NAG Library Function Document

nag_wav_3d_coeff_ext (c09fyc)

1

Purpose

2

Specification

3

Description

4

References

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Arguments

1:    $\mathbf{ilev}$ – IntegerInput

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 function nag_dwt_3d (c09fac).

If $\mathbf{ilev}>0$, it is assumed that the coefficient array c was produced by a preceding call to the multi-level function nag_mldwt_3d (c09fcc).

Constraints:

• $\mathbf{ilev}=0$ (following a call to nag_dwt_3d (c09fac));
• $0\le \mathbf{ilev}\le \mathbf{nwl}$, where nwl is as used in a preceding call to nag_mldwt_3d (c09fcc);
• if $\mathbf{cindex}=0$, $\mathbf{ilev}=\mathbf{nwl}$ (following a call to nag_mldwt_3d (c09fcc)).

2:    $\mathbf{cindex}$ – 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, rows and frames of $A$ (LLL). After a call to the multi-level transform function nag_mldwt_3d (c09fcc) (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 nag_mldwt_3d (c09fcc).

$\mathbf{cindex}=1$

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 nag_mldwt_3d (c09fcc) transforming nwl levels, $0\le \mathbf{cindex}\le 7$;
• otherwise $1\le \mathbf{cindex}\le 7$.

3:    $\mathbf{lenc}$ – IntegerInput

On entry: the dimension of the array c.

Constraint: lenc must be unchanged from the value used in the preceding call to either nag_dwt_3d (c09fac) or nag_mldwt_3d (c09fcc)..

4:    $\mathbf{c}\left[\mathbf{lenc}\right]$ – const doubleInput

On entry: DWT coefficients, as computed by nag_dwt_3d (c09fac) or nag_mldwt_3d (c09fcc).

5:    $\mathbf{d}\left[\mathit{dim}\right]$ – doubleOutput

Note: the dimension, dim, of the array d must be at least $\mathbf{ldd}\times \mathbf{sdd}\times n_{\mathrm{cfr}}$.

On exit: the requested coefficients.

If the DWT coefficients were computed by nag_dwt_3d (c09fac) then

• if $\mathbf{cindex}=0$, the approximation coefficients are stored in $\mathbf{d}\left[\left(\mathit{k}-1\right)\times \mathbf{ldd}\times \mathbf{sdd}+\left(\mathit{j}-1\right)\times \mathbf{ldd}+i-1\right]$, 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 $\mathbf{d}\left[\left(\mathit{k}-1\right)\times \mathbf{ldd}\times \mathbf{sdd}+\left(\mathit{j}-1\right)\times \mathbf{ldd}+i-1\right]$, 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 nag_mldwt_3d (c09fcc) then

• if $\mathbf{cindex}=0$ and $\mathbf{ilev}=\mathbf{nwl}$, the approximation coefficients are stored in $\mathbf{d}\left[\left(\mathit{k}-1\right)\times \mathbf{ldd}\times \mathbf{sdd}+\left(\mathit{j}-1\right)\times \mathbf{ldd}+i-1\right]$, 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 $\mathbf{d}\left[\left(\mathit{k}-1\right)\times \mathbf{ldd}\times \mathbf{sdd}+\left(\mathit{j}-1\right)\times \mathbf{ldd}+i-1\right]$, 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:    $\mathbf{ldd}$ – IntegerInput

On entry: the stride separating row elements of each of the sets of frame coefficients in the three-dimensional data stored in d.

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

7:    $\mathbf{sdd}$ – IntegerInput

On entry: the stride separating corresponding coefficients of consecutive frames in the three-dimensional data stored in d.

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

8:    $\mathbf{icomm}\left[260\right]$ – IntegerCommunication Array

On entry: contains details of the discrete wavelet transform and the problem dimension as setup in the call to the initialization function nag_wfilt_3d (c09acc).

9:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INITIALIZATION

Either the initialization function has not been called first or icomm has been corrupted.

NE_INT

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

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

On entry, $\mathbf{ilev}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ilev}=0$ following a call to the single level function nag_dwt_3d (c09fac).

On entry, $\mathbf{ilev}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ilev}>0$ following a call to the multi-level function nag_mldwt_3d (c09fcc).

NE_INT_2

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 nag_mldwt_3d (c09fcc).

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, $\mathbf{lenc}=〈\mathit{\text{value}}〉$ 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 nag_dwt_3d (c09fac).

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 nag_mldwt_3d (c09fcc).

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.

NE_INT_3

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 nag_mldwt_3d (c09fcc).

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, $\mathbf{sdd}=〈\mathit{\text{value}}〉$ 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.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

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Accuracy

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Parallelism and Performance

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Further Comments

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Example