NAG Library Function Document

nag_imldwt_3d (c09fdc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{nwlinv}$ – IntegerInput

On entry: the number of levels to be used in the inverse multi-level transform. The number of levels must be less than or equal to $n_{\mathrm{fwd}}$, which has the value of argument nwl as used in the computation of the wavelet coefficients using nag_mldwt_3d (c09fcc). The data will be reconstructed to level $\left(\mathbf{nwl}-\mathbf{nwlinv}\right)$, where level $0$ is the original input dataset provided to nag_mldwt_3d (c09fcc).

Constraint: $1\le \mathbf{nwlinv}\le \mathbf{nwl}$, where nwl is the value used in a preceding call to nag_mldwt_3d (c09fcc).

2:    $\mathbf{lenc}$ – 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 nwlinv levels.

3:    $\mathbf{c}\left[\mathbf{lenc}\right]$ – const doubleInput

On entry: the coefficients of the multi-level discrete wavelet transform. This will normally be the result of some transformation on the coefficients computed by function nag_mldwt_3d (c09fcc).

Note that the coefficients in c may be extracted according to level and type into three-dimensional arrays using nag_wav_3d_coeff_ext (c09fyc), and inserted using nag_wav_3d_coeff_ins (c09fzc).

4:    $\mathbf{m}$ – IntegerInput

On entry: the number of elements, $m$, in the first dimension of the reconstructed array $B$. For a full reconstruction of nwl levels, where nwl is as supplied to nag_mldwt_3d (c09fcc), this must be the same as argument m used in a preceding call to nag_mldwt_3d (c09fcc). For a partial reconstruction of $\mathbf{nwlinv}<\mathbf{nwl}$ levels, this must be equal to $\mathbf{dwtlvm}\left[\mathbf{nwlinv}\right]$, as returned from nag_mldwt_3d (c09fcc)

5:    $\mathbf{n}$ – IntegerInput

On entry: the number of elements, $n$, in the second dimension of the reconstructed array $B$. For a full reconstruction of nwl, levels, where nwl is as supplied to nag_mldwt_3d (c09fcc), this must be the same as argument n used in a preceding call to nag_mldwt_3d (c09fcc). For a partial reconstruction of $\mathbf{nwlinv}<\mathbf{nwl}$ levels, this must be equal to $\mathbf{dwtlvn}\left[\mathbf{nwlinv}\right]$, as returned from nag_mldwt_3d (c09fcc).

6:    $\mathbf{fr}$ – IntegerInput

On entry: the number of elements, $\mathit{fr}$, in the third dimension of the reconstructed array $B$. For a full reconstruction of nwl levels, where nwl is as supplied to nag_mldwt_3d (c09fcc), this must be the same as argument fr used in a preceding call to nag_mldwt_3d (c09fcc). For a partial reconstruction of $\mathbf{nwlinv}<\mathbf{nwl}$ levels, this must be equal to $\mathbf{dwtlvfr}\left[\mathbf{nwlinv}\right]$, as returned from nag_mldwt_3d (c09fcc).

7:    $\mathbf{b}\left[\mathit{dim}\right]$ – doubleOutput

Note: the dimension, dim, of the array b must be at least $\mathbf{ldb}\times \mathbf{sdb}\times \mathbf{fr}$.

On exit: the $m$ by $n$ by $\mathit{fr}$ reconstructed array, $B$, with $B_{ijk}$ stored in $\mathbf{b}\left[\left(k-1\right)\times \mathbf{ldb}\times \mathbf{sdb}+\left(j-1\right)\times \mathbf{ldb}+i-1\right]$. The reconstruction is based on the input multi-level wavelet transform coefficients and the transform options supplied to the initialization function nag_wfilt_3d (c09acc).

8:    $\mathbf{ldb}$ – IntegerInput

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

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

9:    $\mathbf{sdb}$ – IntegerInput

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

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

10:  $\mathbf{icomm}\left[260\right]$ – const 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).

11:  $\mathbf{fail}$ – 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: $\mathbf{fr}\ge 〈\mathit{\text{value}}〉$, the number of coefficients in the third dimension at the required level of reconstruction.

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}\ge 〈\mathit{\text{value}}〉$, the number of coefficients in the first dimension at the required level of reconstruction.

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 〈\mathit{\text{value}}〉$, the number of coefficients in the second dimension at the required level of reconstruction.

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

NE_INT_2

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

On entry, $\mathbf{lenc}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lenc}\ge 〈\mathit{\text{value}}〉$, the number of wavelet coefficients required for a transform operating on nwlinv levels. If $\mathbf{nwlinv}=\mathbf{nwlmax}$, the maximum number of levels as returned by the initial call to nag_wfilt_3d (c09acc), lenc must be at least $n_{\mathrm{ct}}$, the value returned in nwct by the same call to nag_wfilt_3d (c09acc).

On entry, $\mathbf{nwlinv}=〈\mathit{\text{value}}〉$ and $\mathbf{nwl}=〈\mathit{\text{value}}〉$ where nwl is as used in the computation of the wavelet coefficients by a call to nag_mldwt_3d (c09fcc).
Constraint: $\mathbf{nwlinv}\le \mathbf{nwl}$ as used in the call to nag_mldwt_3d (c09fcc).

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

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