/* F07AD_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 << "F07AD_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;
  cin >> n;

  // Allocate arrays containing A and its factorized form, B
  // and the solution X.
  nagad_a1w_w_rtype *a=0, *a_in=0, *work=0;
  double            *ar=0;
  Integer           *ipiv=0;
  Integer           lwork = 64*n;
  if (!(a    = NAG_ALLOC(n*n,   nagad_a1w_w_rtype)) ||
      !(a_in = NAG_ALLOC(n*n,   nagad_a1w_w_rtype)) ||
      !(work = NAG_ALLOC(lwork, nagad_a1w_w_rtype)) ||
      !(ipiv = NAG_ALLOC(n,     Integer)) ||
      !(ar   = NAG_ALLOC(n*n,   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<n; ++j) {
      cin >> dd;
      Integer k = i + j*n;
      a_in[k].value = dd;
      a_in[k].id = 0;
      if (i==j) {
        nagad_a1w_ir_register_variable(&a_in[k]);
      }
      a[k] = a_in[k];
    }
  }

  // Print matrix A
  for (int i = 0; i<n; i++) {
    for (int j = 0; j<n; j++) {
      Integer k = i + j*n;
      ar[k] = nagad_a1w_get_value(a[k]);
    }
  }
  cout << endl;
  NagError  fail;
  INIT_FAIL(fail);
  x04cac(Nag_ColMajor,Nag_GeneralMatrix,Nag_NonUnitDiag,n,n,ar,n,
         "  A",0,&fail);

  // 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);

  // Invert A
  ifail = 0;
  f07aj_a1w_f_(ad_handle,n,a,n,ipiv,work,lwork,ifail);
  
  // Print Inverse
  for (int i = 0; i<n; i++) {
    for (int j = 0; j<n; j++) {
      int k = i + j*n;
      ar[k] = nagad_a1w_get_value(a[k]);
    }
  }
  cout << endl;
  // NagError  fail;
  INIT_FAIL(fail);
  x04cac(Nag_ColMajor,Nag_GeneralMatrix,Nag_NonUnitDiag,n,n,ar,n,
         "  Inverse",0,&fail);

  cout << "\n\n Derivatives calculated: First order adjoints\n";
  cout << " Computational mode    : algorithmic\n";
  cout << "\n Derivatives of inverse diagonal w.r.t diagonal of A:\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;
    Integer k = i*n + i;
    nagad_a1w_inc_derivative(&a[k],inc);
    ifail = 0;
    nagad_a1w_ir_interpret_adjoint_sparse(ifail);

    for (int j=0; j<n; j++) {
      Integer k = j + j*n;
      double dd = nagad_a1w_get_derivative(a_in[k]);
      ar[i+j*n] = dd;
    }
  }
  // Print derivatives
  cout << endl;
  INIT_FAIL(fail);
  x04cac(Nag_ColMajor,Nag_GeneralMatrix,Nag_NonUnitDiag,n,n,ar,n,
         "           dai(i,i)/da(j,j)",0,&fail);

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

  return exit_status;
}