naginterfaces.library.wav.dim3_​coeff_​ins

naginterfaces.library.wav.dim3_coeff_ins(ilev, cindex, c, d, comm)

dim3_coeff_ins inserts a selected set of three-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 reconstruction functions dim3_sngl_inv() or dim3_mxolap_multi_inv().

For full information please refer to the NAG Library document for c09fz

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/c09/c09fzf.html

Parameters

ilevint

The level at which coefficients are to be inserted.

If $ilev=0$, it is assumed that the coefficient array $c$ was produced by a preceding call to the single level function dim3_sngl_fwd().

If $ilev>0$, it is assumed that the coefficient array $c$ was produced by a preceding call to the multi-level function dim3_multi_fwd().

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, rows and frames of $A$ (LLL). After a call to the multi-level transform function dim3_multi_fwd() (which implies that $ilev>0$) the approximation coefficients are present only for $ilev=\text{nwl}$, where $\text{nwl}$ is the value used in a preceding call to dim3_multi_fwd().

$cindex=1$

The detail coefficients produced by applying the low pass filter over columns and rows of $A$ and the high pass filter over frames (LLH).

$cindex=2$

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).

$cindex=3$

The detail coefficients produced by applying the low pass filter over columns of $A$ and high pass filter over rows and frames (LHH).

$cindex=4$

The detail coefficients produced by applying the high pass filter over columns of $A$ and low pass filter over rows and frames (HLL).

$cindex=5$

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).

$cindex=6$

The detail coefficients produced by applying the high pass filter over columns and rows of $A$ and the low pass filter over frames (HHL).

$cindex=7$

The detail coefficients produced by applying the high pass filter over columns, rows and frames of $A$ (HHH).

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

Contains the DWT coefficients inserted by previous calls to dim3_coeff_ins, or computed by a previous call to either dim3_sngl_fwd() or dim3_multi_fwd().

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

The coefficients to be inserted.

If the DWT coefficients were computed by dim3_sngl_fwd() then

if $cindex=0$, the approximation coefficients must be stored in $d[i-1,\text{j}-1,\text{k}-1]$, for $\text{k}=1,2,\dots ,n_{\text{cfr}}$, for $\text{j}=1,2,\dots ,n_{\text{cn}}$, for $\text{i}=1,2,\dots ,n_{\text{cm}}$;

if $1\le cindex\le 7$, the detail coefficients, as indicated by $cindex$, must be stored in $d[i-1,\text{j}-1,\text{k}-1]$, for $\text{k}=1,2,\dots ,n_{\text{cfr}}$, for $\text{j}=1,2,\dots ,n_{\text{cn}}$, for $\text{i}=1,2,\dots ,n_{\text{cm}}$.

If the DWT coefficients were computed by dim3_multi_fwd() then

if $cindex=0$ and $ilev=\text{nwl}$, the approximation coefficients must be stored in $d[i-1,\text{j}-1,\text{k}-1]$, for $\text{k}=1,2,\dots ,n_{\text{cfr}}$, for $\text{j}=1,2,\dots ,n_{\text{cn}}$, for $\text{i}=1,2,\dots ,n_{\text{cm}}$;

if $1\le cindex\le 7$, the detail coefficients, as indicated by $cindex$, for level $ilev$ must be stored in $d[i-1,\text{j}-1,\text{k}-1]$, for $\text{k}=1,2,\dots ,n_{\text{cfr}}$, 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 dim3_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 one of the reconstruction functions dim3_sngl_inv() (if dim3_sngl_fwd() was called previously) or dim3_mxolap_multi_inv() (if dim3_multi_fwd() was called previously).

Raises

NagValueError

(errno $1$)

On entry, $ilev=⟨value⟩$.

Constraint: $ilev=0$ following a call to the single level function dim3_sngl_fwd().

(errno $1$)

On entry, $ilev=⟨value⟩$.

Constraint: $ilev>0$ following a call to the multi-level function dim3_multi_fwd().

(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 dim3_multi_fwd().

(errno $2$)

On entry, $cindex=⟨value⟩$.

Constraint: $cindex\ge 0$.

(errno $2$)

On entry, $cindex=⟨value⟩$.

Constraint: $cindex\le 7$.

(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 dim3_sngl_fwd().

(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 dim3_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 dim3_multi_fwd().

(errno $6$)

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

Notes

dim3_coeff_ins inserts a selected set of three-dimensional DWT coefficients into the full set of coefficients stored in compact form in a one-dimensional array $c$. It is required that dim3_coeff_ins is preceded by a call to the initialization function dim3_init() and either the forwards transform function dim3_sngl_fwd() or multi-level forwards transform function dim3_multi_fwd().

Given an initial three-dimensional data set $A$, a prior call to dim3_sngl_fwd() or dim3_multi_fwd() computes the approximation coefficients (at the highest requested level in the case of dim3_multi_fwd()) and, seven sets of detail coefficients (at all levels in the case of dim3_multi_fwd()) and stores these in compact form in a one-dimensional array $c$. dim3_coeff_ext() can then extract either the approximation coefficients or one of the sets of detail coefficients (at one of the levels following dim3_multi_fwd()) into a three-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 dim3_coeff_ins. Several extractions and insertions may be performed. dim3_sngl_inv() or dim3_mxolap_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 either: the arrays $\text{dwtlvm}$, $\text{dwtlvn}$ and $\text{dwtlvfr}$ as returned by dim3_multi_fwd() if this was called first; or, otherwise from $\text{nwct}$, $\text{nwcn}$ and $\text{nwcfr}$ as returned by dim3_init(). See the C09 Introduction for a discussion of the three-dimensional DWT.