/* nag_correg_robustm_user (g02hdc) Example Program.
 *
 * Copyright 2020 Numerical Algorithms Group.
 *
 * Mark 27.1, 2020.
 */

#include <math.h>
#include <nag.h>
#include <stdio.h>

#ifdef __cplusplus
extern "C" {
#endif
static double NAG_CALL chi(double t, Nag_Comm *comm);
static double NAG_CALL psi(double t, Nag_Comm *comm);
static void NAG_CALL betcal(Integer n, double wgt[], double *beta);
#ifdef __cplusplus
}
#endif

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 */
  static double ruser[2] = {-1.0, -1.0};
  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;
  printf("nag_correg_robustm_user (g02hdc) Example Program Results\n");

  /* For communication with user-supplied functions: */
  comm.user = ruser;

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

  /* Read in the dimensions of X */
  scanf("%" NAG_IFMT "%" NAG_IFMT "%*[^\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))) {
    printf("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)
      scanf("%lf", &X(i, j));
    scanf("%lf%*[^\n] ", &y[i - 1]);
    X(i, 1) = 1.0;
  }

  /* Read in weights */
  for (i = 1; i <= n; ++i) {
    scanf("%lf", &wgt[i - 1]);
    scanf("%*[^\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_correg_robustm_user (g02hdc).
   * Robust regression, compute regression with user-supplied
   * functions and weights
   */
  nag_correg_robustm_user(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);

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

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

  return exit_status;
}

double NAG_CALL psi(double t, Nag_Comm *comm) {
  double ret_val;
  if (comm->user[0] == -1.0) {
    printf("(User-supplied callback psi, first invocation.)\n");
    comm->user[0] = 0.0;
  }
  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 NAG_CALL chi(double t, Nag_Comm *comm) {
  /* Scalars */
  double ret_val;
  double ps;

  if (comm->user[1] == -1.0) {
    printf("(User-supplied callback chi, first invocation.)\n");
    comm->user[1] = 0.0;
  }
  ps = 1.5;
  if (fabs(t) < 1.5)
    ps = t;
  ret_val = ps * ps / 2.0;
  return ret_val;
}

static void NAG_CALL 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_machine_real_smallest (x02akc).
   * The smallest positive model number
   */
  amaxex = -log(nag_machine_real_smallest);
  /* nag_math_pi (x01aac).
   * pi
   */
  anormc = sqrt(nag_math_pi * 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_specfun_cdf_normal (s15abc).
     * Cumulative Normal distribution function P(x)
     */
    pc = nag_specfun_cdf_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;
}