C09CBF (PDF version)
C09 Chapter Contents
C09 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

C09CBF

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

+− Contents

    1  Purpose
    2  Specification
    3  Description
    4  References
    5  Parameters
    6  Error Indicators and Warnings
    7  Accuracy
    8  Further Comments
    9  Example

1  Purpose

C09CBF computes the inverse one-dimensional discrete wavelet transform (DWT) at a single level. The initialization routine C09AAF must be called first to set up the DWT options.

2  Specification

SUBROUTINE C09CBF (LENC, CA, CD, N, Y, ICOMM, IFAIL)
INTEGERLENC, N, ICOMM(100), IFAIL
double precisionCA(LENC), CD(LENC), Y(N)

3  Description

C09CBF performs the inverse operation of C09CAF. That is, given sets of nc approximation coefficients and detail coefficients, computed by C09CAF using a DWT as set up by the initialization routine C09AAF, on a real data array of length n, C09CBF will reconstruct the data array yi, for i=1,2,…,n, from which the coefficients were derived.

4  References

None.

5  Parameters

1:     LENC – INTEGERInput
On entry: the dimension of the arrays CA and CD as declared in the (sub)program from which C09CBF is called.
Constraint: LENC≥nc, where nc is the value returned in NWC by the call to the initialization routine C09AAF.
2:     CA(LENC) – double precision arrayInput
On entry: the nc approximation coefficients, Ca. These will normally be the result of some transformation on the coefficients computed by C09CAF.
3:     CD(LENC) – double precision arrayInput
On entry: the nc detail coefficients, Cd. These will normally be the result of some transformation on the coefficients computed by C09CAF.
4:     N – INTEGERInput
On entry: n, the length of the original data array from which the wavelet coefficients were computed by C09CAF and the length of the data array Y that is to be reconstructed by this routine.
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 reconstructed data based on approximation and detail coefficients Ca and Cd and the transform 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 and, possibly, additional information on the previously computed forward transform.
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

If on entry IFAIL=0 or -1, explanatory error messages are output on the current error message unit (as defined by X04AAF).
Errors or warnings detected by the routine:
IFAIL=1
On entry, LENC<nc, where nc is the value returned in NWC by the call to the initialization routine C09AAF.
IFAIL=4
On entry, N is inconsistent with the value passed 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='M', or the communication array ICOMM has become corrupted.

7  Accuracy

The accuracy of the wavelet transform depends only on the floating point operations used in the convolution and downsampling and should thus be close to machine precision.

8  Further Comments

None.

9  Example

See Section 9 in C09CAF.
C09CBF (PDF version)
C09 Chapter Contents
C09 Chapter Introduction
NAG Library Manual
© The Numerical Algorithms Group Ltd, Oxford, UK. 2009