NAG Library Manual, Mark 28.5
/* F07FE_T1W_F C++ Header Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
* Mark 28.5, 2022.
*/

#include <dco.hpp>
#include <iostream>
#include <nag.h>
#include <nagx04.h>
#include <stdio.h>
#include <string>
using namespace std;

int main()
{
int               exit_status = 0;
Integer           ifail = 0;

cout << "F07FE_T1W_F C++ Header Example Program Results\n\n";
// Skip heading in data file
string mystr;
getline(cin, mystr);

// Read problem size and number of right-hand-sides
Integer n, nrhs;
cin >> n;
cin >> nrhs;

// Allocate arrays containing A and its factorized form, B
// and the solution X.
nagad_t1w_w_rtype *a = 0, *ax = 0, *b = 0, *x = 0;
double *           xr = 0, *dxdb = 0;
a    = new nagad_t1w_w_rtype[n * n];
ax   = new nagad_t1w_w_rtype[n * n];
b    = new nagad_t1w_w_rtype[n * nrhs];
x    = new nagad_t1w_w_rtype[n * nrhs];
xr   = new double[n * nrhs];
dxdb = new double[n * n];

// Read the lower triangular matrix A, register and copy
double dd;
for (int i = 0; i < n; ++i)
{
for (int j = 0; j <= i; ++j)
{
cin >> dd;
int k = i + j * n;
a[k]  = dd;
}
}
// Read the right-hand-sides, register and copy
for (int i = 0; i < n; ++i)
{
for (int j = 0; j < nrhs; ++j)
{
cin >> dd;
int k = i + j * n;
b[k]  = dd;
}
}

// Create AD configuration data object
ifail = 0;

double inc = 1.0, zero = 0.0;
for (int i = 0; i < n; ++i)
{
dco::derivative(b[i]) = inc;

for (int l = 0; l < n; ++l)
{
for (int j = 0; j <= l; ++j)
{
int k = l + j * n;
ax[k] = a[k];
}
}
for (int j = 0; j < n * nrhs; ++j)
{
x[j] = b[j];
}
// Factorize the matrix A
ifail = 0;

// Solve the system
ifail = 0;

dco::derivative(b[i]) = zero;
for (int j = 0; j < n; ++j)
{
dxdb[i * n + j] = dco::derivative(x[j]);
}
}
// Print solution
for (int i = 0; i < n; i++)
{
for (int j = 0; j < nrhs; j++)
{
int k = i + j * n;
xr[k] = dco::value(x[k]);
}
}
cout << endl;
NagError fail;
INIT_FAIL(fail);
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, xr, n,
"  Solution", 0, &fail);

cout << "\n\n Derivatives calculated: First order tangents\n";
cout << " Computational mode    : algorithmic\n";
cout << "\n Derivatives of column-1 solution x w.r.t column-1 of b:\n";

cout << endl;
INIT_FAIL(fail);
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, dxdb, n,
"  Derivatives dX_i1/dB_j1", 0, &fail);

ifail = 0;

delete[] a;
delete[] ax;
delete[] b;
delete[] x;
delete[] xr;
delete[] dxdb;
return exit_status;
}