/* nag_wav_dim2_coeff_ins (c09ezc) Example Program.
 *
 * Copyright 2022 Numerical Algorithms Group.
 *
 * Mark 28.3, 2022.
 */
#include <math.h>
#include <nag.h>
#include <stdio.h>

#define A(I, J) a[(J - 1) * lda + I - 1]
#define AN(I, J) an[(J - 1) * lda + I - 1]
#define B(I, J) b[(J - 1) * ldb + I - 1]
#define D(I, J) d[(J - 1) * ldd + I - 1]

int main(void) {
  /* Scalars */
  Integer exit_status = 0;
  Integer lstate = 1, lseed = 1;
  Integer i, j, k, lda, ldb, ldd, lenc, m, n, mn, nf, nwcn, nwct, nwl;
  Integer subid, denoised, cindex, ilev;
  Nag_BaseRNG genid;
  double mse, thresh, var, xmu;
  /* Arrays */
  char mode[25], wavnam[25];
  double *a = 0, *an = 0, *b = 0, *c = 0, *d = 0, *x = 0;
  Integer *dwtlvm = 0, *dwtlvn = 0, *state = 0;
  Integer icomm[180], seed[1];
  /* 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_dim2_coeff_ins (c09ezc) Example Program Results\n\n");
  /* Skip heading in data file and read problem parameters. */
  scanf("%*[^\n] %" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &m, &n);
  scanf("%24s%24s%*[^\n] ", wavnam, mode);

  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", n);
  fflush(stdout);

  /* Allocate arrays to hold the original data, A, original data plus noise,
   * AN, reconstruction using denoised coefficients, B, and randomly generated
   * noise, X.
   */
  lda = m;
  ldb = m;
  if (!(a = NAG_ALLOC((lda) * (n), double)) ||
      !(an = NAG_ALLOC((lda) * (n), double)) ||
      !(b = NAG_ALLOC((ldb) * (n), double)) ||
      !(x = NAG_ALLOC((m * n), double))) {
    printf("Allocation failure\n");
    exit_status = 1;
    goto END;
  }

  /* 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 in the original data. */
  for (i = 1; i <= m; i++)
    for (j = 1; j <= n; j++)
      scanf("%lf", &A(i, j));

  /* Output the original data. */
  nag_file_print_matrix_real_gen_comp(order, matrix, diag, m, n, a, lda,
                                      "%11.4e", "Input data :", 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");
  fflush(stdout);

  /* Set up call to nag_rand_dist_normal (g05skc) in order to create some
   * randomnoise from a normal distribution to add to the original data.
   * Initial call to RNG initializer to get size of STATE array.
   */
  seed[0] = 642521;
  genid = Nag_MersenneTwister;
  subid = 0;
  if (!(state = NAG_ALLOC((lstate), Integer))) {
    printf("Allocation failure\n");
    exit_status = 3;
    goto END;
  }

  /* nag_rand_init_repeat (g05kfc).
   * Query the size of state.
   */
  lstate = 0;
  nag_rand_init_repeat(genid, subid, seed, lseed, state, &lstate, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_rand_init_repeat (g05kfc).\n%s\n", fail.message);
    exit_status = 4;
    goto END;
  }

  /* Reallocate STATE */
  NAG_FREE(state);
  if (!(state = NAG_ALLOC((lstate), Integer))) {
    printf("Allocation failure\n");
    exit_status = 5;
    goto END;
  }

  /* nag_rand_init_repeat (g05kfc).
   * Initialize the generator to a repeatable sequence.
   */
  nag_rand_init_repeat(genid, subid, seed, lseed, state, &lstate, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_rand_init_repeat (g05kfc).\n%s\n", fail.message);
    exit_status = 6;
    goto END;
  }

  /* Set the distribution parameters for the random noise. */
  xmu = 0.0;
  var = 0.1E-3;

  /* Generate the noise variates */

  /* nag_rand_dist_normal (g05skc).
   * Generates a vector of pseudorandom numbers from a Normal distribution.
   */
  mn = n * m;
  nag_rand_dist_normal(mn, xmu, var, state, x, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_rand_dist_normal (g05skc).\n%s\n", fail.message);
    exit_status = 7;
    goto END;
  }

  /* Add the noise to the original input and save in AN */
  k = 0;
  for (j = 1; j <= n; j++) {
    for (i = 1; i <= m; i++) {
      AN(i, j) = A(i, j) + x[k];
      k = k + 1;
    }
  }

  /* Output the noisy data */
  nag_file_print_matrix_real_gen_comp(
      order, matrix, diag, m, n, an, lda, "%11.4e",
      "Original data plus noise :", 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 = 8;
    goto END;
  }
  printf("\n");

  /* nag_wav_dim2_init (c09abc).
   * Two-dimensional wavelet filter initialization.
   */
  nag_wav_dim2_init(wavnamenum, Nag_MultiLevel, modenum, m, n, &nwl, &nf, &nwct,
                    &nwcn, icomm, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_wav_dim2_init (c09abc).\n%s\n", fail.message);
    exit_status = 9;
    goto END;
  }

  /* Allocate arrays to hold the coefficients, c, and the dimensions
   * of the coefficients at each level, dwtlvm, dwtlvn.
   */
  lenc = nwct;
  if (!(c = NAG_ALLOC((lenc), double)) ||
      !(dwtlvm = NAG_ALLOC((nwl), Integer)) ||
      !(dwtlvn = NAG_ALLOC((nwl), Integer))) {
    printf("Allocation failure\n");
    exit_status = 10;
    goto END;
  }

  /* Perform a forwards multi-level transform on the noisy data. */

  /* nag_wav_dim2_multi_fwd (c09ecc).
   * Two-dimensional multi-level discrete wavelet transform.
   */
  nag_wav_dim2_multi_fwd(m, n, an, lda, lenc, c, nwl, dwtlvm, dwtlvn, icomm,
                         &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_wav_dim2_multi_fwd (c09ecc).\n%s\n", fail.message);
    exit_status = 11;
    goto END;
  }

  /* Reconstruct without thresholding of detail coefficients. */

  /* nag_wav_dim2_multi_inv (c09edc).
   * Two-dimensional inverse multi-level discrete wavelet transform.
   */
  nag_wav_dim2_multi_inv(nwl, lenc, c, m, n, b, ldb, icomm, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_wav_dim2_multi_inv (c09edc).\n%s\n", fail.message);
    exit_status = 12;
    goto END;
  }

  /* Calculate the Mean Square Error of the noisy reconstruction. */
  mse = 0.0;
  for (j = 1; j <= n; j++)
    for (i = 1; i <= m; i++)
      mse = mse + pow((A(i, j) - B(i, j)), 2);
  mse = mse / (double)(m * n);
  printf("Without denoising Mean Square Error is %11.4e\n\n", mse);
  fflush(stdout);

  /* Now perform the denoising by extracting each of the detail
   * coefficients at each level and applying hard thresholding
   * Allocate a 2D array to hold the detail coefficients
   */
  ldd = dwtlvm[nwl - 1];
  if (!(d = NAG_ALLOC((ldd) * (dwtlvn[nwl - 1]), double))) {
    printf("Allocation failure\n");
    exit_status = 13;
    goto END;
  }

  /* Calculate the threshold based on VisuShrink denoising. */
  thresh = sqrt(var) * sqrt(2. * log((double)(m * n)));
  denoised = 0;
  /* For each level */
  for (ilev = nwl; ilev >= 1; ilev -= 1) {
    /* Select detail coefficients */
    for (cindex = 1; cindex <= 3; cindex++) {
      /* Extract coefficients into the 2D array d */

      /* nag_wav_dim2_coeff_ext (c09eyc).
       * Two-dimensional discrete wavelet transform coefficient extraction.
       */
      nag_wav_dim2_coeff_ext(ilev, cindex, lenc, c, d, ldd, icomm, &fail);
      if (fail.code != NE_NOERROR) {
        printf("Error from nag_wav_dim2_coeff_ext (c09eyc).\n%s\n",
               fail.message);
        exit_status = 14;
        goto END;
      }

      /* Perform the hard thresholding operation */
      for (j = 1; j <= dwtlvn[nwl - ilev]; j++)
        for (i = 1; i <= dwtlvm[nwl - ilev]; i++)
          if (fabs(D(i, j)) < thresh) {
            D(i, j) = 0.0;
            denoised = denoised + 1;
          }

      /* Insert the denoised coefficients back into c. */

      /* nag_wav_dim2_coeff_ins (c09ezc).
       * Two-dimensional discrete wavelet transform coefficient insertion.
       */
      nag_wav_dim2_coeff_ins(ilev, cindex, lenc, c, d, ldd, icomm, &fail);
      if (fail.code != NE_NOERROR) {
        printf("Error from nag_wav_dim2_coeff_ins (c09ezc).\n%s\n",
               fail.message);
        exit_status = 15;
        goto END;
      }
    }
  }

  /* Output the number of coefficients that were set to zero */
  printf("Number of coefficients denoised is %4" NAG_IFMT " out of %4" NAG_IFMT
         "\n\n",
         denoised, nwct - dwtlvm[0] * dwtlvn[0]);
  fflush(stdout);

  /* Reconstruct original data following thresholding of detail coefficients */

  /* nag_wav_dim2_multi_inv (c09edc).
   * Two-dimensional inverse multi-level discrete wavelet transform.
   */
  nag_wav_dim2_multi_inv(nwl, lenc, c, m, n, b, ldb, icomm, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_wav_dim2_multi_inv (c09edc).\n%s\n", fail.message);
    exit_status = 16;
    goto END;
  }

  /* Calculate the Mean Square Error of the denoised reconstruction. */
  mse = 0.0;
  for (j = 1; j <= n; j++)
    for (i = 1; i <= m; i++)
      mse = mse + pow((A(i, j) - B(i, j)), 2);
  mse = mse / (double)(m * n);
  printf("With denoising Mean Square Error is %11.4e \n\n", mse);
  fflush(stdout);

  /* Output the denoised reconstruction. */
  nag_file_print_matrix_real_gen_comp(
      order, matrix, diag, m, n, b, ldb, "%11.4e",
      "Reconstruction of denoised input :", 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 = 17;
    goto END;
  }

END:
  NAG_FREE(a);
  NAG_FREE(an);
  NAG_FREE(b);
  NAG_FREE(c);
  NAG_FREE(d);
  NAG_FREE(x);
  NAG_FREE(dwtlvm);
  NAG_FREE(dwtlvn);
  NAG_FREE(state);
  return exit_status;
}