NAG Toolbox: nag_wav_1d_sngl_inv (c09cb)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

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

The $n_c$ approximation coefficients, $C_a$. These will normally be the result of some transformation on the coefficients computed by nag_wav_1d_sngl_fwd (c09ca).

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

The $n_c$ detail coefficients, $C_d$. These will normally be the result of some transformation on the coefficients computed by nag_wav_1d_sngl_fwd (c09ca).

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

$n$, the length of the original data array from which the wavelet coefficients were computed by nag_wav_1d_sngl_fwd (c09ca) 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_wav_1d_init (c09aa).

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

Contains details of the discrete wavelet transform and the problem dimension and, possibly, additional information on the previously computed forward transform.

Optional Input Parameters

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

Default: the dimension of the arrays ca, cd. (An error is raised if these dimensions are not equal.)

The dimension of the arrays ca and cd.

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).

Output Parameters

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

The reconstructed data based on approximation and detail coefficients $C_a$ and $C_d$ and the transform options supplied to the initialization function nag_wav_1d_init (c09aa).

2:     $\mathrm{ifail}$ – 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, array dimension lenc not large enough.

   $\mathbf{ifail}=4$

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

   $\mathbf{ifail}=6$

Either the initialization function has not been called first or array icomm has been corrupted.

Either the initialization function was called with $\mathbf{wtrans}=\text{'M'}$ or array icomm has been 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: c09cb_example

function c09cb_example


fprintf('c09cb example results\n\n');

n = int64(8);
wavnam = 'DB4';
mode = 'zero';
wtrans = 'Single Level';
x = [1; 3; 5; 7; 6; 4; 5; 2];
fprintf('\n Input Data:\n');
fprintf('%8.4f ', x);
fprintf('\n');

% Query wavelet filter dimensions
[nwl, nf, nwc, icomm, ifail] = c09aa(wavnam, wtrans, mode, n);

if ifail == int64(0)
  % Compute the transform
  [ca, cd, icomm, ifail] = c09ca(x, nwc, icomm);

  if ifail == int64(0)
    fprintf(' Approximation coefficients CA :\n');
    fprintf('%8.4f ', ca);
    fprintf('\n');
    fprintf(' Detail coefficients        CD :\n');
    fprintf('%8.4f ', cd);
    fprintf('\n');

    % Reconstruct original data
    [y, ifail] = c09cb(ca, cd, n, icomm);

    if ifail == int64(0)
      fprintf(' Reconstruction       Y : \n');
      fprintf('%8.4f ', y);
      fprintf('\n');
    end
  end
end

c09cb example results


 Input Data:
  1.0000   3.0000   5.0000   7.0000   6.0000   4.0000   5.0000   2.0000 
 Approximation coefficients CA :
  0.0011  -0.0043  -0.0174   4.4778   8.9557   7.3401   2.5816 
 Detail coefficients        CD :
  0.0237   0.0410  -0.5966   1.7763  -0.7517   0.3332  -0.1188 
 Reconstruction       Y : 
  1.0000   3.0000   5.0000   7.0000   6.0000   4.0000   5.0000   2.0000