NAG Library Manual, Mark 28.6
```/* nag_linsys_real_symm_solve (f04bhc) Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
*
* Mark 28.6, 2022.
*/

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

int main(void) {
/* Scalars */
double errbnd, rcond;
Integer exit_status, i, j, n, nrhs, pda, pdb;

/* Arrays */
char nag_enum_arg[40];
double *a = 0, *b = 0;
Integer *ipiv = 0;

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

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

exit_status = 0;
INIT_FAIL(fail);

printf("nag_linsys_real_symm_solve (f04bhc) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &n, &nrhs);
if (n > 0 && nrhs > 0) {
/* Allocate memory */
if (!(a = NAG_ALLOC(n * n, double)) || !(b = NAG_ALLOC(n * nrhs, double)) ||
!(ipiv = NAG_ALLOC(n, Integer))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
#ifdef NAG_COLUMN_MAJOR
pda = n;
pdb = n;
#else
pda = n;
pdb = nrhs;
#endif
} else {
printf("%s\n", "n and/or nrhs too small");
exit_status = 1;
return exit_status;
}
scanf("%39s%*[^\n] ", nag_enum_arg);
/* nag_enum_name_to_value (x04nac).
* Converts NAG enum member name to value
*/
uplo = (Nag_UploType)nag_enum_name_to_value(nag_enum_arg);

if (uplo == Nag_Upper) {
/* Read the upper triangular part of A from data file */
for (i = 1; i <= n; ++i) {
for (j = i; j <= n; ++j) {
scanf("%lf", &A(i, j));
}
}
scanf("%*[^\n] ");
} else {
/* Read the lower triangular part of A from data file */
for (i = 1; i <= n; ++i) {
for (j = 1; j <= i; ++j) {
scanf("%lf", &A(i, j));
}
}
scanf("%*[^\n] ");
}

/* Read B from data file */
for (i = 1; i <= n; ++i) {
for (j = 1; j <= nrhs; ++j) {
scanf("%lf", &B(i, j));
}
}
scanf("%*[^\n] ");

/* Solve the equations AX = B for X */
/* nag_linsys_real_symm_solve (f04bhc).
* Computes the solution and error-bound to a real symmetric
* system of linear equations
*/
nag_linsys_real_symm_solve(order, uplo, n, nrhs, a, pda, ipiv, b, pdb, &rcond,
&errbnd, &fail);
if (fail.code == NE_NOERROR) {
/* Print solution, estimate of condition number and approximate */
/* error bound */

/* nag_file_print_matrix_real_gen (x04cac).
* Print real general matrix (easy-to-use)
*/
fflush(stdout);
nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
nrhs, b, pdb, "Solution", 0, &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;
}
printf("\n%s\n%6s%10.1e\n", "Estimate of condition number", "", 1. / rcond);
printf("\n\n");
printf("%s\n%6s%10.1e\n\n",
"Estimate of error bound for computed solutions", "", errbnd);
} else if (fail.code == NE_RCOND) {
/* Matrix A is numerically singular.  Print estimate of */
/* reciprocal of condition number and solution */

printf("\n");
printf("%s\n%6s%10.1e\n\n\n", "Estimate of reciprocal of condition number",
"", rcond);
/* nag_file_print_matrix_real_gen (x04cac), see above. */
fflush(stdout);
nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
nrhs, b, pdb, "Solution", 0, &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 if (fail.code == NE_SINGULAR) {
/* The upper triangular matrix U is exactly singular.  Print */
/* details of factorization */

printf("\n");
/* nag_file_print_matrix_real_gen (x04cac), see above. */
fflush(stdout);
nag_file_print_matrix_real_gen(order, Nag_UpperMatrix, Nag_NonUnitDiag, n,
n, a, pda, "Details of factorization", 0,
&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;
}

/* Print pivot indices */
printf("\n%s\n", "Pivot indices");
for (i = 1; i <= n; ++i) {
printf("%11" NAG_IFMT "%s", ipiv[i - 1],
i % 7 == 0 || i == n ? "\n" : " ");
}
printf("\n");
} else {
printf("Error from nag_linsys_real_symm_solve (f04bhc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
END:
NAG_FREE(a);
NAG_FREE(b);
NAG_FREE(ipiv);

return exit_status;
}
```