/* nag_regsn_mult_linear (g02dac) Example Program.
 *
 * Copyright 2017 Numerical Algorithms Group.
 *
 * Mark 26.2, 2017.
 */

#include <nag.h>
#include <math.h>
#include <stdio.h>
#include <nag_stdlib.h>
#include <nagg02.h>

static int ex1(void);
static int ex2(void);

int main(void)
{
  Integer exit_status_ex1 = 0;
  Integer exit_status_ex2 = 0;

  printf("nag_regsn_mult_linear (g02dac) Example Program Results\n\n");

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

  exit_status_ex1 = ex1();
  exit_status_ex2 = ex2();

  return (exit_status_ex1 == 0 && exit_status_ex2 == 0) ? 0 : 1;
}

#define X(I, J) x[(I) *tdx + J]

static int ex1(void)
{
  Integer exit_status = 0, i, ip, j, m, n, rank, *sx = 0, tdq, tdx;
  char nag_enum_arg[40];
  double *b = 0, *com_ar = 0, *cov = 0, df, *h = 0, *p = 0, *q = 0;
  double *res = 0, rss, *se = 0, tol, *wt = 0, *wtptr, *x = 0, *y = 0;
  Nag_Boolean svd, weight;
  Nag_IncludeMean mean;
  NagError fail;

  INIT_FAIL(fail);

  printf("Example 1\n");
  /* Skip heading in data file */
  scanf("%*[^\n]");
  scanf("%" NAG_IFMT " %" NAG_IFMT "", &n, &m);
  scanf(" %39s", nag_enum_arg);
  /* nag_enum_name_to_value (x04nac).
   * Converts NAG enum member name to value
   */
  weight = (Nag_Boolean) nag_enum_name_to_value(nag_enum_arg);
  scanf(" %39s", nag_enum_arg);
  mean = (Nag_IncludeMean) nag_enum_name_to_value(nag_enum_arg);
  if (n >= 2 && m >= 1) {
    if (!(h = NAG_ALLOC(n, double)) ||
        !(res = NAG_ALLOC(n, double)) ||
        !(wt = NAG_ALLOC(n, double)) ||
        !(x = NAG_ALLOC(n * m, double)) ||
        !(y = NAG_ALLOC(n, double)) || !(sx = NAG_ALLOC(m, Integer)))
    {
      printf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }
    tdx = m;
  }
  else {
    printf("Invalid n or m.\n");
    exit_status = 1;
    return exit_status;
  }
  if (weight) {
    wtptr = wt;
    for (i = 0; i < n; i++) {
      for (j = 0; j < m; j++)
        scanf("%lf", &X(i, j));
      scanf("%lf%lf", &y[i], &wt[i]);
    }
  }
  else {
    wtptr = (double *) 0;
    for (i = 0; i < n; i++) {
      for (j = 0; j < m; j++)
        scanf("%lf", &X(i, j));
      scanf("%lf", &y[i]);
    }
  }
  for (j = 0; j < m; j++)
    scanf("%" NAG_IFMT "", &sx[j]);
  /* Calculate ip */
  ip = 0;
  if (mean == Nag_MeanInclude)
    ip += 1;
  for (i = 0; i < m; i++)
    if (sx[i] > 0)
      ip += 1;

  if (!(b = NAG_ALLOC(ip, double)) ||
      !(cov = NAG_ALLOC((ip * ip + ip) / 2, double)) ||
      !(p = NAG_ALLOC(ip * (ip + 2), double)) ||
      !(q = NAG_ALLOC(n * (ip + 1), double)) ||
      !(com_ar = NAG_ALLOC(ip * ip + ip, double)) ||
      !(se = NAG_ALLOC(ip, double)))
  {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }
  tdq = ip + 1;

  /* Set tolerance */
  tol = 0.00001e0;
  /* nag_regsn_mult_linear (g02dac).
   * Fits a general (multiple) linear regression model
   */
  nag_regsn_mult_linear(mean, n, x, tdx, m, sx, ip, y,
                        wtptr, &rss, &df, b, se, cov, res, h, q,
                        tdq, &svd, &rank, p, tol, com_ar, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_regsn_mult_linear (g02dac).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  if (svd)
    printf("Model not of full rank, rank = %4" NAG_IFMT "\n\n", rank);
  printf("Residual sum of squares = %13.4e\n", rss);
  printf("Degrees of freedom = %3.1f\n\n", df);
  printf("Variable    Parameter estimate   Standard error\n\n");
  for (j = 0; j < ip; j++)
    printf("%6" NAG_IFMT "%20.4e%20.4e\n", j + 1, b[j], se[j]);
  printf("\n");
  printf("    Obs         Residuals              h\n\n");
  for (i = 0; i < n; i++)
    printf("%6" NAG_IFMT "%20.4e%20.4e\n", i + 1, res[i], h[i]);

END:
  NAG_FREE(h);
  NAG_FREE(res);
  NAG_FREE(wt);
  NAG_FREE(x);
  NAG_FREE(y);
  NAG_FREE(sx);
  NAG_FREE(b);
  NAG_FREE(cov);
  NAG_FREE(p);
  NAG_FREE(q);
  NAG_FREE(com_ar);
  NAG_FREE(se);

  return exit_status;
}

#undef x

#define X(I, J) x[(I) *tdx + J]
static int ex2(void)
{
  Integer exit_status = 0;
  double rss, tol;
  Integer i, ip, rank, j, m, mmax, n, degree, digits, tdx, tdq;
  double df;
  Nag_Boolean svd;
  Nag_IncludeMean mean;
  double *h = 0, *res = 0, *wt = 0, *x = 0, *y = 0;
  double *b = 0, *cov = 0, *p = 0, *q = 0, *com_ar = 0, *se = 0;
  double *wtptr = (double *) 0; /* don't use weights */
  Integer *sx = 0;
  NagError fail;

  INIT_FAIL(fail);

  printf("\n\n\nExample 2\n");
  /* Skip heading in data file */
  scanf(" %*[^\n]");

  /* Use mean = Nag_MeanInclude */

  mean = Nag_MeanInclude;
  scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "", &degree, &n, &digits);
  mmax = degree + 1;
  if (n >= 1) {
    if (!(h = NAG_ALLOC(n, double)) ||
        !(res = NAG_ALLOC(n, double)) ||
        !(wt = NAG_ALLOC(n, double)) ||
        !(x = NAG_ALLOC(n * mmax, double)) ||
        !(y = NAG_ALLOC(n, double)) || !(sx = NAG_ALLOC(mmax, Integer)))
    {
      printf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }
    tdx = mmax;
  }
  else {
    printf("Invalid n.\n");
    exit_status = 1;
    return exit_status;
  }

  /* Set tolerance */
  tol = pow(10.0, -(double) digits);
  m = degree;
  ip = degree + 1;
  if (!(b = NAG_ALLOC(ip, double)) ||
      !(cov = NAG_ALLOC((ip * ip + ip) / 2, double)) ||
      !(p = NAG_ALLOC(ip * (ip + 2), double)) ||
      !(q = NAG_ALLOC(n * (ip + 1), double)) ||
      !(com_ar = NAG_ALLOC(ip * ip + ip, double)) ||
      !(se = NAG_ALLOC(ip, double)))
  {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }
  tdq = ip + 1;

  for (i = 0; i < ip - 1; ++i)
    sx[i] = 1;

  for (i = 0; i < n; i++) {
    scanf("%lf%lf", &X(i, degree - 1), &y[i]);
    for (j = 0; j < degree; ++j)
      X(i, j) = pow(X(i, degree - 1), (double) (degree - j));
  }

  /* nag_regsn_mult_linear (g02dac), see above. */
  nag_regsn_mult_linear(mean, n, x, tdx, m, sx, ip, y,
                        wtptr, &rss, &df, b, se, cov, res, h, q,
                        tdq, &svd, &rank, p, tol, com_ar, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_regsn_mult_linear (g02dac).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  printf("Regression estimates  (mean = Nag_MeanInclude) \n\n");
  printf("Coefficient    Estimate         Standard error\n\n");
  for (j = 1; j < ip; j++)
    printf("a(%" NAG_IFMT ")%20.4e%20.4e\n", degree + 1 - j, b[j], se[j]);
  printf("a(0)%20.4e%20.4e\n", b[0], se[0]);
  printf("\n\n");

  /* Use mean = Nag_MeanZero */

  mean = Nag_MeanZero;

  m = degree + 1;
  for (i = 0; i < ip; ++i)
    sx[i] = 1;

  for (i = 0; i < n; i++)
    X(i, m - 1) = 1.0;

  /* nag_regsn_mult_linear (g02dac), see above. */
  nag_regsn_mult_linear(mean, n, x, tdx, m, sx, ip, y,
                        wtptr, &rss, &df, b, se, cov, res, h, q,
                        tdq, &svd, &rank, p, tol, com_ar, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_regsn_mult_linear (g02dac).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  printf("Regression estimates  (mean = Nag_MeanZero) \n\n");
  printf("Coefficient    Estimate         Standard error\n\n");
  for (j = 0; j < ip; j++)
    printf("a(%" NAG_IFMT ")%20.4e%20.4e\n", degree - j, b[j], se[j]);
  printf("\n\n");

END:
  NAG_FREE(h);
  NAG_FREE(res);
  NAG_FREE(wt);
  NAG_FREE(x);
  NAG_FREE(y);
  NAG_FREE(sx);
  NAG_FREE(b);
  NAG_FREE(cov);
  NAG_FREE(p);
  NAG_FREE(q);
  NAG_FREE(com_ar);
  NAG_FREE(se);

  return exit_status;
}