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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 2.7 in How to Use the NAG Library and its Documentation).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
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.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

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.