/* F07AE_A1W_F C++ Header Example Program.
 *
 * Copyright 2019 Numerical Algorithms Group.
 * Mark 27, 2019.
 */

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

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

  cout << "F07AE_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 >> nrhs;

  // Allocate arrays containing A and its factorized form, B
  // and the solution X.
  nagad_a1w_w_rtype *a=0, *a_in=0, *b=0, *b_in=0;
  double            *ar=0, *br=0;
  Integer           *ipiv=0;
  a    = new nagad_a1w_w_rtype [n*n];
  a_in = new nagad_a1w_w_rtype [n*n];
  b    = new nagad_a1w_w_rtype [n*nrhs];
  b_in = new nagad_a1w_w_rtype [n*nrhs];
  ipiv = new Integer [n];
  ar   = new double [n*n];
  br   = new double [n*nrhs];
  
  // Create AD tape
  nagad_a1w_ir_create();

  // Read the matrix A and copy
  double dd;
  for (int i = 0; i<n; ++i) {
    for (int j = 0; j<n; ++j) {
      cin >> dd;
      Integer k = i + j*n;
      a_in[k] = dd;
      a[k] = a_in[k];
    }
  }

  // Read the matrix B, register and copy
  for (int i = 0; i<n; ++i) {
    for (int j = 0; j<nrhs; ++j) {
      cin >> dd;
      Integer k = i + j*n;
      b_in[k] = dd;
      if (j==0) {
        nagad_a1w_ir_register_variable(&b_in[k]);
      }
      b[k] = b_in[k];
    }
  }

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

  // Factorize the matrix A
  ifail = 0;
  f07ad_a1w_f_(ad_handle,n,n,a,n,ipiv,ifail);

  // Solve AX = B
  ifail = 0;
  f07ae_a1w_f_(ad_handle,"N",n,nrhs,a,n,ipiv,b,n,ifail,1);
  
  // Print Solution
  for (int i = 0; i<n; i++) {
    for (int j = 0; j<nrhs; j++) {
      int k = i + j*n;
      br[k] = nagad_a1w_get_value(b[k]);
    }
  }
  NagError  fail;
  INIT_FAIL(fail);
  x04cac(Nag_ColMajor,Nag_GeneralMatrix,Nag_NonUnitDiag,n,nrhs,br,n,
         "  Solution",0,&fail);

  cout << "\n Derivatives calculated: First order adjoints\n";
  cout << " Computational mode    : algorithmic\n";
  cout << "\n Derivatives of solution X w.r.t. RHS B (A inverse)\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(&b[i],inc);
    ifail = 0;
    nagad_a1w_ir_interpret_adjoint_sparse(ifail);

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

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

  delete [] a;
  delete [] a_in;
  delete [] b;
  delete [] b_in;
  delete [] ipiv;
  delete [] ar;
  delete [] br;
  return exit_status;
}