/* F07CA_A1T1W_F C++ Header Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
* Mark 27.2, 2021.
*/
#include <dco.hpp>
#include <nag.h>
#include <nagad.h>
#include <stdio.h>
#include <iostream>
#include <string>
using namespace std;
int main(void)
{
int exit_status = 0;
void *ad_handle = 0;
Integer nrhs = 1, ifail = 0;
double inc = 1.0;
nagad_t1w_w_rtype dt;
cout << "F07CA_A1T1W_F C++ Header Example Program Results\n\n";
// Skip heading in data file
string mystr;
getline (cin, mystr);
// Read number of x values and algorithmic mode
Integer n, mode;
cin >> n;
cin >> mode;
// Allocate arrays containing A and its factorized form, B
// and the solution X.
nagad_a1t1w_w_rtype *dl=0, *d=0, *du=0, *b=0;
nagad_a1t1w_w_rtype *dlf=0, *df=0, *duf=0, *x=0;
Integer n1 = n-1;
dl = new nagad_a1t1w_w_rtype [n1];
d = new nagad_a1t1w_w_rtype [n];
du = new nagad_a1t1w_w_rtype [n1];
b = new nagad_a1t1w_w_rtype [n];
dlf = new nagad_a1t1w_w_rtype [n1];
df = new nagad_a1t1w_w_rtype [n];
duf = new nagad_a1t1w_w_rtype [n1];
x = new nagad_a1t1w_w_rtype [n];
// Create AD tape
nagad_a1t1w_ir_create();
// Read the tridiagonal matrix A and right hand side B, register and copy
double dd;
for (int i = 0; i<n1; i++) {
cin >> dd;
dt = dd;
nagad_t1w_set_derivative(&dt,inc);
du[i] = dt;
nagad_a1t1w_ir_register_variable(&du[i]);
duf[i] = du[i];
}
for (int i = 0; i<n; i++) {
cin >> dd;
dt = dd;
nagad_t1w_set_derivative(&dt,inc);
d[i] = dt;
nagad_a1t1w_ir_register_variable(&d[i]);
df[i] = d[i];
}
for (int i = 0; i<n1; i++) {
cin >> dd;
dt = dd;
nagad_t1w_set_derivative(&dt,inc);
dl[i] = dt;
nagad_a1t1w_ir_register_variable(&dl[i]);
dlf[i] = dl[i];
}
for (int i = 0; i<n; i++) {
cin >> dd;
dt = dd;
nagad_t1w_set_derivative(&dt,inc);
b[i] = dt;
nagad_a1t1w_ir_register_variable(&b[i]);
x[i] = b[i];
}
// Create AD configuration data object
ifail = 0;
nag::ad::x10aa(ad_handle,ifail);
// Set AD computational mode
ifail = 0;
nag::ad::x10ac(ad_handle,mode,ifail);
// Solve the equations Ax = b for x
ifail = 0;
nag::ad::f07ca(ad_handle,n,nrhs,dlf,df,duf,x,n,ifail);
// Print primal solution
cout << " Solution:\n";
cout.precision(4);
cout.width(12); cout << " ";
for (int i=0; i<n; i++) {
nagad_t1w_w_rtype xv = nagad_a1t1w_get_value(x[i]);
cout.width(10); cout << nagad_t1w_get_value(xv);
}
cout << "\n\n Derivatives calculated: First order adjoints\n";
if (mode==nagad_symbolic) {
cout << " Computational mode : symbolic\n";
} else {
cout << " Computational mode : algorithmic\n";
}
// Obtain derivatives for each output solution point
cout.setf(ios::scientific,ios::floatfield);
cout.setf(ios::right);
cout.precision(2);
// Set second derivative seeds all to 1 and evaluate adjoint
for (int i=0; i<n; i++) {
dt = inc;
nagad_a1t1w_set_derivative(&x[i],dt);
}
ifail = 0;
nagad_a1t1w_ir_interpret_adjoint_sparse(ifail);
dd = 0.0;
for (int j=0; j<n1; j++) {
nagad_t1w_w_rtype tang = nagad_a1t1w_get_derivative(du[j]);
dd += nagad_t1w_get_derivative(tang);
tang = nagad_a1t1w_get_derivative(dl[j]);
dd += nagad_t1w_get_derivative(tang);
}
for (int j=0; j<n; j++) {
nagad_t1w_w_rtype tang = nagad_a1t1w_get_derivative(d[j]);
dd += nagad_t1w_get_derivative(tang);
tang = nagad_a1t1w_get_derivative(b[j]);
dd += nagad_t1w_get_derivative(tang);
}
cout << "\n Sum of all Hessian elements of solution x w.r.t. l, d, u and b" << endl;
cout << " sum_ij [d2x/dall2]_ij = " << dd << endl;
// Remove computational data object and tape
ifail = 0;
nag::ad::x10ab(ad_handle,ifail);
nagad_a1t1w_ir_remove();
delete [] dl;
delete [] d;
delete [] du;
delete [] b;
delete [] dlf;
delete [] df;
delete [] duf;
delete [] x;
return exit_status;
}