function [lo, hi] = afb3D(x, af1, af2, af3)

% 3D Analysis Filter Bank
%
% USAGE:
%    [lo, hi] = extra.candle.afb3D(x, af1, af2, af3);
% INPUT:
%    x - N1 by N2 by N3 array matrix, where
%        1) N1, N2, N3 all even
%        2) N1 >= 2*length(af1)
%        3) N2 >= 2*length(af2)
%        4) N3 >= 2*length(af3)
%    afi - analysis filters for dimension i
%       afi(:, 1) - lowpass filter
%       afi(:, 2) - highpass filter
% OUTPUT:
%    lo - lowpass subband
%    hi{d}, d = 1..7 - highpass subbands
% EXAMPLE:
%    x = rand(32,64,16);
%    [af, sf] = extra.candle.farras;
%    [lo, hi] = extra.candle.afb3D(x, af, af, af);
%    y = extra.candle.sfb3D(lo, hi, sf, sf, sf);
%    err = x - y;
%    max(max(max(abs(err))))
%
% WAVELET SOFTWARE AT POLYTECHNIC UNIVERSITY, BROOKLYN, NY
% http://taco.poly.edu/WaveletSoftware/

if nargin < 3
   af2 = af1;
   af3 = af1;
end

% filter along dimension 1
[L, H] = afb3D_A(x, af1, 1);

% filter along dimension 2
[LL LH] = afb3D_A(L, af2, 2);
[HL HH] = afb3D_A(H, af2, 2);

% filter along dimension 3
[LLL LLH] = afb3D_A(LL, af3, 3);
[LHL LHH] = afb3D_A(LH, af3, 3);
[HLL HLH] = afb3D_A(HL, af3, 3);
[HHL HHH] = afb3D_A(HH, af3, 3);

lo    = LLL;
hi{1} = LLH;
hi{2} = LHL;
hi{3} = LHH;
hi{4} = HLL;
hi{5} = HLH;
hi{6} = HHL;
hi{7} = HHH;


% LOCAL FUNCTION

function [lo, hi] = afb3D_A(x, af, d)

% 3D Analysis Filter Bank
% (along one dimension only)
%
% [lo, hi] = afb3D_A(x, af, d);
% INPUT:
%    x - N1xN2xN2 matrix, where min(N1,N2,N3) > 2*length(filter)
%           (Ni are even)
%    af - analysis filter for the columns
%    af(:, 1) - lowpass filter
%    af(:, 2) - highpass filter
%    d - dimension of filtering (d = 1, 2 or 3)
% OUTPUT:
%     lo, hi - lowpass, highpass subbands
%
% % Example
% x = rand(32,64,16);
% [af, sf] = extra.candle.farras;
% d = 2;
% [lo, hi] = afb3D_A(x, af, d);
% y = extra.candle.sfb3D_A(lo, hi, sf, d);
% err = x - y;
% max(max(max(abs(err))))

lpf = af(:, 1);     % lowpass filter
hpf = af(:, 2);     % highpass filter

% permute dimensions of x so that dimension d is first.
p = mod(d-1+[0:2], 3) + 1;
x = permute(x, p);

% filter along dimension 1
[N1, N2, N3] = size(x);
L = size(af, 1)/2;
x = extra.candle.cshift3D(x, -L, 1);
lo = zeros(L+N1/2, N2, N3);
hi = zeros(L+N1/2, N2, N3);

for k = 1:N3
   lo(:, :, k) = extra.candle.upfirdn(x(:, :, k), lpf, 1, 2);
end
lo(1:L, :, :) = lo(1:L, :, :) + lo([1:L]+N1/2, :, :);
lo = lo(1:N1/2, :, :);

for k = 1:N3
   hi(:, :, k) = extra.candle.upfirdn(x(:, :, k), hpf, 1, 2);
end
hi(1:L, :, :) = hi(1:L, :, :) + hi([1:L]+N1/2, :, :);
hi = hi(1:N1/2, :, :);

% permute dimensions of x (inverse permutation)
lo = ipermute(lo, p);
hi = ipermute(hi, p);

