NAG Toolbox: nag_wav_2d_sngl_fwd (c09ea)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{a}\left(\mathit{lda},\mathbf{n}\right)$ – double array

lda, the first dimension of the array, must satisfy the constraint $\mathit{lda}\ge \mathbf{m}$.

The $m$ by $n$ data matrix $A$.

2:     $\mathrm{icomm}\left(180\right)$ – 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_2d_init (c09ab).

Optional Input Parameters

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

Default: the first dimension of the array a.

Number of rows, $m$, of data matrix $A$.

Constraint: this must be the same as the value m passed to the initialization function nag_wav_2d_init (c09ab).

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

Default: the second dimension of the array a.

Number of columns, $n$, of data matrix $A$.

Constraint: this must be the same as the value n passed to the initialization function nag_wav_2d_init (c09ab).

Output Parameters

1:     $\mathrm{ca}\left(\mathit{ldca},:\right)$ – double array

The first dimension of the array ca will be $n_{\mathrm{cm}}$ where $n_{\mathrm{cm}}=n_{\mathrm{ct}}/\left(4n_{\mathrm{cn}}\right)$ and $n_{\mathrm{cn}}$, $n_{\mathrm{ct}}$ are returned by the initialization function nag_wav_2d_init (c09ab).

The second dimension of the array ca will be $\mathit{ncn}$ where $n_{\mathrm{cn}}$ is the argument nwcn returned by function nag_wav_2d_init (c09ab).

Contains the $n_{\mathrm{cm}}$ by $n_{\mathrm{cn}}$ matrix of approximation coefficients, $C_a$.

2:     $\mathrm{ch}\left(\mathit{ldch},:\right)$ – double array

The first dimension of the array ch will be $n_{\mathrm{cm}}$ where $n_{\mathrm{cm}}=n_{\mathrm{ct}}/\left(4n_{\mathrm{cn}}\right)$ and $n_{\mathrm{cn}}$, $n_{\mathrm{ct}}$ are returned by the initialization function nag_wav_2d_init (c09ab).

The second dimension of the array ch will be $\mathit{ncn}$ where $n_{\mathrm{cn}}$ is the argument nwcn returned by function nag_wav_2d_init (c09ab).

Contains the $n_{\mathrm{cm}}$ by $n_{\mathrm{cn}}$ matrix of horizontal coefficients, $C_h$.

3:     $\mathrm{cv}\left(\mathit{ldcv},:\right)$ – double array

The first dimension of the array cv will be $n_{\mathrm{cm}}$ where $n_{\mathrm{cm}}=n_{\mathrm{ct}}/\left(4n_{\mathrm{cn}}\right)$ and $n_{\mathrm{cn}}$, $n_{\mathrm{ct}}$ are returned by the initialization function nag_wav_2d_init (c09ab).

The second dimension of the array cv will be $\mathit{ncn}$ where $n_{\mathrm{cn}}$ is the argument nwcn returned by function nag_wav_2d_init (c09ab).

Contains the $n_{\mathrm{cm}}$ by $n_{\mathrm{cn}}$ matrix of vertical coefficients, $C_v$.

4:     $\mathrm{cd}\left(\mathit{ldcd},:\right)$ – double array

The first dimension of the array cd will be $n_{\mathrm{cm}}$ where $n_{\mathrm{cm}}=n_{\mathrm{ct}}/\left(4n_{\mathrm{cn}}\right)$ and $n_{\mathrm{cn}}$, $n_{\mathrm{ct}}$ are returned by the initialization function nag_wav_2d_init (c09ab).

The second dimension of the array cd will be $\mathit{ncn}$ where $n_{\mathrm{cn}}$ is the argument nwcn returned by function nag_wav_2d_init (c09ab).

Contains the $n_{\mathrm{cm}}$ by $n_{\mathrm{cn}}$ matrix of diagonal coefficients, $C_d$.

5:     $\mathrm{icomm}\left(180\right)$ – int64int32nag_int array

Communication array, used to store information between calls to nag_wav_2d_sngl_fwd (c09ea).

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

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

Error Indicators and Warnings

   $\mathbf{ifail}=1$

Constraint: $\mathbf{m}=\_$, the value of m on initialization (see nag_wav_2d_init (c09ab)).

Constraint: $\mathbf{n}=\_$, the value of n on initialization (see nag_wav_2d_init (c09ab)).

   $\mathbf{ifail}=2$

Constraint: $\mathit{lda}\ge \mathbf{m}$.

   $\mathbf{ifail}=3$

ldca is too small, the number of wavelet coefficients in the first dimension.

ldcd is too small, the number of wavelet coefficients in the first dimension.

ldch is too small, the number of wavelet coefficients in the first dimension.

ldcv is too small, the number of wavelet coefficients in the first dimension.

   $\mathbf{ifail}=6$

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

Either the initialization function was called with $\mathbf{wtrans}=\text{'M'}$ or 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: c09ea_example

function c09ea_example


fprintf('c09ea example results\n\n');

m = int64(6);
n = int64(6);
wavnam = 'DB4';
mode = 'Half';
wtrans = 'Single level';
a = [8, 7, 3, 3, 1, 1;
     4, 6, 1, 5, 2, 9;
     8, 1, 4, 9, 3, 7;
     9, 3, 8, 2, 4, 3;
     1, 3, 7, 1, 5, 2;
     4, 3, 7, 7, 6, 1];






fprintf('\nInput data a:\n');
disp(a);
[nwl, nf, nwct, nwcn, icomm, ifail] = c09ab(wavnam, wtrans, mode, m, n);

nwcm = double(nwct)/(4*double(nwcn));

% Perform Discrete Wavelet transform
[ca, ch, cv, cd, ifail] = c09ea(a, icomm);

fprintf('Approximation coefficients    CA:\n');
disp(ca);
fprintf('Diagonal coefficients         CD:\n');
disp(cd);
fprintf('Horizontal coefficients       CH:\n');
disp(ch);
fprintf('Vertical coefficients         CV:\n');
disp(cv);

% Reconstruct original data
[b, ifail] = c09eb(m, n, ca, ch, cv, cd, icomm);
fprintf('Reconstruction       b:\n');
disp(b);

c09ea example results


Input data a:
     8     7     3     3     1     1
     4     6     1     5     2     9
     8     1     4     9     3     7
     9     3     8     2     4     3
     1     3     7     1     5     2
     4     3     7     7     6     1

Approximation coefficients    CA:
    6.3591   10.3477    8.0995   10.3210    8.7587    3.5783
   11.5754    6.3762   12.1704    7.4521    8.6977   14.8535
    2.0630    8.4499   15.4726   12.1764    3.8920    2.7112
   10.2143    6.2445   13.8571    8.1060    7.7701   13.2127
    6.3353    8.7805   10.2727   10.0472    6.8614    7.5814
   11.7141   11.1018    5.2923    8.1272   14.5540    2.5729

Diagonal coefficients         CD:
    0.4777    1.0230   -0.3147    0.0625    0.0831   -1.3316
    1.0689    1.5671   -2.1422    0.5565    1.7593   -2.8097
   -0.9555   -1.9276    0.9195   -0.2228   -0.5125    2.6989
    0.2899    0.4453   -0.5695    0.1541    0.4749   -0.7946
    0.4944    1.4145    0.3488   -0.1187   -0.6212   -1.5177
   -1.3753   -2.5224    1.7581   -0.4316   -1.1835    3.7547

Horizontal coefficients       CH:
    0.4100   -0.1827    1.5354    0.0784    0.8101   -1.3594
    2.3496   -0.9422    2.3780   -1.0540    2.7743   -2.2648
   -1.2690    0.0152   -6.9338   -1.7435   -1.6917    1.2388
    0.6317   -0.0969    2.3300    0.4637    0.6365   -0.1162
   -0.2343    0.3923    5.5457    2.1818    0.2103   -0.8573
   -1.8880    0.8142   -4.8552    0.0736   -2.7395    3.3590

Vertical coefficients         CV:
    1.5365    5.9678    3.4309   -1.0585   -5.0275   -4.8492
    0.6779   -0.0294   -5.3274    1.6483    4.8689   -1.8383
   -1.1065   -2.8791    0.1535    0.0982    0.8417    2.8923
   -0.1359   -2.6633   -5.8549    1.8440    6.2403    0.5697
    1.4244    5.2140    1.6410   -0.4669   -3.2369   -4.5757
    1.0288    2.2521    0.0574   -0.1359   -0.5170   -2.6854

Reconstruction       b:
    8.0000    7.0000    3.0000    3.0000    1.0000    1.0000
    4.0000    6.0000    1.0000    5.0000    2.0000    9.0000
    8.0000    1.0000    4.0000    9.0000    3.0000    7.0000
    9.0000    3.0000    8.0000    2.0000    4.0000    3.0000
    1.0000    3.0000    7.0000    1.0000    5.0000    2.0000
    4.0000    3.0000    7.0000    7.0000    6.0000    1.0000