NAG Library Function Document

nag_imldwt_3d (c09fdc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     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:     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:     c[lenc] – 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:     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:     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:     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:     b[$\mathit{dim}$] – 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:     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:     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:   icomm[$260$] – 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:   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: $\mathbf{fr}\ge ⟨\mathit{\text{value}}⟩$, 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), then 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.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example