NAG Library Function Document

nag_mldwt_3d (c09fcc)

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 with $A_{ijk}$ 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 that correspond to a transform with nwl levels.

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.

Let $q\left(\mathit{i}\right)$ denote the number of coefficients of each type at level $\mathit{i}$, for $\mathit{i}=1,2,\dots ,n_{\mathrm{fwd}}$, such that $q\left(i\right)=\mathbf{dwtlvm}\left[n_{\mathrm{fwd}}-i\right]\times \mathbf{dwtlvn}\left[n_{\mathrm{fwd}}-i\right]\times \mathbf{dwtlvfr}\left[n_{\mathrm{fwd}}-i\right]$. Then, letting $k_1=q\left(n_{\mathrm{fwd}}\right)$ and $k_{\mathit{j}+1}=k_{\mathit{j}}+q\left(n_{\mathrm{fwd}}-⌈\mathit{j}/7⌉+1\right)$, for $\mathit{j}=1,2,\dots ,7n_{\mathrm{fwd}}$, the coefficients are stored in c as follows:

$\mathbf{c}\left[\mathit{i}-1\right]$, for $\mathit{i}=1,2,\dots ,k_1$

Contains the level $n_{\mathrm{fwd}}$ approximation coefficients, $a_{n_{\mathrm{fwd}}}$. Note that for computational efficiency reasons these coefficients are stored as $\mathbf{dwtlvm}\left[0\right]\times \mathbf{dwtlvn}\left[0\right]\times \mathbf{dwtlvfr}\left[0\right]$ in c.

$\mathbf{c}\left[\mathit{i}-1\right]$, for $\mathit{i}=k_j+1,\dots ,k_{j+1}$

Contains the level $n_{\mathrm{fwd}}-⌈j/7⌉+1$ detail coefficients. These are:

• LLH coefficients if $j\mathrm{ mod }7=1$;
• LHL coefficients if $j\mathrm{ mod }7=2$;
• LHH coefficients if $j\mathrm{ mod }7=3$;
• HLL coefficients if $j\mathrm{ mod }7=4$;
• HLH coefficients if $j\mathrm{ mod }7=5$;
• HHL coefficients if $j\mathrm{ mod }7=6$;
• HHH coefficients if $j\mathrm{ mod }7=0$,

for $j=1,\dots ,7n_{\mathrm{fwd}}$. See Section 2.1 in the c09 Chapter Introduction for a description of how these coefficients are produced.

Note that for computational efficiency reasons these coefficients are stored as $\mathbf{dwtlvfr}\left[⌈j/7⌉-1\right]\times \mathbf{dwtlvm}\left[⌈j/7⌉-1\right]\times \mathbf{dwtlvn}\left[⌈j/7⌉-1\right]$ in c.

9:    $\mathbf{nwl}$ – IntegerInput

On entry: the number of levels, $n_{\mathrm{fwd}}$, in the multi-level resolution to be performed.

Constraint: $1\le \mathbf{nwl}\le l_{\max }$, where $l_{\max }$ is the value returned in nwlmax (the maximum number of levels) by the call to the initialization function nag_wfilt_3d (c09acc).

10:  $\mathbf{dwtlvm}\left[\mathbf{nwl}\right]$ – IntegerOutput

On exit: the number of coefficients in the first dimension for each coefficient type at each level. $\mathbf{dwtlvm}\left[\mathit{i}-1\right]$ contains the number of coefficients in the first dimension (for each coefficient type computed) at the ($n_{\mathrm{fwd}}-\mathit{i}+1$)th level of resolution, for $\mathit{i}=1,2,\dots ,n_{\mathrm{fwd}}$.

11:  $\mathbf{dwtlvn}\left[\mathbf{nwl}\right]$ – IntegerOutput

On exit: the number of coefficients in the second dimension for each coefficient type at each level. $\mathbf{dwtlvn}\left[\mathit{i}-1\right]$ contains the number of coefficients in the second dimension (for each coefficient type computed) at the ($n_{\mathrm{fwd}}-\mathit{i}+1$)th level of resolution, for $\mathit{i}=1,2,\dots ,n_{\mathrm{fwd}}$.

12:  $\mathbf{dwtlvfr}\left[\mathbf{nwl}\right]$ – IntegerOutput

On exit: the number of coefficients in the third dimension for each coefficient type at each level. $\mathbf{dwtlvfr}\left[\mathit{i}-1\right]$ contains the number of coefficients in the third dimension (for each coefficient type computed) at the ($n_{\mathrm{fwd}}-\mathit{i}+1$)th level of resolution, for $\mathit{i}=1,2,\dots ,n_{\mathrm{fwd}}$.

13:  $\mathbf{icomm}\left[260\right]$ – 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.

14:  $\mathbf{fail}$ – 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 $\mathbf{wtrans}=\mathrm{Nag\_SingleLevel}$.

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)).

On entry, $\mathbf{nwl}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nwl}\ge 1$.

NE_INT_2

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

On entry, $\mathbf{lenc}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lenc}\ge 〈\mathit{\text{value}}〉$, the total number of coefficents to be generated.

On entry, $\mathbf{nwl}=〈\mathit{\text{value}}〉$ and $\mathbf{nwlmax}=〈\mathit{\text{value}}〉$ in nag_wfilt_3d (c09acc).
Constraint: $\mathbf{nwl}\le \mathbf{nwlmax}$ in nag_wfilt_3d (c09acc).

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.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (c09fcce.c)

10.2

Program Data

Program Data (c09fcce.d)

10.3

Program Results

Program Results (c09fcce.r)