NAG Library Manual, Mark 27.2
```/* nag_stat_pdf_multi_normal_vector (g01lbc) Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
*
* Mark 27.2, 2021.
*/

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

#define X(I, J) x[(J)*pdx + I]
#define SIG(I, J) sig[(J)*pdsig + I]

int main(void) {
/* Integer scalar and array declarations */
Integer i, j, k, n, pdx, pdsig, rank;
Integer exit_status = 0;

/* NAG structures and types */
NagError fail;
Nag_MatrixType iuld;
Nag_Boolean ilog;

/* Double scalar and array declarations */
double *x = 0, *xmu = 0, *sig = 0, *pdf = 0;

/* Character scalar and array declarations */
char ciuld[40], cilog[40];

/* Initialize the error structure */
INIT_FAIL(fail);

printf(
"nag_stat_pdf_multi_normal_vector (g01lbc) Example Program Results\n\n");
fflush(stdout);

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

/* Read in the problem size */
scanf("%" NAG_IFMT "%" NAG_IFMT "%39s%39s%*[^\n] ", &k, &n, ciuld, cilog);
ilog = (Nag_Boolean)nag_enum_name_to_value(cilog);
iuld = (Nag_MatrixType)nag_enum_name_to_value(ciuld);

pdx = n;
pdsig = (iuld == Nag_DiagonalMatrix) ? 1 : n;
if (!(x = NAG_ALLOC(pdx * k, double)) || !(xmu = NAG_ALLOC(n, double)) ||
!(sig = NAG_ALLOC(pdsig * n, double)) || !(pdf = NAG_ALLOC(k, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Read in and echo the vector of means */
for (i = 0; i < n; i++)
scanf("%lf", &xmu[i]);
scanf("%*[^\n] ");

printf("Vector of Means:\n");
for (i = 0; i < n; i++)
printf("%8.4f ", xmu[i]);
printf("\n\n");
fflush(stdout);

/* Read in and echo the covariance matrix */

if (iuld == Nag_DiagonalMatrix) {

for (i = 0; i < n; i++)
scanf("%lf", &SIG(1, i));
scanf("%*[^\n] ");

printf("Diagonal Elements of Covariance Matrix:\n");
for (i = 0; i < n; i++)
printf("%8.4f ", SIG(1, i));
printf("\n\n");

} else if (iuld == Nag_LowerMatrix || iuld == Nag_LowerFactored) {

for (i = 0; i < n; i++) {
for (j = 0; j <= i; j++)
scanf("%lf", &SIG(i, j));
scanf("%*[^\n] ");
}
/* Print details of Covariance matrix using
* nag_file_print_matrix_real_gen (x04cac)
*/
if (iuld == Nag_LowerMatrix)
nag_file_print_matrix_real_gen(Nag_ColMajor, Nag_LowerMatrix,
Nag_NonUnitDiag, n, n, sig, pdsig,
"Covariance Matrix:", NULL, &fail);
else
nag_file_print_matrix_real_gen(Nag_ColMajor, Nag_LowerMatrix,
Nag_NonUnitDiag, n, n, sig, pdsig,
"Lower Triangular Cholesky Factor "
"of Covariance Matrix:",
NULL, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_real_gen (x04cac).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

} else {
/* Upper triangle of matrix or factor is stored */

for (i = 0; i < n; i++) {
for (j = i; j < n; j++)
scanf("%lf", &SIG(i, j));
scanf("%*[^\n] ");
}
/* Print details of Covariance matrix using
* nag_file_print_matrix_real_gen (x04cac)
*/
if (iuld == Nag_UpperMatrix)
nag_file_print_matrix_real_gen(Nag_ColMajor, Nag_UpperMatrix,
Nag_NonUnitDiag, n, n, sig, pdsig,
"Covariance Matrix:", NULL, &fail);
else
nag_file_print_matrix_real_gen(Nag_ColMajor, Nag_UpperMatrix,
Nag_NonUnitDiag, n, n, sig, pdsig,
"Upper Triangular Cholesky Factor "
"of Covariance Matrix:",
NULL, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_real_gen (x04cac).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
}

/* Read in the points at which to evaluate the PDF */
for (j = 0; j < k; j++)
for (i = 0; i < n; i++)
scanf("%lf", &X(i, j));

/* nag_stat_pdf_multi_normal_vector (g01lbc): evaluate the PDF */
nag_stat_pdf_multi_normal_vector(ilog, k, n, x, pdx, xmu, iuld, sig, pdsig,
pdf, &rank, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_stat_pdf_multi_normal_vector (g01lbc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

/* Display results */
printf("\nRank of the covariance matrix: %" NAG_IFMT "\n\n", rank);
if (ilog)
printf("     log(PDF)                  X\n");
else
printf("       PDF                     X\n");
printf("  ------------------------------------------------\n");
for (j = 0; j < k; j++) {
printf(" %13.4e", pdf[j]);
for (i = 0; i < n; i++)
printf(" %8.4f", X(i, j));
printf("\n");
}

END:
NAG_FREE(x);
NAG_FREE(xmu);
NAG_FREE(sig);
NAG_FREE(pdf);

return exit_status;
}
```