NAG Library Routine Document

C09CDF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     NWL – INTEGERInput

On entry: the number, nl, of levels to be used in the inverse multi-level transform. The number of levels must be the same as the number used in the computation of the wavelet coefficients.

Constraint: NWL=nl, where nl is the value of NWL used in a preceding call to C09CCF.

2:     LENC – INTEGERInput

On entry: the dimension of the array C as declared in the (sub)program from which C09CDF is called.

Constraint: LENC≥nc, where nc is the number of approximation and detail coefficients that correspond to a transform with NWL levels and is unchanged from the preceding call to C09CCF.

3:     C(LENC) – double precision arrayInput

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

If nanl and ndi, for i=nl,nl-1,…,1, are the numbers of approximation and detail coefficients, then setting k1=nanl and kj+1=nanl+ ∑ i=1 j n d nl -i+1 , for j=1,2,…,nl, the coefficients are stored in C as follows:

C1:k1

Contains the level nl approximation coefficients, anl.

Ck1+1:k2

Contains the level nl detail coefficients dnl.

Ckj+1:kj+1

Contains the level nl-j+1 detail coefficients, for j=2,…,nl.

The values nanl and ndnl-i+1, for i=1,2,…,nl are contained in DWTLEV which is produced as output by a preceding call to C09CCF. See C09CCF for details.

4:     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 routine C09AAF.

5:     Y(N) – double precision arrayOutput

On exit: the dataset reconstructed from the multi-level wavelet transform coefficients and the transformation options supplied to the initialization routine C09AAF.

6:     ICOMM(100) – INTEGER arrayCommunication Array

On entry: contains details of the discrete wavelet transform and the problem dimension for the forward transform previously computed by C09CCF.

7:     IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to 0, -1​ or ​1. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

On exit: IFAIL=0 unless the routine detects an error (see Section 6).

For environments where it might be inappropriate to halt program execution when an error is detected, the value -1​ or ​1 is recommended. If the output of error messages is undesirable, then the value 1 is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is 0. When the value -1​ or ​1 is used it is essential to test the value of IFAIL on exit.

6  Error Indicators and Warnings

IFAIL=1

On entry,	NWL<1,
or	NWL>nl, the maximum number of levels as returned in NWL by the call to the initialization routine C09AAF.
or	NWL> the number of levels used in the computation of the wavelet coefficients by a call to C09CCF.

IFAIL=2

On entry, LENC is too small. LENC must be at least the number of wavelet coefficients required for a transform operating on NWL levels. If NWL=nl, the maximum number of levels as returned in NWL by the initial call to C09AAF, then LENC must be at least nc, the value returned in NWC by the same call to C09AAF.

IFAIL=4

On entry, N is inconsistent with the value passed in the call to the initialization routine C09AAF.

IFAIL=6

On entry, the initialization routine C09AAF has not been called first or it has been called with WTRANS='S', or the communication array ICOMM has become corrupted.

7  Accuracy

8  Further Comments

9  Example