/* E04GB_T1W_F C++ Header Example Program.
 *
 * Copyright 2019 Numerical Algorithms Group.
 * Mark 27, 2019.
 */

#include <nag.h>
#include <dco.hpp>
#include <nagad.h>
#include <stdio.h>
#include <math.h>
#include <nagx02.h>
#include <iostream>
#include <string>
using namespace std;

extern "C"
{
  static void NAG_CALL lsqgrd(const Integer &m,
                              const Integer &n,
                              const nagad_t1w_w_rtype fvec[],
                              const nagad_t1w_w_rtype fjac[],
                              const Integer &ldfjac,
                              nagad_t1w_w_rtype g[]);
  static void NAG_CALL lsqfun(void* &ad_handle,
                              Integer &iflag,
                              const Integer &m,
                              const Integer &n,
                              const nagad_t1w_w_rtype xc[],
                              nagad_t1w_w_rtype fvec[],
                              nagad_t1w_w_rtype fjac[],
                              const Integer &ldfjac,
                              Integer iuser[],
                              nagad_t1w_w_rtype ruser[]);
  static void NAG_CALL lsqmon(void* &ad_handle,
                              const Integer &m,
                              const Integer &n,
                              const nagad_t1w_w_rtype xc[],
                              const nagad_t1w_w_rtype fvec[],
                              const nagad_t1w_w_rtype fjac[],
                              const Integer &ldfjac,
                              const nagad_t1w_w_rtype s[],
                              const Integer &igrade,
                              const Integer &niter,
                              const Integer &nf,
                              Integer iuser[],
                              nagad_t1w_w_rtype ruser[]);
}

int main(void)
{
  // Scalars
  int               exit_status = 0;
  const Integer     m = 15, ldfjac = 15, n = 3, nt = 3, ldv = 3;

  cout << "E04GB_T1W_F C++ Header Example Program Results\n\n";

  // Create AD configuration data object
  Integer ifail = 0;
  void    *ad_handle = 0;
  x10aa_t1w_f_(ad_handle,ifail);

  // Skip first line of data file
  string mystr;
  getline (cin, mystr);

  // Read problem parameters and register for differentiation

  double            yr;
  nagad_t1w_w_rtype ruser[m*nt+m];
  for (int i=0; i<m; i++) {
    cin >> yr;
    ruser[i] = yr;
    for (int j=1; j<=nt; j++) {
      cin >> yr;
      Integer k = j*m + i;
      ruser[k] = yr;
    }
  }

  // AD routine arguments
  Integer           iprint, maxcal, niter, nf, selct;
  Integer           iuser[1];
  double            inc = 1.0, zero = 0.0;
  nagad_t1w_w_rtype eta, stepmx, xtol, fsumsq;
  nagad_t1w_w_rtype x[n], fvec[m], fjac[m*n], g[n], s[n], v[ldv*n];
  double            dfdy[m], dxdy[m*n];
  
  iprint = -1;
  selct = 2;
  maxcal = 200*n;
  eta = 0.5;
  xtol = 10.0*sqrt(X02AJC);
  stepmx = 10.0;
  
  for (int i=0; i<m; i++) {
    
    nagad_t1w_inc_derivative(&ruser[i],inc);
    // Starting points
    x[0] = 0.5;
    for (int j=1; j<n; j++) {
      x[j] = x[j-1] + 0.5;
    }

    // Call the AD routine
    ifail = -1;
    e04gb_t1w_f_(ad_handle,m,n,selct,lsqfun,lsqmon,iprint,maxcal,eta,xtol,
                 stepmx,x,fsumsq,fvec,fjac,ldfjac,s,v,ldv,niter,nf,
                 iuser,ruser,ifail);
    if (ifail<0 || ifail==1) {
      cout << "e04gb_t1w_f_ failed with ifail = "<< ifail << endl;
      goto END;
    }
    nagad_t1w_set_derivative(&ruser[i],zero);
    for (int j=0; j<n; ++j) {
      dxdy[j+i*n] = nagad_t1w_get_derivative(x[j]);
    }
    dfdy[i] = nagad_t1w_get_derivative(fsumsq);
  }
  // Primal results
  cout.setf(ios::scientific,ios::floatfield);
  cout.precision(4);
  cout << "\n Sum of squares = ";
  cout.width(12); cout << nagad_t1w_get_value(fsumsq);
  cout << "\n Solution point = ";
  for (int i=0; i<n; i++) {
    cout.width(12); cout << nagad_t1w_get_value(x[i]);
  }
  cout << endl;
    
  lsqgrd(m,n,fvec,fjac,m,g);
    
  cout.precision(3);
  cout << " Estim gradient = ";
  for (int i=0; i<n; i++) {
    cout.width(12); cout << nagad_t1w_get_value(g[i]);
  }

  cout.precision(1);
  cout << "\n Residuals :\n";
  for (int i=0; i<m; i++) {
    cout.width(12); cout << nagad_t1w_get_value(fvec[i]);
    if (i%3==2) {
      cout << endl;
    }
  }

  cout << "\n Derivatives calculated: First order tangents\n";
  cout << " Computational mode    : algorithmic\n\n";
  cout << " Derivatives:\n\n";
  
  // Get derivatives of fsumsq
  cout << "  sum of squares w.r.t y:\n";
  for (int i=0; i<m; i++) {
    cout.width(12); cout << dfdy[i];
    if (i%3==2) {
      cout << endl;
    }
  }

  // Get derivatives of solution points w.r.t. y
  for (int j=0; j<n; j++) {
    cout << "\n dx(";
    cout.width(1); cout << j+1;
    cout << ")/dy :\n";
    for (int i=0; i<m; i++) {
      cout.width(12); cout << dxdy[j+i*n];
      if (i%3==2) {
        cout << endl;
      }
    }
  }

 END:    
  // Remove computational data object
  x10ab_t1w_f_(ad_handle,ifail);

  return exit_status;
}

// dco/c++ used to perform AD of callbacks

static void NAG_CALL lsqgrd(const Integer &m,
                            const Integer &n,
                            const nagad_t1w_w_rtype fvec[],
                            const nagad_t1w_w_rtype fjac[],
                            const Integer &ldfjac,
                            nagad_t1w_w_rtype g[]){
  Integer k;
  for (int i=0; i<n; i++) {
    g[i] = 0.0;
    k = i*ldfjac;
    for (int j=0; j<m; j++) {
      g[i] = g[i] + fjac[k]*fvec[j];
      k++;
    }
    g[i] = 2.0*g[i];
  }
  
  return;
}

static void NAG_CALL lsqfun(void* &ad_handle,
                            Integer &iflag,
                            const Integer &m,
                            const Integer &n,
                            const nagad_t1w_w_rtype xc[],
                            nagad_t1w_w_rtype fvec[],
                            nagad_t1w_w_rtype fjac[],
                            const Integer &ldfjac,
                            Integer iuser[],
                            nagad_t1w_w_rtype ruser[])
{
  for (int i=0;i<m; i++) {
    nagad_t1w_w_rtype d1, d2, denom;
    d1 = xc[1]*ruser[2*m+i];
    d2 = xc[2]*ruser[3*m+i];
    denom = d1 + d2;
    d1 = xc[0]- ruser[i];
    d2 = ruser[m+i]/denom;
    fvec[i] = d1 + d2;
    if (iflag>0) {
      fjac[i] = 1.0;
      d1 = 1.0/denom;
      d2 = -d1*d1;
      d1 = ruser[m+i]*d2;
      fjac[m+i] = d1*ruser[2*m+i];
      fjac[2*m+i] = d1*ruser[3*m+i];
    }
  }
  return;
}

static void NAG_CALL lsqmon(void* &ad_handle,
                            const Integer &m,
                            const Integer &n,
                            const nagad_t1w_w_rtype xc[],
                            const nagad_t1w_w_rtype fvec[],
                            const nagad_t1w_w_rtype fjac[],
                            const Integer &ldfjac,
                            const nagad_t1w_w_rtype s[],
                            const Integer &igrade,
                            const Integer &niter,
                            const Integer &nf,
                            Integer iuser[],
                            nagad_t1w_w_rtype ruser[])
{
  double fsumsq = 0.0;
  for (int i=0;i<m; i++) {
    double f = nagad_t1w_get_value(fvec[i]);
    fsumsq = fsumsq + f*f;
  }
  nagad_t1w_w_rtype g[3];
  lsqgrd(m,n,fvec,fjac,ldfjac,g);

  double gtg = 0.0;
  for (int i=0;i<n; i++) {
    double gg = nagad_t1w_get_value(g[i]);
    gtg += gg*gg;
  }

  cout.setf(ios::scientific,ios::floatfield);
  cout.precision(4);
  cout << "  Itn      F evals        SUMSQ             GTG        Grade\n";
  cout.width(4); cout << niter;
  cout.width(11); cout << nf;
  cout.width(19); cout << fsumsq;
  cout.width(15); cout << gtg;
  cout.width(9); cout << igrade; cout << endl;
  cout << "\n       x                    g           Singular values\n";
  for (int i=0;i<n;i++) {
    cout.width(13); cout << nagad_t1w_get_value(xc[i]);
    cout.width(19); cout << nagad_t1w_get_value(g[i]);
    cout.width(19); cout << nagad_t1w_get_value(s[i]);
    cout << endl;
  }
  return;
}