NAG Library Function Document

nag_dwt_3d (c09fac)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{m}$ – IntegerInput

On entry: the number of rows of each two-dimensional frame.

Constraint: this must be the same as the value m passed to the initialization function nag_wfilt_3d (c09acc).

2:    $\mathbf{n}$ – IntegerInput

On entry: the number of columns of each two-dimensional frame.

Constraint: this must be the same as the value n passed to the initialization function nag_wfilt_3d (c09acc).

3:    $\mathbf{fr}$ – IntegerInput

On entry: the number of two-dimensional frames.

Constraint: this must be the same as the value fr passed to the initialization function nag_wfilt_3d (c09acc).

4:    $\mathbf{a}\left[\mathit{dim}\right]$ – const doubleInput

Note: the dimension, dim, of the array a must be at least $\mathbf{lda}\times \mathbf{sda}\times \mathbf{fr}$.

On entry: the $m$ by $n$ by $\mathit{fr}$ three-dimensional input data $A$, where $A_{ijk}$ is stored in $\mathbf{a}\left[\left(k-1\right)\times \mathbf{lda}\times \mathbf{sda}+\left(j-1\right)\times \mathbf{lda}+i-1\right]$.

5:    $\mathbf{lda}$ – IntegerInput

On entry: the stride separating row elements of each of the sets of frame coefficients in the three-dimensional data stored in a.

Constraint: $\mathbf{lda}\ge \mathbf{m}$.

6:    $\mathbf{sda}$ – IntegerInput

On entry: the stride separating corresponding coefficients of consecutive frames in the three-dimensional data stored in a.

Constraint: $\mathbf{sda}\ge \mathbf{n}$.

7:    $\mathbf{lenc}$ – IntegerInput

On entry: the dimension of the array c.

Constraint: $\mathbf{lenc}\ge n_{\mathrm{ct}}$, where $n_{\mathrm{ct}}$ is the total number of wavelet coefficients, as returned by nag_wfilt_3d (c09acc).

8:    $\mathbf{c}\left[\mathbf{lenc}\right]$ – doubleOutput

On exit: 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 nag_wav_3d_coeff_ext (c09fyc) or nag_wav_3d_coeff_ins (c09fzc) 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 m, the rows of length n and then the frames of length fr. Note that for computational efficiency reasons each set of coefficients is stored in the order $n_{\mathrm{cfr}}\times n_{\mathrm{cm}}\times n_{\mathrm{cn}}$ (see output arguments nwcfr, nwct and nwcn in nag_wfilt_3d (c09acc)). See Section 10 for details of how to access each set of coefficients in order to perform extraction from c following a call to this function, or insertion into c before a call to the three-dimensional inverse function nag_idwt_3d (c09fbc).

9:    $\mathbf{icomm}\left[260\right]$ – IntegerCommunication Array

On entry: contains details of the discrete wavelet transform and the problem dimension as setup in the call to the initialization function nag_wfilt_3d (c09acc).

On exit: contains additional information on the computed transform.

10:  $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INITIALIZATION

Either the communication array icomm has been corrupted or there has not been a prior call to the initialization function nag_wfilt_3d (c09acc).

The initialization function was called with $\mathbf{wtrans}=\mathrm{Nag\_MultiLevel}$.

NE_INT

On entry, $\mathbf{fr}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{fr}=〈\mathit{\text{value}}〉$, the value of fr on initialization (see nag_wfilt_3d (c09acc)).

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}=〈\mathit{\text{value}}〉$, the value of m on initialization (see nag_wfilt_3d (c09acc)).

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}=〈\mathit{\text{value}}〉$, the value of n on initialization (see nag_wfilt_3d (c09acc)).

NE_INT_2

On entry, $\mathbf{lda}=〈\mathit{\text{value}}〉$ and $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lda}\ge \mathbf{m}$.

On entry, $\mathbf{lenc}=〈\mathit{\text{value}}〉$ and $n_{\mathrm{ct}}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lenc}\ge n_{\mathrm{ct}}$, where $n_{\mathrm{ct}}$ is the number of DWT coefficients returned by nag_wfilt_3d (c09acc) in argument nwct.

On entry, $\mathbf{sda}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{sda}\ge \mathbf{n}$.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

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Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (c09face.c)

10.2

Program Data

Program Data (c09face.d)

10.3

Program Results

Program Results (c09face.r)