NAG Library Function Document

nag_mldwt_3d (c09fcc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     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:     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:     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:     a[$\mathit{dim}$] – 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:     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:     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:     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:     c[lenc] – 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:     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:   dwtlvm[nwl] – 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:   dwtlvn[nwl] – 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:   dwtlvfr[nwl] – 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:   icomm[$260$] – 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:   fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.

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.

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)