NAG Library Manual, Mark 28.4
```/* nag_correg_corrmat_fixed (g02asc) Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
*
* Mark 28.4, 2022.
*/

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

int main(void) {

#define G(I, J) g[(J - 1) * pdg + I - 1]
#define H(I, J) h[(J - 1) * pdh + I - 1]

/* Scalars */
Integer exit_status = 0;
Integer one = 1;
double alpha, errtol, norm;
Integer i, j, iter, maxit, m, n, pdg, pdh, pdx;

/* Arrays */
double *eig = 0, *g = 0, *x = 0;
Integer *h = 0;

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

INIT_FAIL(fail);

/* Output preamble */
printf("nag_correg_corrmat_fixed (g02asc)");
printf(" Example Program Results\n\n");
fflush(stdout);

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

/* Read in the problem size, alpha and m */
scanf("%" NAG_IFMT "%lf%" NAG_IFMT "%*[^\n] ", &n, &alpha, &m);

pdg = n;
pdh = n;
pdx = n;
if (!(g = NAG_ALLOC(pdg * n, double)) || !(h = NAG_ALLOC(pdh * n, Integer)) ||
!(x = NAG_ALLOC(pdx * n, double)) || !(eig = NAG_ALLOC(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] ");

/* Read in the matrix h, only the strictly lower triangle need be set */
for (i = 2; i <= n; i++)
for (j = 1; j < i; j++)
scanf("%" NAG_IFMT "", &H(i, j));
scanf("%*[^\n] ");

/* Use the defaults for errtol, maxit and m */
errtol = 0.0;
maxit = 0;

/*
* nag_correg_corrmat_fixed (g02asc).
* Calculate nearest correlation matrix with some fixed elements
*/
nag_correg_corrmat_fixed(g, pdg, n, alpha, h, pdh, errtol, maxit, m, x, pdx,
&iter, &norm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_correg_corrmat_fixed (g02asc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Display results */

order = Nag_ColMajor;
/*
* nag_file_print_matrix_real_gen (x04cac).
* Prints real general matrix
*/
nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
n, g, pdg, "Symmetrised Input Matrix, G", NULL,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_real_gen (x04cac).\n%s\n",
fail.message);
exit_status = 2;
goto END;
}

/* Print H */
printf("\n Lower Triangle of H\n");
for (i = 1; i <= n; i++) {
for (j = 1; j <= i - 1; j++)
printf("%6" NAG_IFMT "", H(i, j));
printf("%6d\n", 1);
}

printf("\n");
fflush(stdout);
nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
n, x, pdx, "Nearest Correlation Matrix, X",
NULL, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_real_gen (x04cac).\n%s\n",
fail.message);
exit_status = 3;
goto END;
}

printf("\n%s %10" NAG_IFMT " \n\n", " Number of iterations:", iter);
printf(" Norm value:%26.4f \n\n", norm);
printf("%s %29.4f \n", " alpha: ", alpha);

/*
* nag_lapackeig_dsyev (f08fac).
* Computes all eigenvalues and, optionally, eigenvectors of a real
* symmetric matrix
*/
nag_lapackeig_dsyev(order, Nag_EigVals, Nag_Upper, n, x, pdx, eig, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dsyev (f08fac).\n%s\n", fail.message);
exit_status = 4;
goto END;
}

printf("\n");
fflush(stdout);
/*
* 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, one,
n, eig, one, "Eigenvalues of X", NULL, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_real_gen (x04cac).\n%s\n",
fail.message);
exit_status = 5;
goto END;
}

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