NAG Library Manual, Mark 28.4
Interfaces:  FL   CL   CPP   AD
```/* nag_linsys_real_posdef_tridiag_solve (f04bgc) Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
*
* Mark 28.4, 2022.
*/

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

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

/* Arrays */
double *b, *d = 0, *e = 0;

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

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

exit_status = 0;
INIT_FAIL(fail);

printf("nag_linsys_real_posdef_tridiag_solve (f04bgc) 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 (!(b = NAG_ALLOC(n * nrhs, double)) || !(d = NAG_ALLOC(n, double)) ||
!(e = NAG_ALLOC(n - 1, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
#ifdef NAG_COLUMN_MAJOR
pdb = n;
#else
pdb = nrhs;
#endif
} else {
printf("%s\n", "n and/or nrhs too small");
exit_status = 1;
return exit_status;
}

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

for (i = 1; i <= n - 1; ++i) {
scanf("%lf", &e[i - 1]);
}
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_posdef_tridiag_solve (f04bgc).
* Computes the solution and error-bound to a real symmetric
* positive-definite tridiagonal system of linear equations
*/
nag_linsys_real_posdef_tridiag_solve(order, n, nrhs, d, e, 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", "",
1.0 / rcond);
printf("\n\n");
printf("%s\n%6s", "Estimate of error bound for computed solutions", "");
printf("%10.1e\n\n", 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", "Estimate of reciprocal of condition number", "",
rcond);
printf("\n\n");

/* 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_POS_DEF) {
printf("%s%3" NAG_IFMT "%s\n\n", "The leading minor of order ", fail.errnum,
" is not positive definite");
} else {
printf("Error from nag_linsys_real_posdef_tridiag_solve (f04bgc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
END:
NAG_FREE(b);
NAG_FREE(d);
NAG_FREE(e);
return exit_status;
}
```