function [y,w] = idctn(y,w)

%IDCTN N-D inverse discrete cosine transform.
%   X = IDCTN(Y) inverts the N-D DCT transform, returning the original
%   array if Y was obtained using Y = DCTN(X).
%
%   Class Support
%   -------------
%   Input array can be numeric or logical. The returned array is of class
%   double.
%
%   Reference
%   ---------
%   Narasimha M. et al, On the computation of the discrete cosine
%   transform, IEEE Trans Comm, 26, 6, 1978, pp 934-936.
%
%   Example
%   -------
%       RGB = imread('autumn.tif');
%       I = rgb2gray(RGB);
%       J = dctn(I);
%       imshow(log(abs(J)),[]), colormap(jet), colorbar
%
%   The commands below set values less than magnitude 10 in the DCT matrix
%   to zero, then reconstruct the image using the inverse DCT.
%
%       J(abs(J)<10) = 0;
%       K = idctn(J);
%       figure, imshow(I)
%       figure, imshow(K,[0 255])
%
%   See also DCTN, IDCT, IDCT2.
%
%   -- Damien Garcia -- 2009/04, revised 2009/11

% ----------
%   [Y,W] = IDCTN(X,W) uses and returns the weights which are used by the
%   program. If IDCTN is required for several large arrays of same size,
%   the weights can be reused to make the algorithm faster. A typical
%   syntax is the following:
%      w = [];
%      for k = 1:10
%          [y{k},w] = idctn(x{k},w);
%      end
%   The weights (w) are calculated during the first call of IDCTN then
%   reused in the next calls.
% ----------

error(nargchk(1,2,nargin))

y = double(y);
sizy = size(y);
y = squeeze(y);

dimy = ndims(y);
if isvector(y)
    dimy = 1;
    y = y(:);
end

if ~exist('w','var') || isempty(w)
    for dim = 1:dimy
        n = (dimy==1)*numel(y) + (dimy>1)*sizy(dim);
        w{dim} = exp(1i*(0:n-1)'*pi/2/n);
    end
end

if ~isreal(y)
    y = complex(idctn(real(y),w),idctn(imag(y),w));
else
        for dim = 1:dimy
            siz = size(y);
            n = siz(1);
            y = reshape(y,n,[]);
            y = bsxfun(@times,y,w{dim});
            y(1,:) = y(1,:)/sqrt(2);
            y = ifft(y,[],1);
            y = real(y*sqrt(2*n));
            I = (1:n)*0.5+0.5;
            I(2:2:end) = n-I(1:2:end-1)+1;
            y = y(I,:);
            y = reshape(y,siz);
            y = shiftdim(y,1);            
        end
end
        
y = reshape(y,sizy);