NAG Library Routine Document

C09DDF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{NWLINV}$ – 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 parameter NWL as used in the computation of the wavelet coefficients using C09DCF. The data will be reconstructed to level $\left(\mathbf{NWL}-\mathbf{NWLINV}\right)$, where level $0$ is the original input dataset provided to C09DCF.

Constraint: $1\le \mathbf{NWLINV}\le \mathbf{NWL}$, where NWL is the value used in a preceding call to C09DCF.

2:     $\mathrm{KEEPA}$ – CHARACTER(1)Input

On entry: determines whether the approximation coefficients are stored in array C for every level of the computed transform or else only for the final level. In both cases, the detail coefficients are stored in C for every level computed.

$\mathbf{KEEPA}=\text{'A'}$

Retain approximation coefficients for all levels computed.

$\mathbf{KEEPA}=\text{'F'}$

Retain approximation coefficients for only the final level computed.

Constraint: $\mathbf{KEEPA}=\text{'A'}$ or $\text{'F'}$.

3:     $\mathrm{LENC}$ – INTEGERInput

On entry: the dimension of the array C as declared in the (sub)program from which C09DDF is called.

Constraints:

• if $\mathbf{KEEPA}=\text{'F'}$, $\mathbf{LENC}\ge \left(n_{\mathrm{l}}+1\right)\times n_a$;
• if $\mathbf{KEEPA}=\text{'A'}$, $\mathbf{LENC}\ge 2\times n_l\times n_a$, where $n_a$ is the number of approximation or detail coefficients at each level and is unchanged from the preceding call to C09DCF.

4:     $\mathrm{C}\left(\mathbf{LENC}\right)$ – REAL (KIND=nag_wp) arrayInput

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

The coefficients are stored in C as follows:

If $\mathbf{KEEPA}=\text{'F'}$,

$\mathbf{C}\left(1:n_a\right)$

Contains the level $n_l$ approximation coefficients;

$\mathbf{C}\left(n_a+\left(i-1\right)\times n_d+1:n_a+i\times n_d\right)$

Contains the level $\left(n_l-\mathit{i}+1\right)$ detail coefficients, for $\mathit{i}=1,2,\dots ,n_l$;

If $\mathbf{KEEPA}=\text{'A'}$,

$\mathbf{C}\left(\left(i-1\right)\times n_a+1:i\times n_a\right)$

Contains the level $\left(n_l-\mathit{i}+1\right)$ approximation coefficients, for $\mathit{i}=1,2,\dots ,n_l$;

$\mathbf{C}\left(n_l\times n_a+\left(i-1\right)\times n_d+1:n_l\times n_a+i\times n_d\right)$

Contains the level $\mathit{i}$ detail coefficients, for $\mathit{i}=1,2,\dots ,n_l$.

The values $n_a$ and $n_d$ denote the numbers of approximation and detail coefficients respectively, which are equal. This number is returned as output in NA from a preceding call to C09DCF. See C09DCF for details.

5:     $\mathrm{N}$ – INTEGERInput

On entry: $n$, the length of the data array, $y$, to be reconstructed.

Constraint: This must be the same as the value N passed to the initialization routine C09AAF.

6:     $\mathrm{Y}\left(\mathbf{N}\right)$ – 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.

7:     $\mathrm{ICOMM}\left(100\right)$ – INTEGER arrayCommunication Array

On entry: contains details of the discrete wavelet transform and the problem dimension for the forward transform previously computed by C09DCF.

8:     $\mathrm{IFAIL}$ – 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, $\mathbf{NWLINV}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{NWLINV}\ge 1$.

On entry, NWLINV is larger than the number of levels computed by the preceding call to C09DCF: $\mathbf{NWLINV}=〈\mathit{\text{value}}〉$, expected $〈\mathit{\text{value}}〉$.

$\mathbf{IFAIL}=2$

On entry, $\mathbf{KEEPA}=〈\mathit{\text{value}}〉$ was an illegal value.

$\mathbf{IFAIL}=3$

On entry, LENC is set too small: $\mathbf{LENC}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{LENC}\ge 〈\mathit{\text{value}}〉$.

$\mathbf{IFAIL}=5$

On entry, N is inconsistent with the value passed to the initialization routine: $\mathbf{N}=〈\mathit{\text{value}}〉$, N should be $〈\mathit{\text{value}}〉$.

$\mathbf{IFAIL}=7$

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

$\mathbf{IFAIL}=-99$

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

See Section 3.8 in the Essential Introduction for further information.

$\mathbf{IFAIL}=-399$

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

See Section 3.7 in the Essential Introduction for further information.

$\mathbf{IFAIL}=-999$

Dynamic memory allocation failed.

See Section 3.6 in the Essential Introduction for further information.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example