/* nag_wav_3d_coeff_ins (c09fzc) Example Program. * * Copyright 2013 Numerical Algorithms Group. * * Mark 24, 2013. */ #include #include #include #include #include #include #define A(I,J,K) a[(K-1)*lda*sda + (J-1)*lda + I-1] #define AN(I,J,K) an[(K-1)*lda*sda + (J-1)*lda + I-1] #define B(I,J,K) b[(K-1)*ldb*sdb + (J-1)*ldb + I-1] #define D(I,J,K) d[(K-1)*ldd*sdd + (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, fr, mnfr, nf; Integer nwcn, nwct, nwcfr; Integer nwl, subid, genid, denoised, cindex, ilev, sda, sdb, sdd, kk; 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, *dwtlvfr = 0, *state = 0; Integer icomm[260], 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_3d_coeff_ins (c09fzc) Example Program Results\n\n"); /* Skip heading in data file and read problem parameters. */ scanf("%*[^\n] %"NAG_IFMT "%"NAG_IFMT "%"NAG_IFMT "%*[^\n] ", &m, &n, &fr); scanf("%25s%25s%*[^\n] ", wavnam, mode); printf("MLDWT :: Wavelet : %s\n", wavnam); printf(" End mode : %s\n", mode); printf(" m : %4ld\n", m); printf(" n : %4ld\n", n); printf(" fr : %4ld\n\n", fr); /* 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; sda = n; sdb = n; if (!(a = NAG_ALLOC((sda)*(lda)*(fr), double)) || !(an = NAG_ALLOC((sda)*(lda)*(fr), double))|| !(b = NAG_ALLOC((sdb)*(ldb)*(fr), double))|| !(x = NAG_ALLOC((m*n*fr), 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 (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]"); } scanf("%*[^\n]"); } /* Output the original data. */ printf("Input data :\n"); for (k=1; k<=fr; k++) { nag_gen_real_mat_print_comp(order, matrix, diag, m, n, &A(1,1,k), lda, "%11.4e", " ", Nag_NoLabels, 0, Nag_NoLabels, 0, 80, 0, 0, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_gen_real_mat_print_comp (x04cbc).\n%s\n", fail.message); exit_status = 2; goto END; } printf("\n"); } /* Set up call to g05skf in order to create some random noise from * a normal distribution to add to the original data. * Initial call to RNG initialiser 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 = -1; goto END; } /* nag_rand_init_repeatable (g05kfc). * Query the size of state. */ lstate = 0; nag_rand_init_repeatable(genid, subid, seed, lseed, state, &lstate, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_rand_init_repeatable (g05kfc).\n%s\n", fail.message); exit_status = 3; goto END; } /* Reallocate STATE. */ NAG_FREE(state); if (!(state = NAG_ALLOC((lstate), Integer))) { printf("Allocation failure\n"); exit_status = 4; goto END; } /* nag_rand_init_repeatable (g05kfc). * Initialize the generator to a repeatable sequence. */ nag_rand_init_repeatable(genid, subid, seed, lseed, state, &lstate, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_rand_init_repeatable (g05kfc).\n%s\n", fail.message); exit_status = 5; goto END; } /* Set the distribution parameters for the random noise. */ xmu = 0.0; var = 0.1E-3; /* Generate the noise variates. */ /* nag_rand_normal (g05skc). * Generates a vector of pseudorandom numbers from a Normal distribution. */ mnfr = n * m * fr; nag_rand_normal(mnfr, xmu, var, state, x, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_rand_normal (g05skc).\n%s\n", fail.message); exit_status = 6; goto END; } /* Add the noise to the original input and save in AN */ kk = 0; for (k=1; k<=n; k++) { for (j=1; j<=n; j++) { for (i=1; i<=m; i++) { AN(i, j, k) = A(i, j, k) + x[kk]; kk = kk + 1; } } } /* Output the noisy data*/ printf("Input data plus noise :\n"); for (k=1; k<=fr; k++) { nag_gen_real_mat_print_comp(order, matrix, diag, m, n, &AN(1,1,k), lda, "%11.4e", " ", Nag_NoLabels, 0, Nag_NoLabels, 0, 80, 0, 0, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_gen_real_mat_print_comp (x04cbc).\n%s\n", fail.message); exit_status = 7; goto END; } printf("\n"); } /* nag_wfilt_3d (c09acc). * Three-dimensional wavelet filter initialization. */ nag_wfilt_3d(wavnamenum, Nag_MultiLevel, modenum, m, n, fr, &nwl, &nf, &nwct, &nwcn, &nwcfr, icomm, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_wfilt_3d (c09acc).\n%s\n", fail.message); exit_status = 8; 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)) || !(dwtlvfr = NAG_ALLOC((nwl), Integer))) { printf("Allocation failure\n"); exit_status = 9; goto END; } /* Perform a forwards multi-level transform on the noisy data. */ /* nag_mldwt_3d (c09fcc). * Two-dimensional multi-level discrete wavelet transform. */ nag_mldwt_3d(m, n, fr, an, lda, sda, lenc, c, nwl, dwtlvm, dwtlvn, dwtlvfr, icomm, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_mldwt_3d (c09fcc).\n%s\n", fail.message); exit_status = 10; goto END; } /* Reconstruct without thresholding of detail coefficients. */ /* nag_imldwt_3d (c09fdc). * Two-dimensional inverse multi-level discrete wavelet transform. */ nag_imldwt_3d(nwl, lenc, c, m, n, fr, b, ldb, sdb, icomm, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_imldwt_3d (c09fdc).\n%s\n", fail.message); exit_status = 11; goto END; } /* Calculate the Mean Square Error of the noisy reconstruction. */ mse = 0.0; for (k=1; k<=fr; k++) for (j=1; j<=n; j++) for (i=1; i<=m; i++) mse = mse + pow((A(i, j, k) - B(i, j, k)), 2); mse = mse/(double)(m * n * fr); printf("Without denoising Mean Square Error is %11.4e\n\n", mse); /* 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]; sdd = dwtlvn[nwl-1]; if (!(d = NAG_ALLOC((ldd)*(sdd)*(dwtlvfr[nwl-1]), double))) { printf("Allocation failure\n"); exit_status = 12; goto END; } /* Calculate the threshold based on VisuShrink denoising. */ thresh = sqrt(var) * sqrt(2. * log((double)(m * n * fr))); denoised = 0; /* For each level */ for (ilev=nwl; ilev>=1; ilev-=1) { /* Select detail coefficients */ for (cindex=1; cindex<=7; cindex++) { /* Extract coefficients into the 2D array d*/ /* nag_wav_3d_coeff_ext (c09fyc). * Three-dimensional discrete wavelet transform coefficient extraction. */ nag_wav_3d_coeff_ext(ilev, cindex, lenc, c, d, ldd, sdd, icomm, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_wav_3d_coeff_ext (c09fyc).\n%s\n", fail.message); exit_status = 13; goto END; } /* Perform the hard thresholding operation*/ for (k=1; k<=dwtlvfr[nwl - ilev]; k++) for (j=1; j<=dwtlvn[nwl - ilev]; j++) for (i=1; i<=dwtlvm[nwl - ilev]; i++) if (fabs(D(i, j, k))< thresh) { D(i, j, k) = 0.0; denoised = denoised + 1; } /* Insert the denoised coefficients back into c. */ /* nag_wav_3d_coeff_ins (c09fzc). * Three-dimensional discrete wavelet transform coefficient insertion. */ nag_wav_3d_coeff_ins(ilev, cindex, lenc, c, d, ldd, sdd, icomm, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_wav_3d_coeff_ins (c09fzc).\n%s\n", fail.message); exit_status = 14; goto END; } } } /* Output the number of coefficients that were set to zero*/ printf("Number of coefficients denoised is %4ld out of %4"NAG_IFMT "\n\n", denoised, nwct - dwtlvm[0]*dwtlvn[0]*dwtlvfr[0]); /* Reconstruct original data following thresholding of detail coefficients */ /* nag_imldwt_3d (c09fdc). * Three-dimensional inverse multi-level discrete wavelet transform. */ nag_imldwt_3d(nwl, lenc, c, m, n, fr, b, ldb, sdb, icomm, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_imldwt_3d (c09fdc).\n%s\n", fail.message); exit_status = 15; goto END; } /* Calculate the Mean Square Error of the denoised reconstruction. */ mse = 0.0; for (k=1; k<=n; k++) for (j=1; j<=n; j++) for (i=1; i<=m; i++) mse = mse + pow((A(i, j, k) - B(i, j, k)), 2); mse = mse/(double)(m * n * fr); printf("With denoising Mean Square Error is %11.4e \n\n", mse); /* Output the denoised reconstruction. */ printf("Reconstruction of denoised input :\n"); for (k=1; k<=fr; k++) { nag_gen_real_mat_print_comp(order, matrix, diag, m, n, &B(1,1,k), ldb, "%11.4e", " ", Nag_NoLabels, 0, Nag_NoLabels, 0, 80, 0, 0, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_gen_real_mat_print_comp (x04cbc).\n%s\n", fail.message); exit_status = 16; goto END; } if (k