NAG Library Routine Document

C09CDF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     NWL – INTEGERInput

On entry: the number, $n_l$, of levels to be used in the inverse multi-level transform. The number of levels must less than or equal to the number used in the computation of the wavelet coefficients.

Constraint: $1\le \mathbf{NWL}\le n_{\mathrm{fwd}}$, where $n_{\mathrm{fwd}}$ is the value used in a preceding call to C09CCF.

2:     LENC – INTEGERInput

On entry: the dimension of the array C as declared in the (sub)program from which C09CDF is called.

Constraint: $\mathbf{LENC}\ge n_c$, where $n_c$ is the total number of coefficients that correspond to a transform with $n_{\mathrm{fwd}}$ levels and is unchanged from the preceding call to C09CCF.

3:     C(LENC) – REAL (KIND=nag_wp) arrayInput

On entry: the coefficients of a multi-level wavelet transform of the dataset.

Let $q\left(\mathit{i}\right)$ be the number of coefficients (of each type) at level $\mathit{i}$, for $\mathit{i}=n_{\mathrm{fwd}},n_{\mathrm{fwd}}-1,\dots ,1$. Then, setting $k_1=q\left(n_{\mathrm{fwd}}\right)$ and $k_{\mathit{j}+1}=k_{\mathit{j}}+q\left(n_{\mathrm{fwd}}-\mathit{j}+1\right)$, for $\mathit{j}=1,2,\dots ,n_{\mathrm{fwd}}$, the coefficients are stored in C as follows:

$\mathbf{C}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,k_1$

Contains the level $n_{\mathrm{fwd}}$ approximation coefficients, $a_{n_{\mathrm{fwd}}}$.

$\mathbf{C}\left(\mathit{i}\right)$, for $\mathit{i}=k_1+1,\dots ,k_2$

Contains the level $n_{\mathrm{fwd}}$ detail coefficients $d_{n_{\mathrm{fwd}}}$.

$\mathbf{C}\left(\mathit{i}\right)$, for $\mathit{i}=k_j+1,\dots ,k_{j+1}$

Contains the level $n_{\mathrm{fwd}}-\mathit{j}+1$ detail coefficients, for $\mathit{j}=2,3,\dots ,n_{\mathrm{fwd}}$.

The values $q\left(\mathit{i}\right)$, for $\mathit{i}=n_{\mathrm{fwd}},n_{\mathrm{fwd}}-1,\dots ,1$, are contained in DWTLEV which is produced as output by a preceding call to C09CCF. See C09CCF for details.

4:     N – INTEGERInput

On entry: $n$, the length of the data array, $y$, to be reconstructed. For a full reconstruction from $n_{\mathrm{fwd}}$ levels, this is the same as parameter N in the preceding call to C09CCF. For a partial reconstruction of $n_l<n_{\mathrm{fwd}}$ levels, this will be equal to $\mathbf{DWTLEV}\left(n_l+2\right)$ as returned from C09CCF.

5:     Y(N) – REAL (KIND=nag_wp) arrayOutput

On exit: the dataset reconstructed from the multi-level wavelet transform coefficients and the transformation options supplied to the initialization routine C09AAF.

6:     ICOMM($100$) – INTEGER arrayCommunication Array

On entry: contains details of the discrete wavelet transform and the problem dimension for the forward transform previously computed by C09CCF.

7:     IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction 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 parameter, 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,	$\mathbf{NWL}<1$,
or	$\mathbf{NWL}>$ the number of levels used in the computation of the wavelet coefficients by a call to C09CCF.

$\mathbf{IFAIL}=2$

On entry, LENC is too small. LENC must be at least the number of wavelet coefficients required for a transform operating on NWL levels. If $\mathbf{NWL}=l_{\max }$, the maximum number of levels as returned in NWL by the initial call to C09AAF, then LENC must be at least $n_c$, the value returned in NWC by the same call to C09AAF.

$\mathbf{IFAIL}=4$

On entry, N is too small for the required level of reconstruction.

$\mathbf{IFAIL}=6$

On entry, the initialization routine C09AAF has not been called first or it has been called with $\mathbf{WTRANS}=\text{'S'}$, or the communication array ICOMM has become corrupted.

7  Accuracy

8  Further Comments

9  Example