/* nag_mv_procustes (g03bcc) Example Program.
 *
 * Copyright 2017 Numerical Algorithms Group.
 *
 * Mark 26.2, 2017.
 *
 */

#include <nag.h>
#include <stdio.h>
#include <nag_stdlib.h>
#include <nagg03.h>

#define R(I, J)    r[(I) *tdr + J]
#define X(I, J)    x[(I) *tdx + J]
#define Y(I, J)    y[(I) *tdy + J]
#define YHAT(I, J) yhat[(I) *tdy + J]
int main(void)
{
  Integer exit_status = 0, i, j, m, n, tdr, tdx, tdy;
  char nag_enum_arg[40];
  double alpha, *r = 0, *res = 0, rss, *x = 0, *y = 0, *yhat = 0;
  Nag_RotationScale scale;
  Nag_TransNorm stand;
  NagError fail;

  INIT_FAIL(fail);

  printf("nag_mv_procustes (g03bcc) Example Program Results\n\n");

  /* Skip heading in data file */
  scanf("%*[^\n]");
  scanf("%" NAG_IFMT "", &n);
  scanf("%" NAG_IFMT "", &m);
  scanf("%39s", nag_enum_arg);
  /* nag_enum_name_to_value (x04nac).
   * Converts NAG enum member name to value
   */
  stand = (Nag_TransNorm) nag_enum_name_to_value(nag_enum_arg);
  scanf("%39s", nag_enum_arg);
  scale = (Nag_RotationScale) nag_enum_name_to_value(nag_enum_arg);
  if (m >= 1 && n >= m) {
    if (!(r = NAG_ALLOC(m * m, double)) ||
        !(res = NAG_ALLOC(n, double)) ||
        !(x = NAG_ALLOC(n * m, double)) ||
        !(y = NAG_ALLOC(n * m, double)) || !(yhat = NAG_ALLOC(n * m, double)))
    {
      printf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }
    tdr = m;
    tdx = m;
    tdy = m;
  }
  else {
    printf("Invalid m or n.\n");
    exit_status = 1;
    return exit_status;
  }
  for (i = 0; i < n; ++i) {
    for (j = 0; j < m; ++j)
      scanf("%lf", &X(i, j));
  }
  for (i = 0; i < n; ++i) {
    for (j = 0; j < m; ++j)
      scanf("%lf", &Y(i, j));
  }

  /* nag_mv_procustes (g03bcc).
   * Procrustes rotations
   */
  nag_mv_procustes(stand, scale, n, m, x, tdx, y, tdy,
                   yhat, r, tdr, &alpha, &rss, res, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_mv_procustes (g03bcc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  printf("\n          Rotation Matrix\n\n");
  for (i = 0; i < m; ++i) {
    for (j = 0; j < m; ++j)
      printf("  %7.3f  ", R(i, j));
    printf("\n");
  }
  if (scale == Nag_LsqScale) {
    printf("\n%s%10.3f\n", " Scale factor = ", alpha);
  }
  printf("\n         Target Matrix \n\n");
  for (i = 0; i < n; ++i) {
    for (j = 0; j < m; ++j)
      printf("  %7.3f  ", Y(i, j));
    printf("\n");
  }
  printf("\n         Fitted Matrix\n\n");
  for (i = 0; i < n; ++i) {
    for (j = 0; j < m; ++j)
      printf("  %7.3f  ", YHAT(i, j));
    printf("\n");
  }
  printf("\n%s%10.3f\n", "RSS = ", rss);
END:
  NAG_FREE(r);
  NAG_FREE(res);
  NAG_FREE(x);
  NAG_FREE(y);
  NAG_FREE(yhat);
  return exit_status;
}