naginterfaces.library.wav.dim1_​multi_​inv

naginterfaces.library.wav.dim1_multi_inv(nwlinv, c, n, comm)

dim1_multi_inv computes the inverse one-dimensional multi-level discrete wavelet transform (DWT). This function reconstructs data from (possibly filtered or otherwise manipulated) wavelet transform coefficients calculated by dim1_multi_fwd() from an original set of data. The initialization function dim1_init() must be called first to set up the DWT options.

For full information please refer to the NAG Library document for c09cd

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/c09/c09cdf.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 dim1_multi_fwd(). The data will be reconstructed to level $(\text{nwl}-nwlinv)$, where level $0$ is the original input dataset provided to dim1_multi_fwd().

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

The coefficients of a multi-level wavelet transform of the dataset.

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 $k_{\text{j}+1}=k_{\text{j}}+q(n_{fwd}-\text{j}+1)$, for $\text{j}=1,2,\dots ,n_{fwd}$, 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 $\text{i}=k_1+1,\dots ,k_2$

Contains the level $n_{fwd}$ detail coefficients $d_{n_{fwd}}$.

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

Contains the level $n_{fwd}-\text{j}+1$ detail coefficients, for $\text{j}=2,3,\dots ,n_{fwd}$.

The values $q\left(\text{i}\right)$, for $\text{i}=n_{fwd},\dots ,1$, are contained in $\text{dwtlev}$ which is produced as output by a preceding call to dim1_multi_fwd().

See dim1_multi_fwd() for details.

nint

$n$, the length of the data array, $y$, to be reconstructed. For a full reconstruction of $\text{nwl}$ levels, where $\text{nwl}$ is as supplied to dim1_multi_fwd(), this must be the same as argument $\text{n}$ used in the call to dim1_multi_fwd(). For a partial reconstruction of $nwlinv<\text{nwl}$, this must be equal to $\text{dwtlev}[nwlinv+1]$, as returned from dim1_multi_fwd().

commdict, communication object

Communication structure.

This argument must have been initialized by a prior call to dim1_init().

Returns

yfloat, ndarray, shape $\left(n\right)$

The dataset reconstructed from the multi-level wavelet transform coefficients and the transformation options supplied to the initialization function dim1_init().

Raises

NagValueError

(errno $1$)

On entry, $nwlinv$ is larger than the number of levels computed by the preceding call to dim1_multi_fwd(): $nwlinv=⟨value⟩$, expected $=⟨value⟩$.

(errno $1$)

On entry, $nwlinv=⟨value⟩$.

Constraint: $nwlinv\ge 1$.

(errno $2$)

On entry, $\text{lenc}$ is set too small: $\text{lenc}=⟨value⟩$.

Constraint: $\text{lenc}\ge ⟨value⟩$.

(errno $4$)

On entry, $n$ is inconsistent with the value passed to the initialization function: $n=⟨value⟩$, $n$ should be $⟨value⟩$.

(errno $6$)

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

(errno $6$)

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

Notes

dim1_multi_inv performs the inverse operation of dim1_multi_fwd(). That is, given a set of wavelet coefficients, computed up to level $n_{fwd}$ by dim1_multi_fwd() using a DWT as set up by the initialization function dim1_init(), on a real data array of length $n$, dim1_multi_inv will reconstruct the data array $y_{\text{i}}$, for $\text{i}=1,2,\dots ,n$, from which the coefficients were derived. If the original input dataset 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 dim1_multi_fwd(). This results in a partial reconstruction.