NAG Library Routine Document

C09FDF

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.

Constraint: $1\le \mathbf{NWL}\le n_{\mathrm{fwd}}$, where $n_{\mathrm{fwd}}$ is the value used in a preceding call to C09FCF.

2:     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 NWL levels.

3:     C(LENC) – 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.

4:     M – INTEGERInput

On entry: the number of elements, $m$, in the first dimension of the reconstructed array $B$. For a full reconstruction of $n_{\mathrm{fwd}}$ levels this must be the same as parameter M used in a preceding call to C09FCF. For reconstruction of $n_l<n_{\mathrm{fwd}}$ levels this must be equal to $\mathbf{DWTLVM}\left(n_l+1\right)$ as returned from C09FCF.

5:     N – INTEGERInput

On entry: the number of elements, $n$, in the second dimension of the reconstructed array $B$. For a full reconstruction of $n_{\mathrm{fwd}}$ levels this must be the same as parameter N used in a preceding call to C09FCF. For a partial reconstruction of $n_l<n_{\mathrm{fwd}}$ levels this must be equal to $\mathbf{DWTLVN}\left(n_l+1\right)$ as returned from C09FCF.

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 $n_{\mathrm{fwd}}$ levels this must be the same as parameter FR used in a preceding call to C09FCF. For a partial reconstruction of $n_l<n_{\mathrm{fwd}}$ levels this must be equal to $\mathbf{DWTLVFR}\left(n_l+1\right)$ as returned from C09FCF.

7:     B(LDB,SDB,FR) – REAL (KIND=nag_wp) arrayOutput

On exit: the $m$ by $n$ by $\mathit{fr}$ reconstructed array, $B$, based on the input multi-level wavelet transform coefficients and the transform options supplied to the initialization routine C09ACF.

8:     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:     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:   ICOMM($260$) – 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:   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, $\mathbf{NWL}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{NWL}\ge 1$.

On entry, $\mathbf{NWL}=⟨\mathit{\text{value}}⟩$ and $n_{\mathrm{fwd}}=⟨\mathit{\text{value}}⟩$ where $n_{\mathrm{fwd}}$ is the number of levels used in the computation of the wavelet coefficients by a call to C09FCF.
Constraint: $\mathbf{NWL}\le n_{\mathrm{fwd}}$.

$\mathbf{IFAIL}=2$

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 NWL levels. If $\mathbf{NWL}=l_{\max }$, the maximum number of levels as returned in NWL by the initial call to C09ACF, then 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 initialization routine has not been called first or the communication array ICOMM has been corrupted.

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

$\mathbf{IFAIL}=-999$

Dynamic memory allocation failed.

7  Accuracy

8  Further Comments

9  Example