NAG Library Routine Document

C09FZF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{ILEV}$ – INTEGERInput

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

If $\mathbf{ILEV}=0$, it is assumed that the coefficient array C was produced by a preceding call to the single level routine C09FAF.

If $\mathbf{ILEV}>0$, it is assumed that the coefficient array C was produced by a preceding call to the multi-level routine C09FCF.

Constraints:

• $\mathbf{ILEV}=0$ (following a call to C09FAF);
• $0\le \mathbf{ILEV}\le \mathbf{NWL}$, where NWL is as used in a preceding call to C09FCF;
• if $\mathbf{CINDEX}=0$, $\mathbf{ILEV}=\mathbf{NWL}$ (following a call to C09FCF).

2:     $\mathrm{CINDEX}$ – INTEGERInput

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

$\mathbf{CINDEX}=0$

The approximation coefficients, produced by application of the low pass filter over columns, rows and frames of $A$ (LLL). After a call to the multi-level transform routine C09FCF (which implies that $\mathbf{ILEV}>0$) the approximation coefficients are present only for $\mathbf{ILEV}=\mathbf{NWL}$, where NWL is the value used in a preceding call to C09FCF.

$\mathbf{CINDEX}=1$

The detail coefficients produced by applying the low pass filter over columns and rows of $A$ and the high pass filter over frames (LLH).

$\mathbf{CINDEX}=2$

The detail coefficients produced by applying the low pass filter over columns, high pass filter over rows and low pass filter over frames of $A$ (LHL).

$\mathbf{CINDEX}=3$

The detail coefficients produced by applying the low pass filter over columns of $A$ and high pass filter over rows and frames (LHH).

$\mathbf{CINDEX}=4$

The detail coefficients produced by applying the high pass filter over columns of $A$ and low pass filter over rows and frames (HLL).

$\mathbf{CINDEX}=5$

The detail coefficients produced by applying the high pass filter over columns, low pass filter over rows and high pass filter over frames of $A$ (HLH).

$\mathbf{CINDEX}=6$

The detail coefficients produced by applying the high pass filter over columns and rows of $A$ and the low pass filter over frames (HHL).

$\mathbf{CINDEX}=7$

The detail coefficients produced by applying the high pass filter over columns, rows and frames of $A$ (HHH).

Constraints:

• if $\mathbf{ILEV}=0$, $0\le \mathbf{CINDEX}\le 7$;
• if $\mathbf{ILEV}=\mathbf{NWL}$, following a call to C09FCF transforming NWL levels, $0\le \mathbf{CINDEX}\le 7$;
• otherwise $1\le \mathbf{CINDEX}\le 7$.

3:     $\mathrm{LENC}$ – INTEGERInput

On entry: the dimension of the array C as declared in the (sub)program from which C09FZF is called.

Constraint: LENC must be unchanged from the value used in the preceding call to either C09FAF or C09FCF..

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

On entry: contains the DWT coefficients inserted by previous calls to C09FZF, or computed by a previous call to either C09FAF or C09FCF.

On exit: contains the same DWT coefficients provided on entry except for those identified by ILEV and CINDEX, which are updated with the values supplied in D, inserted into the correct locations as expected by one of the reconstruction routines C09FBF (if C09FAF was called previously) or C09FDF (if C09FCF was called previously).

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

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

On entry: the coefficients to be inserted.

If the DWT coefficients were computed by C09FAF then

• if $\mathbf{CINDEX}=0$, the approximation coefficients must be stored in $\mathbf{D}\left(i,\mathit{j},\mathit{k}\right)$, for $\mathit{i}=1,2,\dots ,n_{\mathrm{cm}}$, $\mathit{j}=1,2,\dots ,n_{\mathrm{cn}}$ and $\mathit{k}=1,2,\dots ,n_{\mathrm{cfr}}$;
• if $1\le \mathbf{CINDEX}\le 7$, the detail coefficients, as indicated by CINDEX, must be stored in $\mathbf{D}\left(i,\mathit{j},\mathit{k}\right)$, for $\mathit{i}=1,2,\dots ,n_{\mathrm{cm}}$, $\mathit{j}=1,2,\dots ,n_{\mathrm{cn}}$ and $\mathit{k}=1,2,\dots ,n_{\mathrm{cfr}}$.

If the DWT coefficients were computed by C09FCF then

• if $\mathbf{CINDEX}=0$ and $\mathbf{ILEV}=\mathbf{NWL}$, the approximation coefficients must be stored in $\mathbf{D}\left(i,\mathit{j},\mathit{k}\right)$, for $\mathit{i}=1,2,\dots ,n_{\mathrm{cm}}$, $\mathit{j}=1,2,\dots ,n_{\mathrm{cn}}$ and $\mathit{k}=1,2,\dots ,n_{\mathrm{cfr}}$;
• if $1\le \mathbf{CINDEX}\le 7$, the detail coefficients, as indicated by CINDEX, for level ILEV must be stored in $\mathbf{D}\left(i,\mathit{j},\mathit{k}\right)$, for $\mathit{i}=1,2,\dots ,n_{\mathrm{cm}}$, $\mathit{j}=1,2,\dots ,n_{\mathrm{cn}}$ and $\mathit{k}=1,2,\dots ,n_{\mathrm{cfr}}$.

6:     $\mathrm{LDD}$ – INTEGERInput

On entry: the first dimension of the array D as declared in the (sub)program from which C09FZF is called.

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

7:     $\mathrm{SDD}$ – INTEGERInput

On entry: the second dimension of the array D as declared in the (sub)program from which C09FZF is called.

Constraint: $\mathbf{SDD}>n_{\mathrm{cn}}$.

8:     $\mathrm{ICOMM}\left(260\right)$ – 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 C09ACF.

9:     $\mathrm{IFAIL}$ – 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: $\mathbf{ILEV}=0$ following a call to the single level routine C09FAF.

On entry, $\mathbf{ILEV}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ILEV}>0$ following a call to the multi-level routine C09FCF.

On entry, $\mathbf{ILEV}=〈\mathit{\text{value}}〉$ and $\mathbf{NWL}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ILEV}\le \mathbf{NWL}$, where $\mathbf{NWL}$ is the number of levels used in the call to C09FCF.

$\mathbf{IFAIL}=2$

On entry, $\mathbf{CINDEX}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{CINDEX}\le 7$.

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 C09FAF.

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 C09FCF.

$\mathbf{IFAIL}=4$

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.

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 following the single level transform.

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

On entry, $\mathbf{SDD}=〈\mathit{\text{value}}〉$ and $n_{\mathrm{cn}}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{SDD}\ge n_{\mathrm{cn}}$, where $n_{\mathrm{cn}}$ is the number of DWT coefficients in the second dimension following the single level transform.

$\mathbf{IFAIL}=5$

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 C09FCF.

$\mathbf{IFAIL}=6$

Either the initialization routine has not been called first 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

10.1  Program Text

Program Text (c09fzfe.f90)

10.2  Program Data

Program Data (c09fzfe.d)

10.3  Program Results

Program Results (c09fzfe.r)