NAG Library Function Document

nag_wav_2d_coeff_ext (c09eyc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     ilev – IntegerInput

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

Constraints:

• $1\le \mathbf{ilev}\le \mathbf{nwl}$, where nwl is as used in a preceding call to nag_mldwt_2d (c09ecc);
• if $\mathbf{cindex}=0$, $\mathbf{ilev}=\mathbf{nwl}$.

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 and rows of the original matrix ($\mathrm{LL}$). The approximation coefficients are available only for $\mathbf{ilev}=\mathbf{nwl}$, where nwl is the value used in a preceding call to nag_mldwt_2d (c09ecc).

$\mathbf{cindex}=1$

The vertical detail coefficients produced by applying the low pass filter over columns of the original matrix and the high pass filter over rows ($\mathrm{LH}$).

$\mathbf{cindex}=2$

The horizontal detail coefficients produced by applying the high pass filter over columns of the original matrix and the low pass filter over rows ($\mathrm{HL}$).

$\mathbf{cindex}=3$

The diagonal detail coefficients produced by applying the high pass filter over columns and rows of the original matrix ($\mathrm{HH}$).

Constraint: $0\le \mathbf{cindex}\le 3$ when $\mathbf{ilev}=\mathbf{nwl}$ as used in nag_mldwt_2d (c09ecc), otherwise $1\le \mathbf{cindex}\le 3$.

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 nag_mldwt_2d (c09ecc)..

4:     c[lenc] – const doubleInput

On entry: DWT coefficients, as computed by a preceding call to nag_mldwt_2d (c09ecc).

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

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

On exit: the requested coefficients.

If $\mathbf{ilev}=\mathbf{nwl}$ (as used in nag_mldwt_2d (c09ecc)) and $\mathbf{cindex}=0$, the $n_{\mathit{cm}}$ by $n_{\mathit{cn}}$ approximation coefficients $a_{ij}$ are stored in $\mathbf{d}\left[\left(\mathit{j}-1\right)\times \mathbf{pdd}+i-1\right]$, for $\mathit{i}=1,2,\dots ,n_{\mathit{cm}}$ and $\mathit{j}=1,2,\dots ,n_{\mathit{cn}}$.

Otherwise the $n_{\mathit{cm}}$ by $n_{\mathit{cn}}$ level ilev detail coefficients (of type specified by cindex) $d_{ij}$ are stored in $\mathbf{d}\left[\left(\mathit{j}-1\right)\times \mathbf{pdd}+i-1\right]$, for $\mathit{i}=1,2,\dots ,n_{\mathit{cm}}$ and $\mathit{j}=1,2,\dots ,n_{\mathit{cn}}$.

6:     pdd – IntegerInput

On entry: the stride separating row elements in the two-dimensional data stored in the array d.

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

7:     icomm[$180$] – 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_2d (c09abc).

8:     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.

Either the initialization function was called with $\mathbf{wtrans}=\mathrm{Nag\_SingleLevel}$ or icomm has been corrupted.

NE_INT

On entry, $\mathbf{cindex}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{cindex}\le 3$.

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

On entry, $\mathbf{ilev}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{ilev}\ge 1$.

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_2d (c09ecc).

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_2d (c09ecc).

On entry, $\mathbf{pdd}=⟨\mathit{\text{value}}⟩$ and $n_{\mathrm{cm}}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{pdd}\ge n_{\mathrm{cm}}$, where $n_{\mathrm{cm}}$ is the number of DWT coefficients in the first dimension at the selected level ilev.

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_2d (c09ecc).

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