/* G02DA_A1W_F C++ Header Example Program.
 *
 * Copyright 2019 Numerical Algorithms Group.
 * Mark 27, 2019.
 */

#include <nag.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;
  nagad_a1w_w_rtype tol;
  Integer   ifail = 0;

  cout << "G02DA_A1W_F C++ Header Example Program Results\n\n";

  tol.value = 0.000001;
  tol.id = 0;

  // Skip heading in data file
  string mystr;
  getline (cin, mystr);

  // Read problem sizes
  Integer n, m;
  cin >> n;
  cin >> m;

  // Allocate arrays depending on m and n.
  nagad_a1w_w_rtype *x=0, *y=0;
  Integer           *isx=0;
  double            *dy=0;
  if (!(x   = NAG_ALLOC(m*n, nagad_a1w_w_rtype)) ||
      !(y   = NAG_ALLOC(n,   nagad_a1w_w_rtype)) ||
      !(dy  = NAG_ALLOC(n,   double)) ||
      !(isx = NAG_ALLOC(m,   Integer))) {
    cout << "Allocation failure\n";
    exit_status = -1;
    exit(exit_status);
  }

  // Create AD tape
  nagad_a1w_ir_create();

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

  // Read model data
  double dd;
  for (int i = 0; i<n; ++i) {
    for (int j = 0; j<m; ++j) {
      cin >> dd;
      int k = i + j*n;
      x[k].value = dd;
      x[k].id = 0;
    }
    cin >> dd;
    y[i].value = dd;
    y[i].id = 0;
    nagad_a1w_ir_register_variable(&y[i]);
  }

  // Calculate ip
  Integer ip = 0;
  for (int j = 0; j<m; ++j) {
    cin >> isx[j];
    if (isx[j]>0) {
      ip++;
    }
  }
  // Mean = 'M'
  ip++;

  // Allocate arrays depending on ip
  nagad_a1w_w_rtype *b=0, *cov=0, *h=0, *p=0, *q=0, *res=0, *se=0, *wk=0;
  double            *dbdy;
  Integer           lcov = (ip*ip+ip)/2, lp = ip*(ip+2), lq = n*(ip+1);
  Integer           lwk  = ip*ip + 5*(ip-1);
  if (!(b   = NAG_ALLOC(ip,     nagad_a1w_w_rtype)) ||
      !(cov = NAG_ALLOC(lcov,   nagad_a1w_w_rtype)) ||
      !(h   = NAG_ALLOC(n,      nagad_a1w_w_rtype)) ||
      !(p   = NAG_ALLOC(lp,     nagad_a1w_w_rtype)) ||
      !(q   = NAG_ALLOC(lq,     nagad_a1w_w_rtype)) ||
      !(res = NAG_ALLOC(n,      nagad_a1w_w_rtype)) ||
      !(se  = NAG_ALLOC(ip,     nagad_a1w_w_rtype)) ||
      !(wk  = NAG_ALLOC(lwk,    nagad_a1w_w_rtype)) ||
      !(dbdy = NAG_ALLOC(n*ip,  double))) {
    cout << "Allocation failure\n";
    exit_status = -2;
    exit(exit_status);
  }

  // Perform Regression
  Integer           idf, irank;
  nagad_a1w_w_rtype rss, wt[1];
  logical           svd;
  ifail = 0;
  g02da_a1w_f_(ad_handle,"M","U",n,x,n,m,isx,ip,y,wt,rss,idf, 
               b,se,cov,res,h,q,n,svd,irank,p,tol,wk,ifail,1,1);
  
  // Display results
  if (svd) {
    cout << "Model is not of full rank, rank = " << irank << endl;
  }
  cout << "Residual sum of squares         = " << nagad_a1w_get_value(rss);
  cout << "\nDegrees of freedom              = " << idf << endl;
  cout << "\nVariable   Parameter estimate   Standard error\n\n";
  cout.setf(ios::scientific,ios::floatfield);
  cout.precision(2);
  for (int i=0; i < ip; ++i) {
    cout.width(5); cout << i << "       ";
    cout.width(12); cout << nagad_a1w_get_value(b[i]) << "       ";
    cout.width(12); cout << nagad_a1w_get_value(se[i]) << endl;
  }

  cout << "\n\n Derivatives calculated: First order adjoints\n";
  cout << " Computational mode    : algorithmic\n";
  cout << "\n Derivatives:\n\n";
  
  // Obtain derivatives
  double inc = 1.0;
  nagad_a1w_inc_derivative(&rss,inc);
  ifail = 0;
  nagad_a1w_ir_interpret_adjoint(ifail);
  for (int j=0; j<n; j++) {
    dy[j] = nagad_a1w_get_derivative(y[j]);
  }
  cout << "    i        d(rss)/dy(i)\n";
  cout.precision(4);
  for (int i=0; i<n; ++i) {
    cout.width(5); cout << i << "       ";
    cout.width(12); cout << dy[i] << endl;
  }

  for (int i=0; i<ip; i++) {
    // Reset adjoints, initialize derivative, and evaluate adjoint
    nagad_a1w_ir_zero_adjoints();
    nagad_a1w_inc_derivative(&b[i],inc);
    ifail = 0;
    nagad_a1w_ir_interpret_adjoint_sparse(ifail);
    for (int j=0; j<n; j++) {
      int k = j + i*n;
      double dd = nagad_a1w_get_derivative(y[j]);
      dbdy[k] = dd;
    }
  }
  // Print matrix routine
  cout << endl;
  NagError fail;
  INIT_FAIL(fail);
  x04cac(Nag_ColMajor,Nag_GeneralMatrix,Nag_NonUnitDiag,n,ip,dbdy,n,
         "  Derivatives db/dy",0,&fail);

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

  return exit_status;
}