NAG Library Manual, Mark 29.3
```/* nag::ad::f07ca Tangent Example Program.
*/

#include <dco.hpp>
#include <iostream>

// Function which calls NAG AD Library routines.
template <typename T>
void func(std::vector<T> &l,
std::vector<T> &d,
std::vector<T> &u,
std::vector<T> &x);

// Driver with the tangent calls.
// Computes the solution to a system of linear equations Ax=b where A is a
// triagonal matrix of size n. Matrix A is stored in arrays l(n-1), d(n), u(n-1)
// that store the lower, the main and the upper diagonals. Also, computes the
// sum of the Jacobian elements of output x w.r.t. all inputs l, d, u, b.
void driver(const std::vector<double> &lv,
const std::vector<double> &dv,
const std::vector<double> &uv,
const std::vector<double> &bv,
std::vector<double> &      xv,
double &                   dxdall);

int main()
{
std::cout << " nag::ad::f07ca Tangent Example Program Results\n";

// Problem dimension
Integer n = 5;
// Matrix A stored in diagonals
std::vector<double> lv = {3.4, 3.6, 7.0, -6.0};
std::vector<double> dv = {3.0, 2.3, -5.0, -0.9, 7.1};
std::vector<double> uv = {2.1, -1.0, 1.9, 8.0};
// Right-hand-side vector b
std::vector<double> bv = {2.7, -0.5, 2.6, 0.6, 2.7};
// Computed solution to the system Ax=b
std::vector<double> xv(n);

double dxdall;
// Call driver
driver(lv, dv, uv, bv, xv, dxdall);

std::cout << "\n Solution point = ";
for (int i = 0; i < n; i++)
{
std::cout.width(5);
std::cout << xv[i];
}
std::cout << std::endl;

std::cout.setf(std::ios::scientific, std::ios::floatfield);
std::cout.precision(12);
std::cout << "\n Derivatives calculated: First order tangents\n";

std::cout
<< "\n Sum of all Jacobian elements of solution x w.r.t. l,d,u and b:\n";
std::cout << " sum_ij [dx/dall]_ij = " << dxdall << std::endl;

return 0;
}

// Driver with the tangents calls.
// Computes the solution to a system of linear equations Ax=b where A is a
// triagonal matrix of size n. Matrix A is stored in arrays l(n-1), d(n), u(n-1)
// that store the lower, the main and the upper diagonals. Also, computes the
// sum of the Jacobian elements of output x w.r.t. all inputs l, d, u, b.
void driver(const std::vector<double> &lv,
const std::vector<double> &dv,
const std::vector<double> &uv,
const std::vector<double> &bv,
std::vector<double> &      xv,
double &                   dxdall)
{
using T = dco::gt1s<double>::type;

Integer n  = xv.size();
Integer n1 = n - 1;
// Stores the lower diagonal of A
std::vector<T> l(n1);
dco::value(l)      = lv;
dco::derivative(l) = std::vector<double>(n1, 1.0);
// Stores the main diagonal of A
std::vector<T> d(n);
dco::value(d)      = dv;
dco::derivative(d) = std::vector<double>(n, 1.0);
// Stores the upper diagonal of A
std::vector<T> u(n1);
dco::value(u)      = uv;
dco::derivative(u) = std::vector<double>(n1, 1.0);
// Stores right-hand-side vector b
std::vector<T> b(n);
dco::value(b)      = bv;
dco::derivative(b) = std::vector<double>(n, 1.0);

// nag::ad::f07ca modifies rhs b and returns solution x into the same array.
// Tangent mode is unaffected.
std::vector<T> &x = b;

// Call the NAG AD Lib functions
func(l, d, u, x);

// Solution point
xv = dco::value(x);

// Get sum of Jacobian elements of solution x w.r.t. b
dxdall = 0;
for (int i = 0; i < n; i++)
{
dxdall += dco::derivative(x[i]);
}
}

// Function which calls NAG AD Library routines.
template <typename T>
void func(std::vector<T> &l,
std::vector<T> &d,
std::vector<T> &u,
std::vector<T> &x)
{
Integer n = x.size(), nrhs = 1;

// Create AD configuration data object
Integer           ifail = 0;