NAG Library Routine Document

C09EYF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{ILEV}$ – INTEGERInput

On entry: the level at which coefficients are to be extracted.

Constraints:

• $1\le \mathbf{ILEV}\le \mathbf{NWL}$, where NWL is as used in a preceding call to C09ECF;
• if $\mathbf{CINDEX}=0$, $\mathbf{ILEV}=\mathbf{NWL}$.

2:     $\mathrm{CINDEX}$ – INTEGERInput

On entry: identifies which coefficients to extract. The coefficients are identified as follows:

$\mathbf{CINDEX}=0$

The approximation coefficients, produced by application of the low pass filter over columns and rows of the original matrix ($\mathrm{LL}$). The approximation coefficients are available only for $\mathbf{ILEV}=\mathbf{NWL}$, where NWL is the value used in a preceding call to C09ECF.

$\mathbf{CINDEX}=1$

The vertical detail coefficients produced by applying the low pass filter over columns of the original matrix and the high pass filter over rows ($\mathrm{LH}$).

$\mathbf{CINDEX}=2$

The horizontal detail coefficients produced by applying the high pass filter over columns of the original matrix and the low pass filter over rows ($\mathrm{HL}$).

$\mathbf{CINDEX}=3$

The diagonal detail coefficients produced by applying the high pass filter over columns and rows of the original matrix ($\mathrm{HH}$).

Constraint: $0\le \mathbf{CINDEX}\le 3$ when $\mathbf{ILEV}=\mathbf{NWL}$ as used in C09ECF, otherwise $1\le \mathbf{CINDEX}\le 3$.

3:     $\mathrm{LENC}$ – INTEGERInput

On entry: the dimension of the array C as declared in the (sub)program from which C09EYF is called.

Constraint: LENC must be unchanged from the value used in the preceding call to C09ECF..

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

On entry: DWT coefficients, as computed by a preceding call to C09ECF.

5:     $\mathrm{D}\left(\mathbf{LDD},*\right)$ – REAL (KIND=nag_wp) arrayOutput

Note: the second dimension of the array D must be at least $n_{\mathrm{cn}}$.

On exit: the requested coefficients.

If $\mathbf{ILEV}=\mathbf{NWL}$ (as used in C09ECF) and $\mathbf{CINDEX}=0$, the $n_{\mathit{cm}}$ by $n_{\mathit{cn}}$ approximation coefficients $a_{ij}$ are stored in $\mathbf{D}\left(i,\mathit{j}\right)$, for $\mathit{i}=1,2,\dots ,n_{\mathit{cm}}$ and $\mathit{j}=1,2,\dots ,n_{\mathit{cn}}$.

Otherwise the $n_{\mathit{cm}}$ by $n_{\mathit{cn}}$ level ILEV detail coefficients (of type specified by CINDEX) $d_{ij}$ are stored in $\mathbf{D}\left(i,\mathit{j}\right)$, for $\mathit{i}=1,2,\dots ,n_{\mathit{cm}}$ and $\mathit{j}=1,2,\dots ,n_{\mathit{cn}}$.

6:     $\mathrm{LDD}$ – INTEGERInput

On entry: the first dimension of the array D as declared in the (sub)program from which C09EYF is called.

Constraint: $\mathbf{LDD}\ge n_{\mathrm{cm}}$.

7:     $\mathrm{ICOMM}\left(180\right)$ – 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 C09ABF.

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

On entry, $\mathbf{ILEV}=〈\mathit{\text{value}}〉$ and $\mathbf{NWL}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ILEV}\le \mathbf{NWL}$, where NWL is the number of levels used in the call to C09ECF.

$\mathbf{IFAIL}=2$

On entry, $\mathbf{CINDEX}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{CINDEX}\le 3$.

On entry, $\mathbf{CINDEX}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{CINDEX}\ge 0$.

$\mathbf{IFAIL}=3$

On entry, $\mathbf{LENC}=〈\mathit{\text{value}}〉$ and $n_{\mathrm{ct}}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{LENC}\ge n_{\mathrm{ct}}$, where $n_{\mathrm{ct}}$ is the number of DWT coefficients computed in a previous call to C09ECF.

$\mathbf{IFAIL}=4$

On entry, $\mathbf{LDD}=〈\mathit{\text{value}}〉$ and $n_{\mathrm{cm}}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{LDD}\ge n_{\mathrm{cm}}$, where $n_{\mathrm{cm}}$ is the number of DWT coefficients in the first dimension at the selected level ILEV.

$\mathbf{IFAIL}=5$

On entry, $\mathbf{ILEV}=〈\mathit{\text{value}}〉$ and $\mathbf{NWL}=〈\mathit{\text{value}}〉$, but $\mathbf{CINDEX}=0$.
Constraint: $\mathbf{CINDEX}>0$ when $\mathbf{ILEV}<\mathbf{NWL}$ in the preceding call to C09ECF.

$\mathbf{IFAIL}=6$

Either the initialization routine has not been called first or ICOMM has been corrupted.

Either the initialization routine was called with $\mathbf{WTRANS}=\text{'S'}$ or ICOMM has been 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