nag_imldwt (c09cdc) (PDF version)
c09 Chapter Contents
c09 Chapter Introduction
NAG Library Manual

NAG Library Function Document

nag_imldwt (c09cdc)

+ Contents

    1  Purpose
    7  Accuracy
    10  Example

1  Purpose

nag_imldwt (c09cdc) computes the inverse one-dimensional multi-level discrete wavelet transform (DWT). This function reconstructs data from (possibly filtered or otherwise manipulated) wavelet transform coefficients calculated by nag_mldwt (c09ccc) from an original set of data. The initialization function nag_wfilt (c09aac) must be called first to set up the DWT options.

2  Specification

#include <nag.h>
#include <nagc09.h>
void  nag_imldwt (Integer nwlinv, Integer lenc, const double c[], Integer n, double y[], const Integer icomm[], NagError *fail)

3  Description

nag_imldwt (c09cdc) performs the inverse operation of nag_mldwt (c09ccc). That is, given a set of wavelet coefficients, computed up to level nfwd by nag_mldwt (c09ccc) using a DWT as set up by the initialization function nag_wfilt (c09aac), on a real data array of length n, nag_imldwt (c09cdc) will reconstruct the data array yi, for i=1,2,,n, from which the coefficients were derived. If the original input dataset is level 0, then it is possible to terminate reconstruction at a higher level by specifying fewer than the number of levels used in the call to nag_mldwt (c09ccc). This results in a partial reconstruction.

4  References


5  Arguments

1:     nwlinvIntegerInput
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 nfwd, 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 nwl-nwlinv, where level 0 is the original input dataset provided to nag_mldwt (c09ccc).
Constraint: 1nwlinvnfwd, where nfwd is the value used in a preceding call to nag_mldwt (c09ccc).
2:     lencIntegerInput
On entry: the dimension of the array c.
Constraint: lencnc, where nc 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:     c[lenc]const doubleInput
On entry: the coefficients of a multi-level wavelet transform of the dataset.
Let qi be the number of coefficients (of each type) at level i, for i=nfwd,nfwd-1,,1. Then, setting k1=qnfwd and kj+1=kj+qnfwd-j+1, for j=1,2,,nfwd, the coefficients are stored in c as follows:
c[i-1], for i=1,2,,k1
Contains the level nfwd approximation coefficients, anfwd.
c[i-1], for i=k1+1,,k2
Contains the level nfwd detail coefficients dnfwd.
c[i-1], for i=kj+1,,kj+1
Contains the level nfwd-j+1 detail coefficients, for j=2,3,,nfwd.
The values qi, for i=nfwd,nfwd-1,,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:     nIntegerInput
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 nwlinv<nwl, this must be equal to dwtlev[nwlinv+1], as returned from nag_mldwt (c09ccc).
5:     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).
6:     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_mldwt (c09ccc).
7:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

Dynamic memory allocation failed.
On entry, lenc is set too small: lenc=value.
Constraint: lencvalue.
On entry, argument value had an illegal value.
Either the initialization function has not been called first or array icomm has been corrupted.
Either the initialization function was called with wtrans=Nag_SingleLevel or array icomm has been corrupted.
On entry, n is inconsistent with the value passed to the initialization function: n=value, n should be value.
On entry, nwlinv=value.
Constraint: nwlinv1.
On entry, nwlinv is larger than the number of levels computed by the preceding call to nag_mldwt (c09ccc): nwlinv=value, expected =value.
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

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  Parallelism and Performance

Not applicable.

9  Further Comments


10  Example

See Section 10 in nag_mldwt (c09ccc).

nag_imldwt (c09cdc) (PDF version)
c09 Chapter Contents
c09 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2014