/* nag_robust_m_regsn_user_fn (g02hdc) Example Program.
 *
 * Copyright 2002 Numerical Algorithms Group.
 *
 * Mark 7, 2002.
 * Mark 7b revised, 2004.
 */

#include <math.h>
#include <stdio.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagg02.h>
#include <nags.h>
#include <nagx01.h>
#include <nagx02.h>
static double chi(double t, Nag_Comm *comm);
static double psi(double t, Nag_Comm *comm);
static void betcal(Integer n, double wgt[], double *beta);

int main(void)
{

  /* Scalars */
  double beta, eps, psip0, sigma, tol;
  Integer exit_status, i, j, k, m, maxit, n, nit, nitmon;
  Integer pdx;
  NagError fail;
  Nag_OrderType order;
  Nag_Comm comm;

  /* Arrays */
  double *rs=0, *theta=0, *wgt=0, *x=0, *y=0;

#ifdef NAG_COLUMN_MAJOR
#define X(I,J) x[(J-1)*pdx + I - 1]
  order = Nag_ColMajor;
#else
#define X(I,J) x[(I-1)*pdx + J - 1]
  order = Nag_RowMajor;
#endif

  INIT_FAIL(fail);
  exit_status = 0;
  Vprintf("nag_robust_m_regsn_user_fn (g02hdc) Example Program Results\n");

  /* Skip heading in data file */
  Vscanf("%*[^\n] ");

  /* Read in the dimensions of X */
  Vscanf("%ld%ld%*[^\n] ", &n, &m);
  /* Allocate memory */
  if ( !(rs = NAG_ALLOC(n, double)) ||
       !(theta = NAG_ALLOC(m, double)) ||
       !(wgt = NAG_ALLOC(n, double)) ||
       !(x = NAG_ALLOC(n * m, double)) ||
       !(y = NAG_ALLOC(n, double)) )
    {
      Vprintf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }

#ifdef NAG_COLUMN_MAJOR
  pdx = n;
#else
  pdx = m;
#endif

  /* Read in the X matrix, the Y values and set X(i,1) to 1 for the */
  /* constant term */
  for (i = 1; i <= n; ++i)
    {
      for (j = 2; j <= m; ++j)
        Vscanf("%lf", &X(i,j));
      Vscanf("%lf%*[^\n] ", &y[i - 1]);
      X(i, 1) = 1.0;
    }

  /* Read in weights */
  for (i = 1; i <= n; ++i)
    {
      Vscanf("%lf", &wgt[i - 1]);
      Vscanf("%*[^\n] ");
    }
  betcal(n, wgt, &beta);

  /* Set other parameter values */
  maxit = 50;
  tol = 5e-5;
  eps = 5e-6;
  psip0 = 1.0;

  /* Set value of isigma and initial value of sigma */
  sigma = 1.0;

  /* Set initial value of theta */
  for (j = 1; j <= m; ++j)
    theta[j - 1] = 0.0;
  /* Change nitmon to a positive value if monitoring information
   * is required
   */
  nitmon = 0;

  /* Schweppe type regression */
  /* nag_robust_m_regsn_user_fn (g02hdc).
   * Robust regression, compute regression with user-supplied
   * functions and weights
   */
  nag_robust_m_regsn_user_fn(order, chi, psi, psip0, beta, Nag_SchweppeReg,
                             Nag_SigmaChi, n, m, x, pdx, y, wgt, theta, &k,
                             &sigma, rs, tol, eps, maxit,
                             nitmon, 0, &nit, &comm, &fail);

  Vprintf("\n");
  if (fail.code != NE_NOERROR && fail.code != NE_FULL_RANK)
    {
      Vprintf("Error from nag_robust_m_regsn_user_fn (g02hdc).\n%s\n",
              fail.message);
      exit_status = 1;
      goto END;
    }
  else
    {
      if (fail.code == NE_FULL_RANK)
        {
          Vprintf("nag_robust_m_regsn_user_fn (g02hdc) returned with message "
                  "%s\n", fail.message);
          Vprintf("\n");

          Vprintf("Some of the following results may be unreliable\n");
        }
      Vprintf("nag_robust_m_regsn_user_fn (g02hdc) required %4ld "
              "iterations to converge\n", nit);
      Vprintf("                   k = %4ld\n", k);
      Vprintf("               Sigma = %9.4f\n", sigma);
      Vprintf("    Theta\n");
      for (j = 1; j <= m; ++j)
        Vprintf("%9.4f\n", theta[j - 1]);
      Vprintf("\n");
      Vprintf("  Weights  Residuals\n");
      for (i = 1; i <= n; ++i)
        Vprintf("%9.4f%9.4f\n", wgt[i - 1], rs[i - 1]);
    }
 END:
  if (rs) NAG_FREE(rs);
  if (theta) NAG_FREE(theta);
  if (wgt) NAG_FREE(wgt);
  if (x) NAG_FREE(x);
  if (y) NAG_FREE(y);

  return exit_status;
}
double psi(double t, Nag_Comm *comm)
{

  double ret_val;
  if (t <= -1.5)
    ret_val = -1.5;
  else if (fabs(t) < 1.5)
    ret_val = t;
  else
    ret_val = 1.5;
  return ret_val;
}
static double chi(double t, Nag_Comm *comm)
{

  /* Scalars */
  double ret_val;
  double ps;

  ps = 1.5;
  if (fabs(t) < 1.5)
    ps = t;
  ret_val = ps * ps / 2.0;
  return ret_val;
}
static void betcal(Integer n, double wgt[], double *beta)
{
  /* Scalars */
  double amaxex, anormc, b, d2, dc, dw, dw2, pc, w2;
  Integer i;

  /* Calculate BETA for Schweppe type regression */

  /* Function Body */
  /* nag_real_smallest_number (x02akc).
   * The smallest positive model number
   */
  amaxex = -log(X02AKC);
  /* nag_pi (x01aac).
   * pi
   */
  anormc = sqrt(X01AAC * 2.0);
  d2 = 2.25;
  *beta = 0.0;
  for (i = 1; i <= n; ++i)
    {
      w2 = wgt[i-1] * wgt[i-1];
      dw = wgt[i-1] * 1.5;
      /* nag_cumul_normal (s15abc).
       * Cumulative Normal distribution function P(x)
       */
      pc = nag_cumul_normal(dw);
      dw2 = dw * dw;
      dc = 0.0;
      if (dw2 < amaxex)
        dc = exp(-dw2 / 2.0) / anormc;
      b = (-dw * dc + pc - 0.5) / w2 + (1.0 - pc) * d2;
      *beta = b * w2 / (double) (n) + *beta;
    }
  return;
}