/* G02DA_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 <iostream>
#include <string>
#include <nagx04.h>

typedef double DCO_BASE_TYPE;
typedef dco::gt1s<DCO_BASE_TYPE> DCO_MODE;
typedef DCO_MODE::type DCO_TYPE;

using namespace std;

int main(void)
{
  int      exit_status = 0;
  void     *ad_handle = 0;
  DCO_TYPE tol;
  Integer  ifail = 0;

  cout << "G02DA_T1W_F C++ Header Example Program Results\n\n";

  tol = 0.000001;

  // 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.
  DCO_TYPE *x=0, *y=0, *y_in=0;
  Integer  *isx=0;
  double   *dy=0;
  x    = new DCO_TYPE [m*n];
  y    = new DCO_TYPE [n];
  y_in = new DCO_TYPE [n];
  dy   = new double [n];
  isx  = new Integer [m];

  // Create AD configuration data object
  ifail = 0;
  x10aa_t1w_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] = dd;
    }
    cin >> dd;
    y_in[i] = dd;
    y[i] = y_in[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
  DCO_TYPE *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);
  b   = new DCO_TYPE [ip];
  cov = new DCO_TYPE [lcov];
  h   = new DCO_TYPE [n];
  p   = new DCO_TYPE [lp];
  q   = new DCO_TYPE [lq];
  res = new DCO_TYPE [n];
  se  = new DCO_TYPE [ip];
  wk  = new DCO_TYPE [lwk];
  dbdy = new double [n*ip];

  // Perform Regression
  Integer           idf, irank;
  DCO_TYPE rss;
  logical           svd;
  ifail = 0;
  g02da_t1w_f_(ad_handle,"M","U",n,x,n,m,isx,ip,y,NULL,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         = " << dco::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 << dco::value(b[i]) << "       ";
    cout.width(12); cout << dco::value(se[i]) << endl;
  }

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

  // Obtain derivatives
  for (int i = 0; i < n; i++) {
    y[i] = y_in[i];
  }
  for (int i = 0; i < n; i++) {
    dco::derivative(y[i]) = 1.0;
    g02da_t1w_f_(ad_handle,"M","U",n,x,n,m,isx,ip,y,NULL,rss,idf,
                 b,se,cov,res,h,q,n,svd,irank,p,tol,wk,ifail,1,1);
    dy[i] = dco::derivative(rss);

    for (int j=0; j<ip; j++) {
      int k = i + j*n;
      dbdy[k] = dco::derivative(b[j]);
    }
    for (int j=0; j<n; ++j) {
      y[j] = y_in[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;
  }

  // Print matrix routine
  cout << endl;

  NagError fail;
  INIT_FAIL(fail);
  x04cac(Nag_ColMajor,Nag_GeneralMatrix,Nag_NonUnitDiag,n,ip,dbdy,n,
         "db/dy",0,&fail);

  // Remove computational data object
  ifail = 0;
  x10ab_t1w_f_(ad_handle,ifail);

  delete [] b;
  delete [] cov;
  delete [] h;
  delete [] p;
  delete [] q;
  delete [] res;
  delete [] se;
  delete [] wk;
  delete [] dbdy;
  delete [] x;
  delete [] y;
  delete [] y_in;
  delete [] dy;
  delete [] isx;
  return exit_status;
}