/* F07CE_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 <string>
#include <iostream>
using namespace std;

int main(void)
{
  int       exit_status = 0;
  void      *ad_handle = 0;
  Integer   nrhs = 1, ifail = 0;

  cout << "F07CE_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;
  cin >> nrhs;

  // Allocate arrays containing A and its factorized form, B
  // and the solution X.
  nagad_a1w_w_rtype *dl=0, *d=0, *du=0, *du2=0, *b=0;
  nagad_a1w_w_rtype *dlf=0, *df=0, *duf=0, *x=0;
  double            *sol=0;
  Integer           *ipiv = 0;
  Integer           n1 = n-1, n2 = n-2;
  if (!(dl  = NAG_ALLOC(n1, nagad_a1w_w_rtype)) ||
      !(d   = NAG_ALLOC(n, nagad_a1w_w_rtype)) ||
      !(du  = NAG_ALLOC(n1, nagad_a1w_w_rtype)) ||
      !(du2 = NAG_ALLOC(n2, nagad_a1w_w_rtype)) ||
      !(dlf = NAG_ALLOC(n1, nagad_a1w_w_rtype)) ||
      !(df  = NAG_ALLOC(n, nagad_a1w_w_rtype)) ||
      !(duf = NAG_ALLOC(n1, nagad_a1w_w_rtype)) ||
      !(b   = NAG_ALLOC(n*nrhs, nagad_a1w_w_rtype)) ||
      !(ipiv   = NAG_ALLOC(n, Integer)) ||
      !(x = NAG_ALLOC(n*n, nagad_a1w_w_rtype)) ||
      !(sol = NAG_ALLOC(n*n, double))) {
    cout << "Allocation failure\n";
    exit_status = -1;
    goto END;
  }
  
  // Create AD tape
  nagad_a1w_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;
    du[i].value = dd;
    du[i].id = 0;
    nagad_a1w_ir_register_variable(&du[i]);
    duf[i] = du[i]; 
  }
  for (int i = 0; i<n; i++) {
    cin >> dd;
    d[i].value = dd;
    d[i].id = 0;
    nagad_a1w_ir_register_variable(&d[i]);
    df[i]  = d[i]; 
  }
  for (int i = 0; i<n1; i++) {
    cin >> dd;
    dl[i].value = dd;
    dl[i].id = 0;
    nagad_a1w_ir_register_variable(&dl[i]);
    dlf[i] = dl[i]; 
  }
  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 tridiagonal matrix A
  ifail = 0;
  f07cd_a1w_f_(ad_handle,n,dlf,df,duf,du2,ipiv,ifail);

  // Solve the equations Ax = b for x
  ifail = 0;
  f07ce_a1w_f_(ad_handle,"N",n,nrhs,dlf,df,duf,du2,ipiv,x,n,ifail,1);

  // Print primal solution
  for (int i=0; i<n*nrhs; i++) {
    sol[i] = nagad_a1w_get_value(x[i]);
  }
    cout << "\n\n";
  NagError  fail;
  INIT_FAIL(fail);
  x04cac(Nag_ColMajor,Nag_GeneralMatrix,Nag_NonUnitDiag,n,nrhs,sol,n,
         "  Solution",0,&fail);

  cout << "\n\n Derivatives calculated: First order adjoints\n";
  cout << " Computational mode    : algorithmic\n";
  cout << "\n Derivatives of first solution column w.r.t. inputs:\n";
  
  // Obtain derivatives for each output solution point

  cout.setf(ios::scientific,ios::floatfield);
  cout.setf(ios::right);
  cout.precision(2);
  for (int i=0; i<n; i++) {
    cout << "\n  Solution point " << i+1 << endl;

    // Reset adjoints, initialize derivative, and evaluate adjoint
    nagad_a1w_ir_zero_adjoints();
    double inc = 1.0;
    nagad_a1w_inc_derivative(&x[i],inc);
    ifail = -1;
    nagad_a1w_ir_interpret_adjoint(ifail);
    if (ifail != 0) {
      exit_status = 3;
      goto END;
    }

    cout << "      dx/d(du) : ";
    cout.width(10); cout << " ";
    for (int j=0; j<n1; j++) {
      double dd = nagad_a1w_get_derivative(du[j]);
      cout.width(10); cout << dd;
    }
      
    cout << "\n      dx/d(d)  : ";
    for (int j=0; j<n; j++) {
      double dd = nagad_a1w_get_derivative(d[j]);
      cout.width(10); cout << dd;
    }

    cout << "\n      dx/d(dl) : ";
    for (int j=0; j<n1; j++) {
      double dd = nagad_a1w_get_derivative(dl[j]);
      cout.width(10); cout << dd;
    }
    cout << "\n      dx/d(b)  : ";
    for (int j=0; j<n; j++) {
      double dd = nagad_a1w_get_derivative(b[j]);
      cout.width(10); cout << dd;
    }
    cout << endl;
  }

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

  return exit_status;
}