/* F07FE_A1W_F C++ Header Example Program.
 *
 * Copyright 2019 Numerical Algorithms Group.
 * Mark 27, 2019.
 */

#include <nag.h>
#include <nagx04.h>
#include <nagad.h>
#include <stdio.h>
#include <nag_stdlib.h>
#include <string>
#include <iostream>
using namespace std;

int main(void)
{
  int       exit_status = 0;
  void      *ad_handle = 0;
  Integer   ifail = 0;

  cout << "F07FE_A1W_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_a1w_w_rtype *a=0, *ax=0, *b=0, *x=0;
  double            *ar, *xr=0;
  if (!(a   = NAG_ALLOC(n*n, nagad_a1w_w_rtype)) ||
      !(ax  = NAG_ALLOC(n*n, nagad_a1w_w_rtype)) ||
      !(b   = NAG_ALLOC(n*nrhs, nagad_a1w_w_rtype)) ||
      !(x   = NAG_ALLOC(n*nrhs, nagad_a1w_w_rtype)) ||
      !(ar  = NAG_ALLOC(n*n, double)) ||
      !(xr  = NAG_ALLOC(n*nrhs, double))) {
    cout << "Allocation failure\n";
    exit_status = -1;
    goto END;
  }
  
  // Create AD tape
  nagad_a1w_ir_create();

  // 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].value = dd;
      a[k].id = 0;
      nagad_a1w_ir_register_variable(&a[k]);
      ax[k] = a[k];
    }
  }
  // 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].value = dd;
      b[k].id = 0;
      nagad_a1w_ir_register_variable(&b[k]);
      x[k] = b[k];
    }
  }

  // Create AD configuration data object
  ifail = 0;
  x10aa_a1w_f_(ad_handle,ifail);

  // Factorize the matrix A
  ifail = 0;
  f07fd_a1w_f_(ad_handle,"L",n,ax,n,ifail,1);

  // Solve the system
  ifail = 0;
  f07fe_a1w_f_(ad_handle,"L",n,nrhs,ax,n,x,n,ifail,1);
  
  // Print solution
  for (int i = 0; i<n; i++) {
    for (int j = 0; j<nrhs; j++) {
      int k = i + j*n;
      xr[k] = nagad_a1w_get_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 adjoints\n";
  cout << " Computational mode    : algorithmic\n";
  cout << "\n Derivatives of first column solution x w.r.t first column of b:\n";
  
  // Obtain derivatives
  for (int i=0; i<n; i++) {

    // Reset adjoints, initialize derivative, and evaluate adjoint
    nagad_a1w_ir_zero_adjoints();
    double inc = 1.0;
    nagad_a1w_inc_derivative(&x[i],inc);
    ifail = 0;
    nagad_a1w_ir_interpret_adjoint_sparse(ifail);

    for (int j=0; j<n; j++) {
      double dd = nagad_a1w_get_derivative(b[j]);
      ar[i+j*n] = dd;
    }
  }
  // Print derivatives
  cout << endl;
  INIT_FAIL(fail);
  x04cac(Nag_ColMajor,Nag_GeneralMatrix,Nag_NonUnitDiag,n,n,ar,n,
         "  Derivatives dX(i,1)/db(j,1)",0,&fail);

 END:
  // Remove computational data object and tape
  ifail = 0;
  x10ab_a1w_f_(ad_handle,ifail);
  nagad_a1w_ir_remove();

  return exit_status;
}