c09dac computes the one-dimensional maximal overlap discrete wavelet transform (MODWT) at a single level. The initialization function c09aac must be called first to set up the MODWT options.

2 Specification

#include <nag.h>

void	c09dac (Integer n, const double x[], Integer lenc, double ca[], double cd[], Integer icomm[], NagError *fail)

The function may be called by the names: c09dac, nag_wav_dim1_mxolap_fwd or nag_modwt.

3 Description

c09dac computes the one-dimensional MODWT of a given input data array,

x_{i}

, for

i = 1, 2, \dots, n

, at a single level. For a chosen wavelet filter pair, the output coefficients are obtained by applying convolution to the input,

x

. The approximation (or smooth) coefficients,

C_{a}

, are produced by the low pass filter and the detail coefficients,

C_{d}

, by the high pass filter. Periodic (circular) convolution is available as an end extension method for application to finite data sets. The number

n_{c}

, of coefficients

C_{a}

C_{d}

is returned by the initialization function c09aac.

4 References

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

5 Arguments

1: $n$ – Integer Input: On entry: the number of elements, $n$ , in the data array $x$ .

Constraint: this must be the same as the value n passed to the initialization function c09aac.
2: $x [n]$ – const double Input: On entry: x contains the input dataset $x_{i}$ , for $i = 1, 2, \dots, n$ .
3: $lenc$ – Integer Input: On entry: the dimension of the arrays ca and cd. This must be at least the number, $n_{c}$ , of approximation coefficients, $C_{a}$ , and detail coefficients, $C_{d}$ , of the discrete wavelet transform as returned in nwc by the call to the initialization function c09aac. Note that $n_{c} = n$ for periodic end extension, but this is not the case for other end extension methods which will be available in future releases.

Constraint: $lenc \geq n_{c}$ , where $n_{c}$ is the value returned in nwc by the call to the initialization function c09aac.
4: $ca [lenc]$ – double Output: On exit: $ca [i - 1]$ contains the $i$ th approximation coefficient, $C_{a} (i)$ , for $i = 1, 2, \dots, n_{c}$ .
5: $cd [lenc]$ – double Output: On exit: $cd [i - 1]$ contains the $i$ th detail coefficient, $C_{d} (i)$ , for $i = 1, 2, \dots, n_{c}$ .
6: $icomm [100]$ – Integer Communication Array: On entry: contains details of the discrete wavelet transform and the problem dimension as setup in the call to the initialization function c09aac.

On exit: contains additional information on the computed transform.
7: $fail$ – NagError * Input/Output: The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface 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 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.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface 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.

8 Parallelism and Performance

c09dac is not threaded in any implementation.

9 Further Comments

None.

10 Example

This example computes the one-dimensional maximal overlap discrete wavelet decomposition for

8

values using the Daubechies wavelet,

wavnam = Nag_Daubechies4

c09da: FL CL CPP AD

NAG CL Interfacec09dac (dim1_​mxolap_​fwd)

▸▿ 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

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG CL Interface
c09dac (dim1_mxolap_fwd)