NAG Library Function Document

nag_imldwt (c09cdc)

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Purpose

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Specification

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Description

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References

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Arguments

1:    $\mathbf{nwlinv}$ – IntegerInput

On entry: the number of levels to be used in the inverse multi-level transform. The number of levels must be less than or equal to $n_{\mathrm{fwd}}$, which has the value of argument nwl as used in the computation of the wavelet coefficients using nag_mldwt (c09ccc). The data will be reconstructed to level $\left(\mathbf{nwl}-\mathbf{nwlinv}\right)$, where level $0$ is the original input dataset provided to nag_mldwt (c09ccc).

Constraint: $1\le \mathbf{nwlinv}\le n_{\mathrm{fwd}}$, where $n_{\mathrm{fwd}}$ is the value used in a preceding call to nag_mldwt (c09ccc).

2:    $\mathbf{lenc}$ – IntegerInput

On entry: the dimension of the array c.

Constraint: $\mathbf{lenc}\ge n_c$, where $n_c$ is the total number of coefficients that correspond to a transform with nwlinv levels and is unchanged from the preceding call to nag_mldwt (c09ccc).

3:    $\mathbf{c}\left[\mathbf{lenc}\right]$ – const doubleInput

On entry: the coefficients of a multi-level wavelet transform of the dataset.

Let $q\left(\mathit{i}\right)$ be the number of coefficients (of each type) at level $\mathit{i}$, for $\mathit{i}=n_{\mathrm{fwd}},n_{\mathrm{fwd}}-1,\dots ,1$. Then, setting $k_1=q\left(n_{\mathrm{fwd}}\right)$ and $k_{\mathit{j}+1}=k_{\mathit{j}}+q\left(n_{\mathrm{fwd}}-\mathit{j}+1\right)$, for $\mathit{j}=1,2,\dots ,n_{\mathrm{fwd}}$, the coefficients are stored in c as follows:

$\mathbf{c}\left[\mathit{i}-1\right]$, for $\mathit{i}=1,2,\dots ,k_1$

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

$\mathbf{c}\left[\mathit{i}-1\right]$, for $\mathit{i}=k_1+1,\dots ,k_2$

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

$\mathbf{c}\left[\mathit{i}-1\right]$, for $\mathit{i}=k_j+1,\dots ,k_{j+1}$

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

The values $q\left(\mathit{i}\right)$, for $\mathit{i}=n_{\mathrm{fwd}},n_{\mathrm{fwd}}-1,\dots ,1$, are contained in dwtlev which is produced as output by a preceding call to nag_mldwt (c09ccc). See nag_mldwt (c09ccc) for details.

4:    $\mathbf{n}$ – IntegerInput

On entry: $n$, the length of the data array, $y$, to be reconstructed. For a full reconstruction of nwl levels, where nwl is as supplied to nag_mldwt (c09ccc), this must be the same as argument n used in the call to nag_mldwt (c09ccc). For a partial reconstruction of $\mathbf{nwlinv}<\mathbf{nwl}$, this must be equal to $\mathbf{dwtlev}\left[\mathbf{nwlinv}+1\right]$, as returned from nag_mldwt (c09ccc).

5:    $\mathbf{y}\left[\mathbf{n}\right]$ – doubleOutput

On exit: the dataset reconstructed from the multi-level wavelet transform coefficients and the transformation options supplied to the initialization function nag_wfilt (c09aac).

6:    $\mathbf{icomm}\left[100\right]$ – const IntegerCommunication Array

On entry: contains details of the discrete wavelet transform and the problem dimension for the forward transform previously computed by nag_mldwt (c09ccc).

7:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_ARRAY_DIM_LEN

On entry, lenc is set too small: $\mathbf{lenc}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lenc}\ge 〈\mathit{\text{value}}〉$.

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 array icomm has been corrupted.

Either the initialization function was called with $\mathbf{wtrans}=\mathrm{Nag\_SingleLevel}$ or array icomm has been corrupted.

On entry, n is inconsistent with the value passed to the initialization function: $\mathbf{n}=〈\mathit{\text{value}}〉$, n should be $〈\mathit{\text{value}}〉$.

NE_INT_2

On entry, $\mathbf{nwlinv}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nwlinv}\ge 1$.

On entry, nwlinv is larger than the number of levels computed by the preceding call to nag_mldwt (c09ccc): $\mathbf{nwlinv}=〈\mathit{\text{value}}〉$, expected $=〈\mathit{\text{value}}〉$.

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.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

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Accuracy

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Parallelism and Performance

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Further Comments

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Example