NAG Library Function Document

nag_imlmodwt (c09ddc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     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:     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:     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:     c[lenc] – 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:     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:     y[n] – 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:     icomm[$100$] – 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:     fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.

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.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example