/* nag_robust_m_regsn_wts (g02hbc) Example Program.
 *
 * Copyright 2017 Numerical Algorithms Group.
 *
 * Mark 26.1, 2017.
 */

#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>

#ifdef __cplusplus
extern "C"
{
#endif
  static double NAG_CALL ucv(double t, Nag_Comm *comm);
#ifdef __cplusplus
}
#endif

int main(void)
{

  /* Scalars */
  double bd, bl, tol;
  Integer exit_status, i, j, k, l1, l2, m, maxit, mm, n, nit, nitmon;
  Integer pdx;
  NagError fail;
  Nag_OrderType order;
  Nag_Comm comm;

  /* Arrays */
  static double ruser[1] = { -1.0 };
  double *a = 0, *x = 0, *z = 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_robust_m_regsn_wts (g02hbc) 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 (!(a = NAG_ALLOC(m * (m + 1) / 2, double)) ||
      !(x = NAG_ALLOC(n * m, double)) || !(z = 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 */
  for (i = 1; i <= n; ++i) {
    for (j = 1; j <= m; ++j)
      scanf("%lf", &X(i, j));
    scanf("%*[^\n] ");
  }
  /* Read in the initial value of A */
  mm = (m + 1) * m / 2;
  for (j = 1; j <= mm; ++j)
    scanf("%lf", &a[j - 1]);
  scanf("%*[^\n] ");

  /* Set the values remaining parameters */
  bl = 0.9;
  bd = 0.9;
  maxit = 50;
  tol = 5e-5;
  /* Change nitmon to a positive value if monitoring information
   * is required
   */
  nitmon = 0;
  /* nag_robust_m_regsn_wts (g02hbc).
   * Robust regression, compute weights for use with
   * nag_robust_m_regsn_user_fn (g02hdc)
   */
  nag_robust_m_regsn_wts(order, ucv, n, m, x, pdx, a, z, bl, bd, tol, maxit,
                         nitmon, 0, &nit, &comm, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_robust_m_regsn_wts (g02hbc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  printf("nag_robust_m_regsn_wts (g02hbc) required %4" NAG_IFMT
         " iterations to " "converge\n\n", nit);
  printf("Matrix A\n");
  l2 = 0;
  for (j = 1; j <= m; ++j) {
    l1 = l2 + 1;
    l2 += j;
    for (k = l1; k <= l2; ++k)
      printf("%9.4f%s", a[k - 1], k % 6 == 0 || k == l2 ? "\n" : " ");
  }

  printf("\n");
  printf("Vector Z\n");
  for (i = 1; i <= n; ++i)
    printf("%9.4f\n", z[i - 1]);

  /* Calculate Krasker-Welsch weights */
  printf("\n");
  printf("Vector of weights\n");
  for (i = 1; i <= n; ++i) {
    z[i - 1] = 1.0 / z[i - 1];
    printf("%9.4f\n", z[i - 1]);
  }

END:
  NAG_FREE(a);
  NAG_FREE(x);
  NAG_FREE(z);

  return exit_status;
}

static double NAG_CALL ucv(double t, Nag_Comm *comm)
{
  /* Scalars */
  double pc, pd, q, q2;
  double ret_val;

  /* ucv function for Krasker-Welsch weights */
  if (comm->user[0] == -1.0) {
    printf("(User-supplied callback ucv, first invocation.)\n");
    comm->user[0] = 0.0;
  }
  ret_val = 1.0;
  if (t != 0.0) {
    q = 2.5 / t;
    q2 = q * q;
    /* nag_cumul_normal (s15abc).
     * Cumulative Normal distribution function P(x)
     */
    pc = nag_cumul_normal(q);
    /* nag_real_smallest_number (x02akc).
     * The smallest positive model number
     */
    if (q2 < -log(nag_real_smallest_number))
      /* nag_pi (x01aac).
       * pi
       */
      pd = exp(-q2 / 2.0) / sqrt(nag_pi * 2.0);
    else
      pd = 0.0;
    ret_val = (pc * 2.0 - 1.0) * (1.0 - q2) + q2 - q * 2.0 * pd;
  }
  return ret_val;
}