NAG Library Function Document

nag_imlmodwt (c09ddc)

1  Purpose

2  Specification

3  Description

4  References

5  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_mlmodwt (c09dcc). The data will be reconstructed to level $\left(\mathbf{nwl}-\mathbf{nwlinv}\right)$, where level $0$ is the original input dataset provided to nag_mlmodwt (c09dcc).

Constraint: $1\le \mathbf{nwlinv}\le n_{\mathrm{fwd}}$, where $n_{\mathrm{fwd}}$ is the value used in a preceding call to nag_mlmodwt (c09dcc).

2:    $\mathbf{keepa}$ – Nag_WaveletCoefficientsInput

On entry: determines whether the approximation coefficients are stored in array c for every level of the computed transform or else only for the final level. In both cases, the detail coefficients are stored in c for every level computed.

$\mathbf{keepa}=\mathrm{Nag\_StoreAll}$

Retain approximation coefficients for all levels computed.

$\mathbf{keepa}=\mathrm{Nag\_StoreFinal}$

Retain approximation coefficients for only the final level computed.

Constraint: $\mathbf{keepa}=\mathrm{Nag\_StoreAll}$ or $\mathrm{Nag\_StoreFinal}$.

3:    $\mathbf{lenc}$ – IntegerInput

On entry: the dimension of the array c.

Constraints:

• if $\mathbf{keepa}=\mathrm{Nag\_StoreFinal}$, $\mathbf{lenc}\ge \left(n_{\mathrm{l}}+1\right)\times n_a$;
• if $\mathbf{keepa}=\mathrm{Nag\_StoreAll}$, $\mathbf{lenc}\ge 2\times n_l\times n_a$, where $n_a$ is the number of approximation or detail coefficients at each level and is unchanged from the preceding call to nag_mlmodwt (c09dcc).

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

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

The coefficients are stored in c as follows:

If $\mathbf{keepa}=\mathrm{Nag\_StoreFinal}$,

$\mathbf{C}\left(1:n_a\right)$

Contains the level $n_l$ approximation coefficients;

$\mathbf{C}\left(n_a+\left(i-1\right)\times n_d+1:n_a+i\times n_d\right)$

Contains the level $\left(n_l-\mathit{i}+1\right)$ detail coefficients, for $\mathit{i}=1,2,\dots ,n_l$;

If $\mathbf{keepa}=\mathrm{Nag\_StoreAll}$,

$\mathbf{C}\left(\left(i-1\right)\times n_a+1:i\times n_a\right)$

Contains the level $\left(n_l-\mathit{i}+1\right)$ approximation coefficients, for $\mathit{i}=1,2,\dots ,n_l$;

$\mathbf{C}\left(n_l\times n_a+\left(i-1\right)\times n_d+1:n_l\times n_a+i\times n_d\right)$

Contains the level $\mathit{i}$ detail coefficients, for $\mathit{i}=1,2,\dots ,n_l$.

The values $n_a$ and $n_d$ denote the numbers of approximation and detail coefficients respectively, which are equal. This number is returned as output in na from a preceding call to nag_mlmodwt (c09dcc). See nag_mlmodwt (c09dcc) for details.

5:    $\mathbf{n}$ – IntegerInput

On entry: $n$, the length of the data array, $y$, to be reconstructed.

Constraint: This must be the same as the value n passed to the initialization function nag_wfilt (c09aac).

6:    $\mathbf{y}\left[\mathbf{n}\right]$ – 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).

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

On entry: contains details of the discrete wavelet transform and the problem dimension for the forward transform previously computed by nag_mlmodwt (c09dcc).

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

The NAG error argument (see Section 2.7 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

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

On entry, the initialization function nag_wfilt (c09aac) has not been called first or it has not been called with $\mathbf{wtrans}=\mathrm{Nag\_MODWTMulti}$, or the communication array icomm has become corrupted.

NE_INT

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

NE_INT_2

On entry, nwlinv is larger than the number of levels computed by the preceding call to nag_mlmodwt (c09dcc): $\mathbf{nwlinv}=〈\mathit{\text{value}}〉$, 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.

An unexpected error has been triggered by this function. Please contact NAG.
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.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example