NAG Library Function Document

nag_wav_3d_coeff_ins (c09fzc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     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 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 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 function nag_mldwt_3d (c09fcc) (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 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] – doubleInput/Output

On entry: contains the DWT coefficients inserted by previous calls to nag_wav_3d_coeff_ins (c09fzc), or computed by a previous call to either nag_dwt_3d (c09fac) or nag_mldwt_3d (c09fcc).

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 functions nag_idwt_3d (c09fbc) (if nag_dwt_3d (c09fac) was called previously) or nag_imldwt_3d (c09fdc) (if nag_mldwt_3d (c09fcc) was called previously).

5:     d[$\mathit{dim}$] – const doubleInput

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

On entry: the coefficients to be inserted.

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

• if $\mathbf{cindex}=0$, the approximation coefficients must be 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, must be 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 must be 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 must be 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 $\mathbf{nwl}$ 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 a previous 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 a previous 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

10.1  Program Text

Program Text (c09fzce.c)

10.2  Program Data

Program Data (c09fzce.d)

10.3  Program Results

Program Results (c09fzce.r)