NAG Library Function Document

nag_wav_2d_coeff_ins (c09ezc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     ilev – IntegerInput

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

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 insert. 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 present 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] – doubleInput/Output

On entry: contains the DWT coefficients inserted by previous calls to nag_wav_2d_coeff_ins (c09ezc), or computed by a previous call to nag_mldwt_2d (c09ecc).

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 the reconstruction function nag_imldwt_2d (c09edc).

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

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

On entry: the coefficients to be inserted.

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

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

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 $\mathbf{nwl}$ 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

10.1  Program Text

Program Text (c09ezce.c)

10.2  Program Data

Program Data (c09ezce.d)

10.3  Program Results

Program Results (c09ezce.r)