naginterfaces.library.wav.dim2_​multi_​inv

naginterfaces.library.wav.dim2_multi_inv(nwlinv, c, m, n, comm)

dim2_multi_inv computes the inverse two-dimensional multi-level discrete wavelet transform (DWT). This function reconstructs data from (possibly filtered or otherwise manipulated) wavelet transform coefficients calculated by dim2_multi_fwd() from an original input matrix. The initialization function dim2_init() must be called first to set up the DWT options.

For full information please refer to the NAG Library document for c09ed

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/c09/c09edf.html

Parameters

nwlinvint

The number of levels to be used in the inverse multi-level transform. The number of levels must be less than or equal to $n_{fwd}$, which has the value of argument $\text{nwl}$ as used in the computation of the wavelet coefficients using dim2_multi_fwd(). The data will be reconstructed to level $(\text{nwl}-nwlinv)$, where level $0$ is the original input dataset provided to dim2_multi_fwd().

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

The coefficients of a multi-level wavelet transform of the original matrix, $A$, which may have been filtered or otherwise manipulated.

Let $q\left(\text{i}\right)$ be the number of coefficients (of each type) at level $\text{i}$, for $\text{i}=n_{fwd},\dots ,1$.

Then, setting $k_1=q\left(n_{fwd}\right)$ and $k_{j+1}=k_j+q(n_{fwd}-\lceil j/3\rceil +1)$, for $j=1,2,\dots ,3n_{fwd}$, the coefficients are stored in $c$ as follows:

$c[\text{i}-1]$, for $\text{i}=1,2,\dots ,k_1$

Contains the level $n_{fwd}$ approximation coefficients, $a_{n_{fwd}}$.

$c[\text{i}-1]$, for $\text{i}=k_j+1,\dots ,k_{j+1}$

Contains the level $n_{fwd}-\lceil j/3\rceil +1$ vertical, horizontal and diagonal coefficients. These are:

vertical coefficients if $mod(j,3)=1$;

horizontal coefficients if $mod(j,3)=2$;

diagonal coefficients if $mod(j,3)=0$,

for $j=1,\dots ,3n_{fwd}$.

Note that the coefficients in $c$ may be extracted according to level and type into two-dimensional arrays using dim2_coeff_ext(), and inserted using dim2_coeff_ins().

mint

The number of elements, $m$, in the first dimension of the reconstructed matrix $B$. For a full reconstruction of $\text{nwl}$ levels, where $\text{nwl}$ is as supplied to dim2_multi_fwd(), this must be the same as argument $\text{m}$ used in the call to dim2_multi_fwd(). For a partial reconstruction of $nwlinv<\text{nwl}$ levels, this must be equal to $\text{dwtlvm}\left[nwlinv\right]$, as returned from dim2_multi_fwd().

nint

The number of elements, $n$, in the second dimension of the reconstructed matrix $B$. For a full reconstruction of $\text{nwl}$ levels, where $\text{nwl}$ is as supplied to dim3_multi_fwd(), this must be the same as argument $\text{n}$ used in the call to dim2_multi_fwd(). For a partial reconstruction of $nwlinv<\text{nwl}$, this must be equal to $\text{dwtlvn}\left[nwlinv\right]$, as returned from dim2_multi_fwd().

commdict, communication object

Communication structure.

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

Returns

bfloat, ndarray, shape $(m,n)$

The $m\times n$ reconstructed matrix, $B$, based on the input multi-level wavelet transform coefficients and the transform options supplied to the initialization function dim2_init().

Raises

NagValueError

(errno $1$)

On entry, $nwlinv=⟨value⟩$ and $n_{fwd}=⟨value⟩$.

Constraint: $nwlinv\le n_{fwd}$.

(errno $1$)

On entry, $nwlinv=⟨value⟩$.

Constraint: $nwlinv\ge 1$.

(errno $3$)

On entry, $\text{lenc}=⟨value⟩$.

Constraint: $\text{lenc}\ge ⟨value⟩$, the total number of coefficients generated by the preceding call to dim2_multi_fwd().

(errno $4$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge ⟨value⟩$, the number of coefficients in the second dimension at the required level of reconstruction.

(errno $4$)

On entry, $m=⟨value⟩$.

Constraint: $m\ge ⟨value⟩$, the number of coefficients in the first dimension at the required level of reconstruction.

(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_multi_inv performs the inverse operation of dim2_multi_fwd(). That is, given a set of wavelet coefficients, computed up to level $n_{fwd}$ by dim2_multi_fwd() using a DWT as set up by the initialization function dim2_init(), on a real matrix, $A$, dim2_multi_inv will reconstruct $A$. The reconstructed matrix is referred to as $B$ in the following since it will not be identical to $A$ when the DWT coefficients have been filtered or otherwise manipulated prior to reconstruction. If the original input matrix is level $0$, then it is possible to terminate reconstruction at a higher level by specifying fewer than the number of levels used in the call to dim2_multi_fwd(). This results in a partial reconstruction.