NAG FL Interface
c09fyf (dim3_​coeff_​ext)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{ilev}$ – Integer Input

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

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: $\mathbf{cindex}$ – Integer Input

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, 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 available 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: $\mathbf{lenc}$ – Integer Input

On entry: the dimension of the array c as declared in the (sub)program from which c09fyf is called.

Constraint: lenc must be unchanged from the value used in the preceding call to either c09faf or c09fcf.

4: $\mathbf{c}\left(\mathbf{lenc}\right)$ – Real (Kind=nag_wp) array Input

On entry: DWT coefficients, as computed by c09faf or c09fcf.

5: $\mathbf{d}\left(\mathbf{ldd},\mathbf{sdd},*\right)$ – Real (Kind=nag_wp) array Output

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

On exit: the requested coefficients.

If the DWT coefficients were computed by c09faf then

• if $\mathbf{cindex}=0$, the approximation coefficients are 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, are 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 are 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 are 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: $\mathbf{ldd}$ – Integer Input

On entry: the first dimension of the array d as declared in the (sub)program from which c09fyf is called.

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

7: $\mathbf{sdd}$ – Integer Input

On entry: the second dimension of the array d as declared in the (sub)program from which c09fyf is called.

Constraint: $\mathbf{sdd}\ge n_{\mathrm{cn}}$.

8: $\mathbf{icomm}\left(260\right)$ – Integer array Communication 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: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 4 in the Introduction to the NAG Library FL Interface 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 argument, 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 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 the preceding call to c09faf.

$\mathbf{ifail}=4$

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 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

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

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example