naginterfaces.library.wav.dim2_​coeff_​ins

naginterfaces.library.wav.dim2_coeff_ins(ilev, cindex, c, d, comm)

dim2_coeff_ins inserts a selected set of two-dimensional discrete wavelet transform (DWT) coefficients into the full set of coefficients stored in compact form, which may be later used as input to the multi-level reconstruction function dim2_multi_inv().

For full information please refer to the NAG Library document for c09ez

https://www.nag.com/numeric/nl/nagdoc_29.3/flhtml/c09/c09ezf.html

Parameters

ilevint

The level at which coefficients are to be inserted.

cindexint

Identifies which coefficients to insert. The coefficients are identified as follows:

$cindex=0$

The approximation coefficients, produced by application of the low pass filter over columns and rows of the original matrix (LL). The approximation coefficients are present only for $ilev=\text{nwl}$, where $\text{nwl}$ is the value used in a preceding call to dim2_multi_fwd().

$cindex=1$

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

$cindex=2$

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

$cindex=3$

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

cfloat, array-like, shape $\left(\text{lenc}\right)$

Contains the DWT coefficients inserted by previous calls to dim2_coeff_ins, or computed by a previous call to dim2_multi_fwd().

dfloat, array-like, shape $({\text{n}}_{\text{cm}},{\text{n}}_{\text{cn}})$

The coefficients to be inserted.

If $ilev=\text{nwl}$ (as used in dim2_multi_fwd()) and $cindex=0$, the $n_{\text{cm}}\times n_{\text{cn}}$ manipulated approximation coefficients $a_{\text{i}\text{j}}$ must be stored in $d[\text{i}-1,\text{j}-1]$, for $\text{i}=1,2,\dots ,n_{\text{cn}}$, for $\text{i}=1,2,\dots ,n_{\text{cm}}$.

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

commdict, communication object, modified in place

Communication structure.

This argument must have been initialized by a prior call to dim2_init().

Returns

cfloat, ndarray, shape $\left(\text{lenc}\right)$

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 dim2_multi_inv().

Raises

NagValueError

(errno $1$)

On entry, $ilev=⟨value⟩$.

Constraint: $ilev\ge 1$.

(errno $1$)

On entry, $ilev=⟨value⟩$ and $\text{nwl}=⟨value⟩$.

Constraint: $ilev\le \text{nwl}$, where $\text{nwl}$ is the number of levels used in the call to dim2_multi_fwd().

(errno $2$)

On entry, $cindex=⟨value⟩$.

Constraint: $cindex\ge 0$.

(errno $2$)

On entry, $cindex=⟨value⟩$.

Constraint: $cindex\le 3$.

(errno $3$)

On entry, $\text{lenc}=⟨value⟩$ and $n_{\text{ct}}=⟨value⟩$.

Constraint: $\text{lenc}\ge n_{\text{ct}}$, where $n_{\text{ct}}$ is the number of DWT coefficients computed in a previous call to dim2_multi_fwd().

(errno $5$)

On entry, $ilev=⟨value⟩$ and $\text{nwl}=⟨value⟩$, but $cindex=0$.

Constraint: $cindex>0$ when $ilev<\text{nwl}$ in the preceding call to dim2_multi_fwd().

(errno $6$)

Either the initialization function has not been called first or $comm$[‘icomm’] has been corrupted.

(errno $6$)

Either the initialization function was called with $wtrans=\text{‘S'}$ or $comm$[‘icomm’] has been corrupted.

Notes

dim2_coeff_ins inserts a selected set of two-dimensional DWT coefficients into the full set of coefficients stored in compact form in a one-dimensional array $c$. It is required that dim2_coeff_ins is preceded by a call to the initialization function dim2_init() and the forward multi-level transform function dim2_multi_fwd().

Given an initial two-dimensional data set $A$, a prior call to dim2_multi_fwd() computes the approximation coefficients (at the highest requested level) and three sets of detail coefficients at all levels and stores these in compact form in a one-dimensional array $c$. dim2_coeff_ext() can then extract either the approximation coefficients or one of the sets of detail coefficients at one of the levels into a two-dimensional array, $d$. Following some calculation on this set of coefficients (for example, denoising), the updated coefficients in $d$ are inserted back into the full set $c$ using dim2_coeff_ins. Several extractions and insertions may be performed at different levels. dim2_multi_inv() can then be used to reconstruct a manipulated data set $\tilde{A}$. The dimensions of $d$ depend on the level extracted and are available from the arrays $\text{dwtlvm}$ and $\text{dwtlvn}$ as returned by dim2_multi_fwd() which contain the first and second dimensions respectively. See the C09 Introduction for a discussion of the multi-level two-dimensional DWT.