/* nag_wav_2d_coeff_ins (c09ezc) Example Program. * * Copyright 2013 Numerical Algorithms Group. * * Mark 24, 2013. */ #include #include #include #include #include #include #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, genid, denoised, cindex, ilev; 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_2d_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("%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", n); /* 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_gen_real_mat_print_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_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 randomnoise 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 = 3; 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 = 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_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 = 6; 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. */ mn = n * m; nag_rand_normal(mn, xmu, var, state, x, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_rand_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_gen_real_mat_print_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_gen_real_mat_print_comp (x04cbc).\n%s\n", fail.message); exit_status = 8; goto END; } printf("\n"); /* nag_wfilt_2d (c09abc). * Two-dimensional wavelet filter initialization. */ nag_wfilt_2d(wavnamenum, Nag_MultiLevel, modenum, m, n, &nwl, &nf, &nwct, &nwcn, icomm, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_wfilt_2d (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_mldwt_2d (c09ecc). * Two-dimensional multi-level discrete wavelet transform. */ nag_mldwt_2d(m, n, an, lda, lenc, c, nwl, dwtlvm, dwtlvn, icomm, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_mldwt_2d (c09ecc).\n%s\n", fail.message); exit_status = 11; goto END; } /* Reconstruct without thresholding of detail coefficients. */ /* nag_imldwt_2d (c09edc). * Two-dimensional inverse multi-level discrete wavelet transform. */ nag_imldwt_2d(nwl, lenc, c, m, n, b, ldb, icomm, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_imldwt_2d (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); /* 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_2d_coeff_ext (c09eyc). * Two-dimensional discrete wavelet transform coefficient extraction. */ nag_wav_2d_coeff_ext(ilev, cindex, lenc, c, d, ldd, icomm, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_wav_2d_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_2d_coeff_ins (c09ezc). * Two-dimensional discrete wavelet transform coefficient insertion. */ nag_wav_2d_coeff_ins(ilev, cindex, lenc, c, d, ldd, icomm, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_wav_2d_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 %4ld out of %4"NAG_IFMT "\n\n", denoised, nwct - dwtlvm[0]*dwtlvn[0]); /* Reconstruct original data following thresholding of detail coefficients */ /* nag_imldwt_2d (c09edc). * Two-dimensional inverse multi-level discrete wavelet transform. */ nag_imldwt_2d(nwl, lenc, c, m, n, b, ldb, icomm, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_imldwt_2d (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); /* Output the denoised reconstruction. */ nag_gen_real_mat_print_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_gen_real_mat_print_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; }