```/* nag_wav_2d_coeff_ins (c09ezc) Example Program.
*
* Copyright 2014 Numerical Algorithms Group.
*
* Mark 24, 2013.
*/
#include <stdio.h>
#include <math.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagc09.h>
#include <nagg05.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, 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_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");
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  : %4ld\n", m);
printf("         n  : %4ld\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.
*/
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");
fflush(stdout);

/* Set up call to nag_rand_normal (g05skc) 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);
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_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]);
fflush(stdout);

/* 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);
fflush(stdout);

/* 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;
}
```