#include "dco.hpp"
/* F08KB_A1W_F C++ Header Example Program.
 *
 * Copyright 2022 Numerical Algorithms Group.
 * Mark 28.5, 2022.
 */

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

int main()
{
  int               exit_status = 0;
  nag::ad::handle_t ad_handle;
  Integer           ifail = 0;
  NagError          fail;
  INIT_FAIL(fail);

  cout << "F08KB_A1W_F C++ Header Example Program Results\n\n";
  // Skip heading in data file
  string mystr;
  getline(cin, mystr);

  // Read matrix dimensions
  Integer m, n;
  cin >> m;
  cin >> n;

  // Allocate arrays containing A and its factorized form, B
  // and the solution X.
  Integer            lda = m, ldu = m, ldvt = n, lwork;
  nagad_a1w_w_rtype *a = 0, *a_in = 0, *s = 0, *u = 0, *vt = 0, *work = 0;
  double *           ur = 0, *vtr = 0;
  Charlen            lena = 1;
  if (!(a = NAG_ALLOC(m * n, nagad_a1w_w_rtype)) ||
      !(a_in = NAG_ALLOC(m * n, nagad_a1w_w_rtype)) ||
      !(s = NAG_ALLOC(m, nagad_a1w_w_rtype)) ||
      !(u = NAG_ALLOC(m * m, nagad_a1w_w_rtype)) ||
      !(vt = NAG_ALLOC(n * n, nagad_a1w_w_rtype)))
  {
    cout << "Allocation failure\n";
    exit_status = -1;
    return exit_status;
  }

  // Create AD tape
  dco::ga1s<double>::global_tape = dco::ga1s<double>::tape_t::create();

  // Read the matrix A, register and copy
  double dd;
  for (int i = 0; i < m; i++)
  {
    for (int j = 0; j < n; j++)
    {
      cin >> dd;
      Integer k = i + j * m;
      a_in[k]   = dd;
      dco::ga1s<double>::global_tape->register_variable(a_in[k]);
      a[k] = a_in[k];
    }
  }

  // Create AD configuration data object
  ifail = 0;

  // Use routine workspace query to get optimal workspace.
  nagad_a1w_w_rtype dummy[1];
  ifail = 0;
  lwork = -1;
  nag::ad::f08kb(ad_handle, "A", "A", m, n, a, lda, s, u, ldu, vt, ldvt, dummy,
                 lwork, ifail);

  lwork = (Integer)dco::value(dummy[0]) + 1;
  if (!(work = NAG_ALLOC(lwork, nagad_a1w_w_rtype)))
  {
    cout << "Allocation failure\n";
    exit_status = -2;
    goto END;
  }

  //  Compute the singular values and left and right singular vectors
  //  of A (A = U*S*(V**T), m < n)
  nag::ad::f08kb(ad_handle, "A", "A", m, n, a, lda, s, u, ldu, vt, ldvt, work,
                 lwork, ifail);

  // Print primal solution
  cout.precision(4);
  cout.width(12);
  cout << " ";
  cout << " Singular values:\n";
  for (int i = 0; i < m; i++)
  {
    cout.width(11);
    cout << dco::value(s[i]);
  }

  // Copy primal values to array for printing
  if (!(ur = NAG_ALLOC(m * m, double)) || !(vtr = NAG_ALLOC(n * n, double)))
  {
    cout << "Allocation failure\n";
    exit_status = -3;
    goto END;
  }

  for (int i = 0; i < m * m; i++)
  {
    ur[i] = dco::value(u[i]);
  }
  for (int j = 0; j < n; j++)
  {
    Integer k = j * n;
    for (int i = 0; i < m; i++)
    {
      vtr[k] = dco::value(vt[k]);
      k++;
    }
  }

  cout << "\n\n";
  x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, m, m, ur, ldu,
         "Left singular vectors by column", 0, &fail);
  cout << "\n";
  x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, m, n, vtr, ldvt,
         "Right singular vectors by row", 0, &fail);

  cout << "\n\n Derivatives calculated: First order adjoints\n";
  cout << " Computational mode    : algorithmic\n";

  cout << "\n Derivatives of Singular values w.r.t first column of A\n";
  // Obtain derivatives for each singular value w.r.t first column of A
  cout.setf(ios::scientific, ios::floatfield);
  cout.setf(ios::right);
  cout.precision(2);
  for (int i = 0; i < m; i++)
  {
    cout << "\n Singular value " << i + 1 << endl;
    // Setup evaluation of derivatives via adjoints
    dco::ga1s<double>::global_tape->zero_adjoints();
    double inc = 1.0;
    dco::derivative(s[i]) += inc;
    dco::ga1s<double>::global_tape->sparse_interpret() = true;
    dco::ga1s<double>::global_tape->interpret_adjoint();
    if (ifail != 0)
    {
      exit_status = 1;
      goto END;
    }
    // Get derivatives
    cout.width(10);
    cout << " ";
    for (int j = 0; j < m; j++)
    {
      double dsda = dco::derivative(a_in[j]);
      cout.width(10);
      cout << dsda;
    }
    cout << endl;
  }
END:

  ifail = 0;

  dco::ga1s<double>::tape_t::remove(dco::ga1s<double>::global_tape);

  NAG_FREE(a);
  NAG_FREE(a_in);
  NAG_FREE(s);
  NAG_FREE(u);
  NAG_FREE(vt);
  NAG_FREE(work);
  NAG_FREE(ur);
  NAG_FREE(vtr);

  return exit_status;
}