NAG Library Routine Document

c09fdf  (dim3_mxolap_multi_inv)

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 c09fcf. The data will be reconstructed to level $\left(\mathbf{nwl}-\mathbf{nwlinv}\right)$, where level $0$ is the original input dataset provided to c09fcf.

Constraint: $1\le \mathbf{nwlinv}\le \mathbf{nwl}$, where nwl is the value used in a preceding call to c09fcf.

2:     $\mathbf{lenc}$ – IntegerInput

On entry: the dimension of the array c as declared in the (sub)program from which c09fdf is called.

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:     $\mathbf{c}\left(\mathbf{lenc}\right)$ – Real (Kind=nag_wp) arrayInput

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 routine c09fcf.

Note that the coefficients in c may be extracted according to level and type into three-dimensional arrays using c09fyf, and inserted using c09fzf.

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 c09fcf, this must be the same as argument m used in a preceding call to c09fcf. For a partial reconstruction of $\mathbf{nwlinv}<\mathbf{nwl}$ levels, this must be equal to $\mathbf{dwtlvm}\left(\mathbf{nwlinv}+1\right)$, as returned from c09fcf

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 c09fcf, this must be the same as argument n used in a preceding call to c09fcf. For a partial reconstruction of $\mathbf{nwlinv}<\mathbf{nwl}$ levels, this must be equal to $\mathbf{dwtlvn}\left(\mathbf{nwlinv}+1\right)$, as returned from c09fcf.

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 c09fcf, this must be the same as argument fr used in a preceding call to c09fcf. For a partial reconstruction of $\mathbf{nwlinv}<\mathbf{nwl}$ levels, this must be equal to $\mathbf{dwtlvfr}\left(\mathbf{nwlinv}+1\right)$, as returned from c09fcf.

7:     $\mathbf{b}\left(\mathbf{ldb},\mathbf{sdb},\mathbf{fr}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: the $m$ by $n$ by $\mathit{fr}$ reconstructed array, $B$, with $B_{ijk}$ stored in $\mathbf{b}\left(i,j,k\right)$. The reconstruction is based on the input multi-level wavelet transform coefficients and the transform options supplied to the initialization routine c09acf.

8:     $\mathbf{ldb}$ – IntegerInput

On entry: the first dimension of the array b as declared in the (sub)program from which c09fdf is called.

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

9:     $\mathbf{sdb}$ – IntegerInput

On entry: the second dimension of the array b as declared in the (sub)program from which c09fdf is called.

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

10:   $\mathbf{icomm}\left(260\right)$ – Integer arrayCommunication Array

On entry: contains details of the discrete wavelet transform and the problem dimension as setup in the call to the initialization routine c09acf.

11:   $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6

Error Indicators and Warnings

$\mathbf{ifail}=1$

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

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 c09fcf.
Constraint: $\mathbf{nwlinv}\le \mathbf{nwl}$ as used in the call to c09fcf.

$\mathbf{ifail}=2$

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

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

$\mathbf{ifail}=3$

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 c09acf, lenc must be at least $n_{\mathrm{ct}}$, the value returned in nwct by the same call to c09acf.

$\mathbf{ifail}=4$

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.

$\mathbf{ifail}=6$

Either the communication array icomm has been corrupted or there has not been a prior call to the initialization routine c09acf.

The initialization routine was called with $\mathbf{wtrans}=\text{'S'}$.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example