/* nag_wav_dim3_init (c09acc) Example Program.
 *
 * Copyright 2022 Numerical Algorithms Group.
 *
 * Mark 28.7, 2022.
 */
#include <math.h>
#include <nag.h>
#include <stdio.h>

#define A(I, J, K) a[I - 1 + (J - 1) * lda + (K - 1) * lda * sda]
#define B(I, J, K) b[I - 1 + (J - 1) * ldb + (K - 1) * ldb * sdb]
#define D(I, J, K) d[I - 1 + (J - 1) * ldd + (K - 1) * ldd * sdd]

int main(void) {
  /* Scalars */
  Integer exit_status = 0;
  Integer i, j, k, lda, ldb, ldd, lenc, nwlmax, m, n, fr;
  Integer nwcfr, nwcm, nwcn, nwct, nwl, sda, sdb, sdd, nf;
  Integer want_coeffs, want_level;
  double frob, esq, eps;
  /* Arrays */
  char mode[25], wavnam[25];
  double *a = 0, *b = 0, *c = 0, *d = 0;
  Integer *dwtlvfr = 0, *dwtlvm = 0, *dwtlvn = 0;
  Integer icomm[260];
  /* Nag Types */
  Nag_Wavelet wavnamenum;
  Nag_WaveletMode modenum;
  Nag_MatrixType matrix = Nag_GeneralMatrix;
  Nag_OrderType order = Nag_ColMajor;
  Nag_DiagType diag = Nag_NonUnitDiag;
  NagError fail;

  INIT_FAIL(fail);

  printf("nag_wav_dim3_init (c09acc) Example Program Results\n\n");
  fflush(stdout);

  /* Skip heading in data file and read problem parameters */
  scanf("%*[^\n] %" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\n]", &m, &n, &fr);
  lda = m;
  sda = n;
  ldb = m;
  sdb = n;
  scanf("%24s%24s%*[^\n]\n", wavnam, mode);

  if (!(a = NAG_ALLOC((lda) * (sda) * (fr), double)) ||
      !(b = NAG_ALLOC((ldb) * (sdb) * (fr), double))) {
    printf("Allocation failure\n");
    exit_status = 1;
    goto END;
  }

  printf("Parameters read from file :: \n");
  printf(" MLDWT :: Wavelet  : %s\n", wavnam);
  printf("          End mode : %s\n", mode);
  printf("          m  : %4" NAG_IFMT "\n", m);
  printf("          n  : %4" NAG_IFMT "\n", n);
  printf("          fr : %4" NAG_IFMT "\n\n", fr);

  /* nag_enum_name_to_value (x04nac).
   * Converts NAG enum member name to value
   */
  wavnamenum = (Nag_Wavelet)nag_enum_name_to_value(wavnam);
  modenum = (Nag_WaveletMode)nag_enum_name_to_value(mode);

  /* Read data array */
  for (k = 1; k <= fr; k++) {
    for (i = 1; i <= m; i++) {
      for (j = 1; j <= n; j++)
        scanf("%lf", &A(i, j, k));
    }
    scanf("%*[^\n] ");
  }

  /* Print out the input data */
  printf("Input Data :\n\n");
  for (k = 1; k <= fr; k++) {
    /* nag_file_print_matrix_real_gen_comp (x04cbc).
     * Prints out a matrix.
     */
    fflush(stdout);
    nag_file_print_matrix_real_gen_comp(order, matrix, diag, m, n, &A(1, 1, k),
                                        lda, "%6.2f", " ", Nag_NoLabels, 0,
                                        Nag_NoLabels, 0, 80, 0, 0, &fail);
    if (fail.code != NE_NOERROR) {
      printf("Error from nag_file_print_matrix_real_gen_comp (x04cbc).\n%s\n",
             fail.message);
      exit_status = 2;
      goto END;
    }
    printf("\n");
  }

  /*
   * nag_wav_dim3_init (c09acc).
   * Three-dimensional wavelet filter initialization
   */
  nag_wav_dim3_init(wavnamenum, Nag_MultiLevel, modenum, m, n, fr, &nwlmax, &nf,
                    &nwct, &nwcn, &nwcfr, icomm, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_wav_dim3_init (c09acc).\n%s\n", fail.message);
    exit_status = 3;
    goto END;
  }

  /* Transform one less than the max possible number of levels. */
  nwl = nwlmax - 1;
  lenc = nwct;
  if (!(c = NAG_ALLOC((lenc), double)) ||
      !(dwtlvm = NAG_ALLOC((nwl), Integer)) ||
      !(dwtlvn = NAG_ALLOC((nwl), Integer)) ||
      !(dwtlvfr = NAG_ALLOC((nwl), Integer))) {
    printf("Allocation failure\n");
    exit_status = 4;
    goto END;
  }

  /* nag_wav_dim3_multi_fwd (c09fcc).
   * Three-dimensional multi-level discrete wavelet transform
   */
  nag_wav_dim3_multi_fwd(m, n, fr, a, lda, sda, lenc, c, nwl, dwtlvm, dwtlvn,
                         dwtlvfr, icomm, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_wav_dim3_multi_fwd (c09fcc).\n%s\n", fail.message);
    exit_status = 5;
    goto END;
  }

  /* nag_wav_dim3_init (c09acc) returns nwct based on max levels, so recalculate
   * for the number of levels required, nwl.
   */
  nwct = dwtlvm[0] * dwtlvn[0] * dwtlvfr[0];
  for (i = 0; i < nwl; i++)
    nwct += 7 * dwtlvm[i] * dwtlvn[i] * dwtlvfr[i];

  printf("Number of Levels :         %4" NAG_IFMT "\n", nwl);
  printf("Length of wavelet filter : %4" NAG_IFMT "\n", nf);
  printf("Total number of wavelet coefficients : %4" NAG_IFMT "\n", nwct);
  printf("Number of coefficients in 1st dimension for each level:\n");
  for (i = 0; i < nwl; i++) {
    printf("%4" NAG_IFMT "%s", dwtlvm[i], i + 1 % 8 ? "" : "\n");
  }
  printf("\nNumber of coefficients in 2nd dimension for each level:\n");
  for (i = 0; i < nwl; i++) {
    printf("%4" NAG_IFMT "%s", dwtlvn[i], i + 1 % 8 ? "" : "\n");
  }
  printf("\nNumber of coefficients in 3rd dimension for each level:\n");
  for (i = 0; i < nwl; i++) {
    printf("%4" NAG_IFMT "%s", dwtlvfr[i], i + 1 % 8 ? "" : "\n");
  }
  printf("\n\n");

  /* Select the deepest level. */
  want_level = nwl;
  /* Select the approximation coefficients. */
  want_coeffs = 0;

  /* Use the extraction routine c09afc to retrieve the required
   * coefficients.
   */
  nwcm = dwtlvm[nwl - want_level];
  nwcn = dwtlvn[nwl - want_level];
  nwcfr = dwtlvfr[nwl - want_level];
  ldd = nwcm;
  sdd = nwcn;
  if (!(d = NAG_ALLOC((ldd) * (sdd) * (nwcfr), double))) {
    printf("Allocation failure\n");
    exit_status = 6;
    goto END;
  }

  /* nag_wav_dim3_coeff_ext (c09fcc).
   * Extract the desired coefficients.
   */
  nag_wav_dim3_coeff_ext(want_level, want_coeffs, lenc, c, d, ldd, sdd, icomm,
                         &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_wav_dim3_coeff_ext (c09afc).\n%s\n", fail.message);
    exit_status = 7;
    goto END;
  }

  /* Print the details of the level */
  printf("-----------------------------------------------------\n");
  printf("Level : %4" NAG_IFMT "", want_level);
  printf("; output is %4" NAG_IFMT "", nwcm);
  printf(" by %4" NAG_IFMT "", nwcn);
  printf(" by %4" NAG_IFMT "\n", nwcfr);
  printf("-----------------------------------------------------\n\n");

  /* Print out the selected set of coefficients */
  switch (want_coeffs) {
  case 0:
    printf("Approximation coefficients (LLL)\n");
    break;
  case 1:
    printf("Detail coefficients (LLH)\n");
    break;
  case 2:
    printf("Detail coefficients (LHL)\n");
    break;
  case 3:
    printf("Detail coefficients (LHH)\n");
    break;
  case 4:
    printf("Detail coefficients (HLL)\n");
    break;
  case 5:
    printf("Detail coefficients (HLH)\n");
    break;
  case 6:
    printf("Detail coefficients (HHL)\n");
    break;
  case 7:
    printf("Detail coefficients (HHH)\n");
    break;
  }

  printf("Level %4" NAG_IFMT ":\n", want_level);
  for (k = 1; k <= nwcfr; k++) {
    printf(" Frame %4" NAG_IFMT " :\n", k);
    for (i = 1; i <= nwcm; i++) {
      for (j = 1; j <= nwcn; j++) {
        printf("%9.3f%s", D(i, j, k), j % 8 ? "" : "\n");
      }
      printf("\n");
    }
  }

  /* nag_wav_dim3_mxolap_multi_inv (c09fdc).
   * Three-dimensional inverse multi-level discrete wavelet transform
   */
  nag_wav_dim3_mxolap_multi_inv(nwl, lenc, c, m, n, fr, b, ldb, sdb, icomm,
                                &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_wav_dim3_mxolap_multi_inv (c09fdc).\n%s\n",
           fail.message);
    exit_status = 8;
    goto END;
  }

  /* Check reconstruction matches original */
  eps = 40.0 * (double)(m + n + fr) * nag_machine_precision;

  frob = 0.0;
  for (k = 1; k <= fr; k++) {
    esq = 0.0;
    for (j = 1; j <= n; j++) {
      for (i = 1; i <= m; i++)
        esq = esq + pow(B(i, j, k) - A(i, j, k), 2);
    }
    frob = MAX(frob, sqrt(esq));
  }

  if (frob > eps) {
    printf("\nFail: Frobenius norm of B-A, where A is the original \n"
           "data and B is the reconstrucion, is too large.\n");
  } else {
    printf("\nSuccess: the reconstruction matches the original.\n");
  }

END:
  NAG_FREE(a);
  NAG_FREE(b);
  NAG_FREE(c);
  NAG_FREE(d);
  NAG_FREE(dwtlvfr);
  NAG_FREE(dwtlvm);
  NAG_FREE(dwtlvn);
  return exit_status;
}