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Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_wav_3d_sngl_inv (c09fb)

▸▿ Contents

    1  Purpose
    2  Syntax
    3  Description
    4  References
▸▿ 5  Parameters
    6  Error Indicators and Warnings
    7  Accuracy
    8  Further Comments
    9  Example

Purpose

nag_wav_3d_sngl_inv (c09fb) computes the three-dimensional inverse discrete wavelet transform (IDWT) at a single level. The initialization function nag_wav_3d_init (c09ac) must be called first to set up the DWT options.

Syntax

[b, ifail] = c09fb(m, n, fr, c, icomm, 'lenc', lenc)
[b, ifail] = nag_wav_3d_sngl_inv(m, n, fr, c, icomm, 'lenc', lenc)

Description

nag_wav_3d_sngl_inv (c09fb) performs the inverse operation of function nag_wav_3d_sngl_fwd (c09fa). That is, given sets of wavelet coefficients computed by function nag_wav_3d_sngl_fwd (c09fa) using a DWT as set up by the initialization function nag_wav_3d_init (c09ac), on a real data array, B, nag_wav_3d_sngl_inv (c09fb) will reconstruct B.

References

None.

Parameters

Compulsory Input Parameters

1:     m – int64int32nag_int scalar
The number of rows of each two-dimensional frame.
Constraint: this must be the same as the value m passed to the initialization function nag_wav_3d_init (c09ac).
2:     n – int64int32nag_int scalar
The number of columns of each two-dimensional frame.
Constraint: this must be the same as the value n passed to the initialization function nag_wav_3d_init (c09ac).
3:     fr – int64int32nag_int scalar
The number two-dimensional frames.
Constraint: this must be the same as the value fr passed to the initialization function nag_wav_3d_init (c09ac).
4:     clenc – double array
The coefficients of the discrete wavelet transform. This will normally be the result of some transformation on the coefficients computed by function nag_wav_3d_sngl_fwd (c09fa).
Note that the coefficients in c may be extracted according to type into three-dimensional arrays using nag_wav_3d_coeff_ext (c09fy), and inserted using nag_wav_3d_coeff_ins (c09fz).
5:     icomm260 – 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_3d_init (c09ac).

Optional Input Parameters

1:     lenc – int64int32nag_int scalar
Default: the dimension of the array c.
The dimension of the array c.
Constraint: lenc≥nct, where nct is the total number of wavelet coefficients, as returned by nag_wav_3d_init (c09ac).

Output Parameters

1:     bldbsdbfr – double array
sdb=n.
The m by n by fr reconstructed array, B, with Bijk stored in bijk. The reconstruction is based on the input wavelet coefficients and the transform options supplied to the initialization function nag_wav_3d_init (c09ac).
2:     ifail – int64int32nag_int scalar
ifail=0 unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:
   ifail=1
Constraint: fr=_, the value of fr on initialization (see nag_wav_3d_init (c09ac)).
Constraint: m=_, the value of m on initialization (see nag_wav_3d_init (c09ac)).
Constraint: n=_, the value of n on initialization (see nag_wav_3d_init (c09ac)).
   ifail=2
Constraint: ldb≥m.
Constraint: sdb≥n.
   ifail=3
Constraint: lenc≥nct, where nct is the number of DWT coefficients returned by nag_wav_3d_init (c09ac) in argument nwct.
   ifail=6
Either the communication array icomm has been corrupted or there has not been a prior call to the initialization function nag_wav_3d_init (c09ac).
The initialization function was called with wtrans='M'.
   ifail=-99
An unexpected error has been triggered by this routine. Please contact NAG.
   ifail=-399
Your licence key may have expired or may not have been installed correctly.
   ifail=-999
Dynamic memory allocation failed.

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.

Further Comments

None.

Example

See Example in nag_wav_3d_sngl_fwd (c09fa).

Open in the MATLAB editor: c09fb_example

function c09fb_example


fprintf('c09fb example results\n\n');

m  = int64(5);
n  = int64(4);
fr = int64(3);
wavnam = 'Haar';
mode = 'half';
wtrans = 'Single Level';
a = zeros(m, n, fr);
a(:, :, 1) = [3, 2, 2, 2;
              2, 9, 1, 2;
              2, 5, 1, 2;
              1, 6, 2, 2;
              5, 3, 2, 2];
a(:, :, 2) = [2, 1, 5, 1;
              2, 9, 5, 2;
              2, 3, 2, 7;
              2, 1, 1, 2;
              2, 1, 2, 8];
a(:, :, 3) = [3, 1, 4, 1;
              1, 1, 2, 1;
              4, 1, 7, 2;
              3, 2, 1, 5;
              1, 1, 2, 2];


% Query wavelet filter dimensions
[lmax, nf, nwct, nwcn, nwcfr, icomm, ifail] = ...
      c09ac(wavnam, wtrans, mode, m, n, fr);

nwcm = nwct/(8*nwcn*nwcfr);

% 3D DWT decomposition
[c, icomm, ifail] = c09fa(n, fr, a, nwct, icomm);

d = zeros(nwcm, nwcn, nwcfr);

for cindex = 0:7

  % Decide which coefficient type we are considering and advance the
  % pointer locc to the first element of that 3D array in C.
  switch (cindex)
    case {0}
      fprintf('Approximation coefficients (LLL)\n');
      locc = 1;
    case {1}
      fprintf('Detail coefficients (LLH)\n');
      % Advance pointer past approximation coefficients
      locc = nwcm*nwcn*nwcfr + 1;
    case {2}
      fprintf('Detail coefficients (LHL)\n');
      % Advance pointer past approximation coefficients and 1 set of
      % detail coefficients
      locc = 2*nwcm*nwcn*nwcfr + 1;
    case {3}
      fprintf('Detail coefficients (LHH)\n');
      % Advance pointer past approximation coefficients and 2 sets of
      % detail coefficients
      locc = 3*nwcm*nwcn*nwcfr + 1;
    case {4}
      fprintf('Detail coefficients (HLL)\n');
      % Advance pointer past approximation coefficients and 3 sets of
      % detail coefficients
      locc = 4*nwcm*nwcn*nwcfr + 1;
    case {5}
      fprintf('Detail coefficients (HLH)\n');
      % Advance pointer past approximation coefficients and 4 sets of
      % detail coefficients
      locc = 5*nwcm*nwcn*nwcfr + 1;
    case {6}
      fprintf('Detail coefficients (HHL)\n');
      % Advance pointer past approximation coefficients and 5 sets of
      % detail coefficients
      locc = 6*nwcm*nwcn*nwcfr + 1;
    case {7}
      fprintf('Detail coefficients (HHH)\n');
      % Advance pointer past approximation coefficients and 6 sets of
      % detail coefficients
      locc = 7*nwcm*nwcn*nwcfr + 1;
  end

  for k = 1:nwcfr
    for j = 1:nwcn
      for i = 1:nwcm
        i1 = locc - 1 + (j-1)*nwcfr*nwcm + (i-1)*nwcfr + k;
        d(i,j,k) = c(i1);
      end
    end
  end

  for j = 1:nwcfr
    if (j==1)
      fprintf('Coefficients        Frame 1');
    else
      fprintf('          Frame %d', j);
    end
  end
  fprintf('\n');
  d2 = reshape(d, nwcm, nwcn*nwcfr);
  for i = 1:nwcm
    if i == 1
      fprintf('    %d         ', cindex);
    else
      fprintf('              ');
    end
    for j=1:nwcn*nwcfr
      fprintf('%8.4f ', d2(i,j));
    end
    fprintf('\n');
  end
end


% 3D DWT reconstruction
[b, ifail] = c09fb(m, n, fr, c, icomm);

fprintf('\nOutput Data          b : \n');
% Convert to int16 to get more compact output
for i=1:nwcm
  fprintf('Frame %d :\n', i);
  disp(b(:, :, i));
end



c09fb example results

Approximation coefficients (LLL)
Coefficients        Frame 1          Frame 2
    0          10.6066   7.0711   4.2426   5.6569 
                7.7782   6.7175   7.0711  10.6066 
                7.7782   9.8995   2.8284   5.6569 
Detail coefficients (LLH)
Coefficients        Frame 1          Frame 2
    1           0.7071  -2.1213   0.0000   0.0000 
                2.1213  -1.7678   0.0000   0.0000 
                3.5355  -4.2426   0.0000   0.0000 
Detail coefficients (LHL)
Coefficients        Frame 1          Frame 2
    2          -4.2426   2.1213   1.4142   2.8284 
               -2.8284  -2.4749   2.8284   0.7071 
                2.1213  -4.2426   0.0000   0.0000 
Detail coefficients (LHH)
Coefficients        Frame 1          Frame 2
    3           0.0000  -2.8284   0.0000   0.0000 
               -2.8284   1.7678   0.0000   0.0000 
                0.7071   4.2426   0.0000   0.0000 
Detail coefficients (HLL)
Coefficients        Frame 1          Frame 2
    4          -4.9497   0.0000   1.4142   1.4142 
                0.7071   1.7678  -0.0000   2.1213 
                0.0000   0.0000   0.0000   0.0000 
Detail coefficients (HLH)
Coefficients        Frame 1          Frame 2
    5           0.7071   0.7071   0.0000   0.0000 
               -0.7071  -2.4749   0.0000   0.0000 
                0.0000   0.0000   0.0000   0.0000 
Detail coefficients (HHL)
Coefficients        Frame 1          Frame 2
    6           5.6569   0.7071   1.4142   1.4142 
                0.0000  -1.7678   1.4142   6.3640 
                0.0000   0.0000   0.0000   0.0000 
Detail coefficients (HHH)
Coefficients        Frame 1          Frame 2
    7           0.0000   0.0000   0.0000   0.0000 
                1.4142   1.0607   0.0000   0.0000 
                0.0000   0.0000   0.0000   0.0000 

Output Data          b : 
Frame 1 :
    3.0000    2.0000    2.0000    2.0000
    2.0000    9.0000    1.0000    2.0000
    2.0000    5.0000    1.0000    2.0000
    1.0000    6.0000    2.0000    2.0000
    5.0000    3.0000    2.0000    2.0000

Frame 2 :
    2.0000    1.0000    5.0000    1.0000
    2.0000    9.0000    5.0000    2.0000
    2.0000    3.0000    2.0000    7.0000
    2.0000    1.0000    1.0000    2.0000
    2.0000    1.0000    2.0000    8.0000

Frame 3 :
    3.0000    1.0000    4.0000    1.0000
    1.0000    1.0000    2.0000    1.0000
    4.0000    1.0000    7.0000    2.0000
    3.0000    2.0000    1.0000    5.0000
    1.0000    1.0000    2.0000    2.0000
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