NAG Library Manual, Mark 28.4
```/* nag_correg_corrmat_nearest_kfactor (g02aec) Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
*
* Mark 28.4, 2022.
*/

#include <nag.h>

int main(void) {

/* Scalars */
Integer exit_status = 0;
double errtol, nrmpgd;
Integer feval, i, iter, j, k, pda, pdg, pdx, maxit, n;

/* Arrays */
double *a = 0, *g = 0, *x = 0;

/* Nag Types */
Nag_OrderType order;
NagError fail;

INIT_FAIL(fail);

#ifdef NAG_COLUMN_MAJOR
#define A(I, J) a[(J - 1) * pda + I - 1]
#define G(I, J) g[(J - 1) * pdg + I - 1]
order = Nag_ColMajor;
#else
#define A(I, J) a[(I - 1) * pda + J - 1]
#define G(I, J) g[(I - 1) * pdg + J - 1]
order = Nag_RowMajor;
#endif

/* Output preamble */
printf("nag_correg_corrmat_nearest_kfactor (g02aec) ");
printf("Example Program Results\n\n");
fflush(stdout);

/* Skip heading in data file */
scanf("%*[^\n]");
/* Read in the problem size */
scanf("%" NAG_IFMT "%*[^\n]", &n);

pda = n;
pdg = n;
pdx = n;
if (!(a = NAG_ALLOC((pda) * (n), double)) ||
!(g = NAG_ALLOC((pdg) * (n), double)) ||
!(x = NAG_ALLOC((pdx) * (n), double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Read in the matrix g */
for (i = 1; i <= n; i++)
for (j = 1; j <= n; j++)
scanf("%lf", &G(i, j));
scanf("%*[^\n] ");

/* Use the defaults for errtol and maxit */
errtol = 0.0;
maxit = 0;
/* Set k value */
k = 2;

/* nag_correg_corrmat_nearest_kfactor (g02aec).
* Computes the nearest correlation matrix with k-factor structure
* to a real square matrix
*/
nag_correg_corrmat_nearest_kfactor(order, g, pdg, n, k, errtol, maxit, x, pdx,
&iter, &feval, &nrmpgd, &fail);
if (fail.code != NE_NOERROR) {
printf("%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_file_print_matrix_real_gen (x04cac).
* Print real general matrix (easy-to-use)
*/
nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
&fail);
if (fail.code != NE_NOERROR) {
printf("%s\n", fail.message);
exit_status = 1;
goto END;
}

printf("\nNumber of steps taken: %" NAG_IFMT "\n", iter);
printf("Number of function evaluations: %" NAG_IFMT "\n\n", feval);
fflush(stdout);

/* Generate Nearest k factor correlation matrix
* nag_blast_dgemm (f16yac) performs matrix-matrix multiplication for a
* real general matrix
*/
nag_blast_dgemm(order, Nag_NoTrans, Nag_Trans, n, n, k, 1.0, x, pdx, x, pdx,
0.0, a, pda, &fail);
if (fail.code != NE_NOERROR) {
printf("%s\n", fail.message);
exit_status = 1;
goto END;
}
for (i = 1; i <= n; i++)
A(i, i) = 1.0;

/* nag_file_print_matrix_real_gen (x04cac).
* Print real general matrix (easy-to-use)
*/
nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
n, a, pda, "Nearest Correlation Matrix", NULL,
&fail);
if (fail.code != NE_NOERROR) {
printf("%s\n", fail.message);
exit_status = 1;
}

END:
NAG_FREE(a);
NAG_FREE(g);
NAG_FREE(x);
return exit_status;
}
```