NAG Library Manual, Mark 30
```/* E02BC_A1W_F C++ Header Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
* Mark 30.0, 2024.
*/

#include <dco.hpp>
#include <iostream>
#include <math.h>
#include <nag.h>
#include <stdio.h>
#include <string>
using namespace std;

int main()
{
Integer exit_status = 0;

cout << "E02BC_A1W_F C++ Header Example Program\n";

Integer           ifail = 0;

// Skip heading in data file
string mystr;
getline(cin, mystr);

Integer ncap, m;
cin >> ncap;
cin >> m;

Integer ncap7 = ncap + 7;

if (m <= 0)
{
printf("Invalid m.\n");
exit_status = 1;
return exit_status;
}
if (ncap <= 0)
{
printf("Invalid ncap.\n");
exit_status = 1;
return exit_status;
}

// Allocate arrays
nagad_a1w_w_rtype *c = 0, *lamda = 0;
double *           dsdl = 0, *dsdc = 0;
dsdc  = new double[2 * m * ncap7];
dsdl  = new double[2 * m * ncap7];

// Read knots and spline coefficients from file
double tmp;
for (int j = 0; j < ncap7; j++)
{
cin >> tmp;
lamda[j] = tmp;
}
for (int j = 0; j < ncap + 3; j++)
{
cin >> tmp;
c[j] = tmp;
}

cout << "\n        x             Spline    1st deriv";
cout << "   2nd deriv   3rd deriv\n";
cout.setf(ios::scientific, ios::floatfield);
cout.setf(ios::right);
cout.precision(4);

for (int i = 0; i < m; i++)
{
cin >> tmp;
x = tmp;

for (Integer left = 1; left <= 2; left++)
{
dco::ga1s<double>::global_tape = dco::ga1s<double>::tape_t::create();
for (int l = 0; l < ncap7; l++)
{
dco::ga1s<double>::global_tape->register_variable(lamda[l]);
}
for (int l = 0; l < ncap7; l++)
{
dco::ga1s<double>::global_tape->register_variable(c[l]);
}

if (ifail != 0)
{
printf("\nError from nag::ad::e02bc.\n%" NAG_IFMT "\n", ifail);
exit_status = 1;
return exit_status;
}

double xv = dco::value(x);
cout.width(11);
cout << xv;

if (left == 1)
{
cout << "   Left";
}
else
{
cout << "  Right";
}
for (int l = 0; l < 4; l++)
{
tmp = dco::value(s[l]);
cout.width(12);
cout << tmp;
}
dco::derivative(s[0])                              = 1.0;
dco::ga1s<double>::global_tape->sparse_interpret() = true;

Integer indx = (left - 1) * m * ncap7 + i * ncap7;
for (int l = 0; l < ncap7; l++)
{
tmp            = dco::derivative(lamda[l]);
dsdl[indx + l] = tmp;
tmp            = dco::derivative(c[l]);
dsdc[indx + l] = tmp;
}
dco::ga1s<double>::tape_t::remove(dco::ga1s<double>::global_tape);
cout << "\n";
}
cout << "\n";
}

cout << "\n Derivatives of spline values with respect to knots\n";
NagError fail;
INIT_FAIL(fail);
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, ncap7, m, dsdl,
ncap7, "Left:  ds/dlamda", 0, &fail);
cout << "\n";
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, ncap7, m,
&dsdl[m * ncap7], ncap7, "Right: ds/dlamda", 0, &fail);
cout << "\n\n Derivatives with respect to spline coefficients\n";

x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, ncap7, m, dsdc,
ncap7, "Left:  ds/dC", 0, &fail);
cout << "\n";
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, ncap7, m,
&dsdc[m * ncap7], ncap7, "Right: ds/dC", 0, &fail);

delete[] c;
delete[] lamda;
delete[] dsdc;
delete[] dsdl;

return exit_status;
}
```