naginterfaces.library.wav.dim3_​sngl_​fwd

naginterfaces.library.wav.dim3_sngl_fwd(a, comm)

dim3_sngl_fwd computes the three-dimensional discrete wavelet transform (DWT) at a single level. The initialization function dim3_init() must be called first to set up the DWT options.

For full information please refer to the NAG Library document for c09fa

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/c09/c09faf.html

Parameters

afloat, array-like, shape $(m,n,\text{fr})$

The $m\times n\times \text{fr}$ three-dimensional input data $A$, where $A_{ijk}$ is stored in $a[i-1,j-1,k-1]$.

commdict, communication object, modified in place

Communication structure.

This argument must have been initialized by a prior call to dim3_init().

Returns

cfloat, ndarray, shape $(:)$

The coefficients of the discrete wavelet transform. If you need to access or modify the approximation coefficients or any specific set of detail coefficients then the use of dim3_coeff_ext() or dim3_coeff_ins() is recommended. For completeness the following description provides details of precisely how the coefficients are stored in $c$ but this information should only be required in rare cases.

The $8$ sets of coefficients are stored in the following order: approximation coefficients (LLL) first, followed by $7$ sets of detail coefficients: LLH, LHL, LHH, HLL, HLH, HHL, HHH, where L indicates the low pass filter, and H the high pass filter being applied to, respectively, the columns of length $\text{m}$, the rows of length $\text{n}$ and then the frames of length $\text{fr}$.

Note that for computational efficiency reasons each set of coefficients is stored in the order $n_{cfr}\times n_{cm}\times n_{cn}$ (see output arguments $\text{nwcfr}$, $\text{nwct}$ and $\text{nwcn}$ in dim3_init()).

Raises

NagValueError

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n=⟨value⟩$, the value of $\text{n}$ on initialization (see dim3_init()).

(errno $1$)

On entry, $m=⟨value⟩$.

Constraint: $m=⟨value⟩$, the value of $\text{m}$ on initialization (see dim3_init()).

(errno $1$)

On entry, $\text{fr}=⟨value⟩$.

Constraint: $\text{fr}=⟨value⟩$, the value of $\text{fr}$ on initialization (see dim3_init()).

(errno $6$)

Either the communication array $comm$[‘icomm’] has been corrupted or there has not been a prior call to the initialization function dim3_init().

(errno $6$)

Either the communication array $comm$[‘icomm’] has been corrupted or $wtrans=\text{‘M'}$ was used in the prior call to the initialization function dim3_init().

Notes

dim3_sngl_fwd computes the three-dimensional DWT of some given three-dimensional input data, considered as a number of two-dimensional frames, at a single level. For a chosen wavelet filter pair, the output coefficients are obtained by applying convolution and downsampling by two to the input data, $A$, first over columns, next over rows and finally across frames. The three-dimensional approximation coefficients are produced by the low pass filter over columns, rows and frames. In addition there are $7$ sets of three-dimensional detail coefficients, each corresponding to a different order of low pass and high pass filters (see the C09 Introduction). All coefficients are packed into a single array. To reduce distortion effects at the ends of the data array, several end extension methods are commonly used. Those provided are: periodic or circular convolution end extension, half-point symmetric end extension, whole-point symmetric end extension and zero end extension. The total number, $n_{ct}$, of coefficients computed is returned by the initialization function dim3_init().

References

Daubechies, I, 1992, Ten Lectures on Wavelets, SIAM, Philadelphia