```/* nag_wav_dim3_multi_fwd (c09fcc) Example Program.
*
* Copyright 2019 Numerical Algorithms Group.
*
* Mark 27.0, 2019.
*/
#include <stdio.h>
#include <math.h>
#include <nag.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 E(I,J,K) e[I-1 + (J-1)* m + (K-1)* m * n]
#define D(I,J,K) d[I-1 + (J-1)* ldd + (K-1)* ldd * sdd]

int main(void)
{

/* Scalars */
Integer exit_status = 0;
Integer lda, ldb, ldd, sda, sdb, sdd, lenc, i, j, k;
Integer m, n, fr, nwcfr, nwcm, nwcn, nwct, nwlmax, nwl, nwlinv, nf;
Integer want_coeffs, want_level;
double eps, esq, frob;
/* Arrays */
char mode[25], wavnam[25];
double *a = 0, *b = 0, *c = 0, *d = 0, *e = 0;
Integer *dwtlvfr = 0, *dwtlvm = 0, *dwtlvn = 0;
Integer icomm[260];
/* 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_dim3_multi_fwd (c09fcc) Example Program Results\n\n");
fflush(stdout);

scanf("%*[^\n] %" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\n]", &m, &n,
&fr);
lda = m;
ldb = m;
sda = n;
sdb = n;
scanf("%24s%24s%*[^\n]\n", wavnam, mode);

if (!(a = NAG_ALLOC((lda) * (sda) * (fr), double)) ||
!(b = NAG_ALLOC((ldb) * (sdb) * (fr), double)) ||
!(e = NAG_ALLOC((m) * (n) * (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
*/
modenum = (Nag_WaveletMode) nag_enum_name_to_value(mode);

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] ");
}

/* Print out the input data */
printf("Input Data :\n");
fflush(stdout);
for (k = 1; k <= fr; k++) {
/* nag_file_print_matrix_real_gen_comp (x04cbc).
* Prints out a matrix.
*/
nag_file_print_matrix_real_gen_comp(order, matrix, diag, m, n, &A(1, 1, k), lda,
"%8.4f", " ", 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);
}

/* 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;
}

lenc = nwct;
if (!(c = NAG_ALLOC((lenc), double)) ||
!(dwtlvm = NAG_ALLOC((nwlmax), Integer)) ||
!(dwtlvn = NAG_ALLOC((nwlmax), Integer)) ||
!(dwtlvfr = NAG_ALLOC((nwlmax), Integer)))
{
printf("Allocation failure\n");
exit_status = 4;
goto END;
}

nwl = nwlmax;

/* 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;
}

printf("Number of Levels : %4" NAG_IFMT "\n", nwl);
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("\n");
printf("Number 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("\n");
printf("Number 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");
fflush(stdout);

/* Print the first level HLL coefficients */
want_level = 1;
want_coeffs = 4;

/* Use the extraction routine c09fyc 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 (c09fyc).
* Extract coefficients into a 3D array D.
*/
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 (c09fyc).\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 "", want_level);
printf(", Coefficients %4" NAG_IFMT ":\n", want_coeffs);
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("%8.4f%s", D(i, j, k), j % 8 ? "" : "\n");
}
printf("\n");
}
}
fflush(stdout);

nwlinv = nwl;

/* nag_wav_dim3_mxolap_multi_inv (c09fdc).
* Three-dimensional inverse multi-level discrete wavelet transform
*/
nag_wav_dim3_mxolap_multi_inv(nwlinv, 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 = 10.0 * (double) (m) * (double) (n) * (double) (fr) *
nag_machine_precision;

for (k = 1; k <= fr; k++)
for (j = 1; j <= n; j++)
for (i = 1; i <= m; i++)
E(i, j, k) = B(i, j, k) - A(i, j, k);

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(E(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(e);
NAG_FREE(dwtlvfr);
NAG_FREE(dwtlvm);
NAG_FREE(dwtlvn);
return exit_status;
}
```