm *comm) {
double t2, cu, cw;
double *userp = (double *)comm->p;

/* Function Body */
cu = userp[0];
*u = 1.0;
*ud = 0.0;
if (t != 0.0) {
t2 = t * t;
if (t2 > cu) {
*u = cu / t2;
*ud = *u * -2.0 / t;
}
}
/* w function and derivative */
cw = userp[1];
if (t > cw) {
*w = cw / t;
*wd = -(*w) / t;
} else {
*w = 1.0;
*wd = 0.0;
}
return;
}
```