NAG Library Manual, Mark 28.6
```/* nag_mv_gaussian_mixture (g03gac) Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
*
* Mark 28.6, 2022.
*/
#include <math.h>
#include <nag.h>
#include <stdio.h>
#include <string.h>

#define S(I, J, K)                                                             \
s[I - 1 + (J - 1) * (sopt == Nag_GroupVar ? ng : nvar) +                     \
(K - 1) * nvar * nvar]
#define X(I, J) x[(I - 1) * tdx + J - 1]
#define PROB(I, J) prob[(I - 1) * tdprob + J - 1]

int main(void) {
/* Integer scalar and array declarations */
Integer exit_status = 0, i, j, lens, m, n, ng, niter, nvar, riter, tdprob,
tdx;
Integer *isx = 0;

/* Double scalar and array declarations */
double loglik, tol;
double *f = 0, *g = 0, *prob = 0, *s = 0, *w = 0, *x = 0;

/* NAG structures */
Nag_Boolean popt;
Nag_VarCovar sopt;
NagError fail;

/* Character scalar and array declarations */
char nag_enum_popt[30 + 1], nag_enum_sopt[30 + 1];

printf("nag_mv_gaussian_mixture (g03gac) Example Program Results\n\n");
fflush(stdout);

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

/* Problem size */
scanf("%" NAG_IFMT "", &n);
scanf("%" NAG_IFMT "", &m);
scanf("%" NAG_IFMT "", &nvar);
scanf("%*[^\n] ");

/* Number of groups */
scanf("%" NAG_IFMT "", &ng);
scanf("%*[^\n] ");

/* Scaling option */
scanf("%30s", nag_enum_sopt);
scanf("%*[^\n] ");

/* Initial probabilities option */
scanf("%30s", nag_enum_popt);
scanf("%*[^\n] ");

/* Maximum number of iterations */
scanf("%" NAG_IFMT "", &niter);
scanf("%*[^\n] ");

/* Principal dimensions */
tdx = nvar;
tdprob = ng;

/* nag_enum_name_to_value (x04nac).
* Converts NAG enum member name to value
*/
popt = (Nag_Boolean)nag_enum_name_to_value(nag_enum_popt);
sopt = (Nag_VarCovar)nag_enum_name_to_value(nag_enum_sopt);

/* Variance/covariance array */
switch (sopt) {
case Nag_GroupCovar:
lens = nvar * nvar * ng;
break;
case Nag_PooledCovar:
lens = nvar * nvar;
break;
case Nag_GroupVar:
lens = nvar * ng;
break;
case Nag_PooledVar:
lens = nvar;
break;
case Nag_OverallVar:
lens = 1;
break;
}

if (!(x = NAG_ALLOC(n * tdx, double)) ||
!(prob = NAG_ALLOC(n * tdprob, double)) ||
!(g = NAG_ALLOC(ng * nvar, double)) || !(w = NAG_ALLOC(ng, double)) ||
!(isx = NAG_ALLOC(m, Integer)) || !(f = NAG_ALLOC(ng * n, double)) ||
!(s = NAG_ALLOC(lens, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Data matrix X */
for (i = 1; i <= n; i++)
for (j = 1; j <= m; j++)
scanf("%lf", &X(i, j));
scanf("%*[^\n] ");

/* Included variables */
if (nvar != m) {
for (j = 1; j <= m; j++)
scanf("%" NAG_IFMT "", &isx[j - 1]);
scanf("%*[^\n] ");
}

/* Optionally read initial probabilities of group membership */
if (popt == Nag_FALSE) {
for (i = 1; i <= n; i++)
for (j = 1; j <= ng; j++)
scanf("%lf", &PROB(i, j));
scanf("%*[^\n] ");
}

/* Optimization parameters */
tol = 0.0;
riter = 5;

/* Fit the model */
/* nag_mv_gaussian_mixture (g03gac).
* Computes a Gaussian mixture model
*/
INIT_FAIL(fail);
nag_mv_gaussian_mixture(n, m, x, tdx, isx, nvar, ng, popt, prob, tdprob,
&niter, riter, w, g, sopt, s, f, tol, &loglik, &fail);

if (fail.code != NE_NOERROR) {
printf("nag_mv_gaussian_mixture (g03gac) failed.\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Results */
/* nag_file_print_matrix_real_gen (x04cac).
* Print real general matrix (easy-to-use)
*/
nag_file_print_matrix_real_gen(Nag_RowMajor, Nag_GeneralMatrix,
Nag_NonUnitDiag, 1, ng, w, ng,
"Mixing proportions", NULL, &fail);

nag_file_print_matrix_real_gen(Nag_RowMajor, Nag_GeneralMatrix,
Nag_NonUnitDiag, nvar, ng, g, ng,
"\n Group means", NULL, &fail);

/* Variance/Covariance */
switch (sopt) {
case Nag_GroupCovar:
for (i = 1; i <= ng; i++) {
nag_file_print_matrix_real_gen(
Nag_RowMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, nvar, nvar,
&S(1, 1, i), nvar, "\n Variance-covariance matrix", NULL, &fail);
}
break;
case Nag_PooledCovar:
nag_file_print_matrix_real_gen(
Nag_RowMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, nvar, nvar, s, nvar,
"\n Pooled Variance-covariance matrix", NULL, &fail);
break;
case Nag_GroupVar:
nag_file_print_matrix_real_gen(Nag_RowMajor, Nag_GeneralMatrix,
Nag_NonUnitDiag, nvar, ng, s, ng,
"\n Groupwise Variance", NULL, &fail);
break;
case Nag_PooledVar:
nag_file_print_matrix_real_gen(Nag_RowMajor, Nag_GeneralMatrix,
Nag_NonUnitDiag, nvar, 1, s, 1,
"\n Pooled Variance", NULL, &fail);
break;
case Nag_OverallVar:
printf("\n Overall Variance = %g\n", S(1, 1, 1));
break;
}

nag_file_print_matrix_real_gen(Nag_RowMajor, Nag_GeneralMatrix,
Nag_NonUnitDiag, n, ng, f, ng, "\n Densities",
NULL, &fail);

nag_file_print_matrix_real_gen(Nag_RowMajor, Nag_GeneralMatrix,
Nag_NonUnitDiag, n, ng, prob, ng,
"\n Membership probabilities", NULL, &fail);

printf("\nNo. iterations: %" NAG_IFMT "\n", niter);
printf("Log-likelihood: %g\n\n", loglik);

END:
NAG_FREE(f);
NAG_FREE(g);
NAG_FREE(prob);
NAG_FREE(s);
NAG_FREE(w);
NAG_FREE(x);
NAG_FREE(isx);

return exit_status;
}
```