NAG Toolbox: nag_wav_1d_mxolap_fwd (c09da)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{x}\left(\mathbf{n}\right)$ – double array

x contains the input dataset $x_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$.

2:     $\mathrm{lenc}$ – int64int32nag_int scalar

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 nag_wav_1d_init (c09aa). 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: $\mathbf{lenc}\ge n_c$, where $n_c$ is the value returned in nwc by the call to the initialization function nag_wav_1d_init (c09aa).

3:     $\mathrm{icomm}\left(100\right)$ – int64int32nag_int array

Contains details of the discrete wavelet transform and the problem dimension as setup in the call to the initialization function nag_wav_1d_init (c09aa).

Optional Input Parameters

1:     $\mathrm{n}$ – int64int32nag_int scalar

Default: the dimension of the array x.

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 nag_wav_1d_init (c09aa).

Output Parameters

1:     $\mathrm{ca}\left(\mathbf{lenc}\right)$ – double array

$\mathbf{ca}\left(i\right)$ contains the $i$th approximation coefficient, $C_a\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,n_c$.

2:     $\mathrm{cd}\left(\mathbf{lenc}\right)$ – double array

$\mathbf{cd}\left(\mathit{i}\right)$ contains the $\mathit{i}$th detail coefficient, $C_d\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,n_c$.

3:     $\mathrm{icomm}\left(100\right)$ – int64int32nag_int array

Contains additional information on the computed transform.

4:     $\mathrm{ifail}$ – int64int32nag_int scalar

$\mathbf{ifail}=\mathbf{0}$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

   $\mathbf{ifail}=1$

On entry, n is inconsistent with the value passed to the initialization function.

   $\mathbf{ifail}=3$

On entry, array dimension lenc not large enough.

   $\mathbf{ifail}=6$

On entry, the initialization function nag_wav_1d_init (c09aa) has not been called first or it has not been called with $\mathbf{wtrans}=\text{'T'}$, or the communication array icomm has become corrupted.

   $\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

   $\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

   $\mathbf{ifail}=-999$

Dynamic memory allocation failed.

Accuracy

Further Comments

Example

Open in the MATLAB editor: c09da_example

function c09da_example


fprintf('c09da example results\n\n');

% 1d maximal overlap discrete wavelet decomposition using a Daubechies wavelet

n      = int64(8);
x      = [1 3 5 7 6 4 5 2];

wavnam = 'DB4';
mode   = 'Periodic';
wtrans = 'Time invariant';

% Setup for wavelet
[nwlmax, nf, nwc, icomm, ifail] = c09aa(wavnam, wtrans, mode, n);

% Compute decomposition
[ca, cd, icomm, ifail] = c09da(x, nwc, icomm);

disp('Approximation coefficients:')
fprintf('%8.4f',ca);
fprintf('\n');
disp('Detail coefficients:')
fprintf('%8.4f',cd);
fprintf('\n');

% Reconstruct
[y, ifail] = c09db(ca, cd, n, icomm);
disp('Reconstruction:')
fprintf('%8.4f',y);
fprintf('\n');

c09da example results

Approximation coefficients:
  2.7781  1.5146  2.2505  4.8788  6.6845  6.3423  4.7869  3.7644
Detail coefficients:
 -0.6187  0.6272  0.1883 -1.1966  1.2618  0.3354 -0.3314 -0.2660
Reconstruction:
  1.0000  3.0000  5.0000  7.0000  6.0000  4.0000  5.0000  2.0000