NAG Library Function Document

nag_imodwt (c09dbc)

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

1 Purpose

nag_imodwt (c09dbc) computes the inverse one-dimensional maximal overlap discrete wavelet transform (MODWT) at a single level. The initialization function nag_wfilt (c09aac) must be called first to set up the MODWT options.

2 Specification

#include <nag.h>

#include <nagc09.h>

void	nag_imodwt (Integer lenc, const double ca[], const double cd[], Integer n, double y[], const Integer icomm[], NagError *fail)

3 Description

nag_imodwt (c09dbc) performs the inverse operation of nag_modwt (c09dac). That is, given sets of

n_{c}

approximation coefficients and detail coefficients, computed by nag_modwt (c09dac) using a MODWT as set up by the initialization function nag_wfilt (c09aac), on a real data array of length

n

, nag_imodwt (c09dbc) will reconstruct the data array

y_{i}

, for

i = 1, 2, \dots, n

, from which the coefficients were derived.

4 References

Percival D B and Walden A T (2000) Wavelet Methods for Time Series Analysis Cambridge University Press

5 Arguments

1: lenc – IntegerInput: On entry: the dimension of the arrays ca and cd.
Constraint: $lenc \geq n_{c}$ , where $n_{c}$ is the value returned in nwc by the call to the initialization function nag_wfilt (c09aac).
2: ca[lenc] – const doubleInput: On entry: the $n_{c}$ approximation coefficients, $C_{a}$ . These will normally be the result of some transformation on the coefficients computed by nag_modwt (c09dac).
3: cd[lenc] – const doubleInput: On entry: the $n_{c}$ detail coefficients, $C_{d}$ . These will normally be the result of some transformation on the coefficients computed by nag_modwt (c09dac).
4: n – IntegerInput: On entry: $n$ , the length of the original data array from which the wavelet coefficients were computed by nag_modwt (c09dac) and the length of the data array y that is to be reconstructed by this function.
Constraint: This must be the same as the value n passed to the initialization function nag_wfilt (c09aac).
5: y[n] – doubleOutput: On exit: the reconstructed data based on approximation and detail coefficients $C_{a}$ and $C_{d}$ and the transform 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 and, possibly, additional information on the previously computed forward transform.
7: fail – NagError *Input/Output: The NAG error argument (see Section 3.6 in the Essential Introduction).

6 Error Indicators and Warnings

NE_ARRAY_DIM_LEN: On entry, array dimension lenc not large enough: $lenc = ⟨value⟩$ but must be at least $⟨value⟩$ .
NE_BAD_PARAM: On entry, argument $⟨value⟩$ had an illegal value.
NE_INITIALIZATION: On entry, n is inconsistent with the value passed to the initialization function: $n = ⟨value⟩$ , n should be $⟨value⟩$ .
On entry, the initialization function nag_wfilt (c09aac) has not been called first or it has not been called with $wtrans = Nag_MODWTSingle$ , or the communication array icomm has become corrupted.
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

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.