NAG Library Function Document

nag_wav_3d_coeff_ext (c09fyc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     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:     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:     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:     c[lenc] – const doubleInput

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

5:     d[$\mathit{dim}$] – 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:     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: $\mathbf{ldd}>n_{\mathrm{cm}}$.

7:     sdd – IntegerInput

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

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

8:     icomm[$260$] – 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:     fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.

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.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example