% IMGAUSSFILT3_FFT apply isotropic gaussian smoothing along all three 
% dimensions, faster than matlab alternative
%
%  A = imgaussfilt3_fft(A,sigma, split)
%
% Inputs: 
%   **A         3D volume to be smoothed 
%   **sigma     gaussian smoothing constant 
%   **split     3x1 int vector to split the volume and save memory 
% *returns*: 
%   ++A         filtered volume 

    
%*-----------------------------------------------------------------------*
%|                                                                       |
%|  Except where otherwise noted, this work is licensed under a          |
%|  Creative Commons Attribution-NonCommercial-ShareAlike 4.0            |
%|  International (CC BY-NC-SA 4.0) license.                             |
%|                                                                       |
%|  Copyright (c) 2017 by Paul Scherrer Institute (http://www.psi.ch)    |
%|                                                                       |
%|       Author: CXS group, PSI                                          |
%*-----------------------------------------------------------------------*
% You may use this code with the following provisions:
%
% If the code is fully or partially redistributed, or rewritten in another
%   computing language this notice should be included in the redistribution.
%
% If this code, or subfunctions or parts of it, is used for research in a 
%   publication or if it is fully or partially rewritten for another 
%   computing language the authors and institution should be acknowledged 
%   in written form in the publication: “Data processing was carried out 
%   using the “cSAXS matlab package” developed by the CXS group,
%   Paul Scherrer Institut, Switzerland.” 
%   Variations on the latter text can be incorporated upon discussion with 
%   the CXS group if needed to more specifically reflect the use of the package 
%   for the published work.
%
% A publication that focuses on describing features, or parameters, that
%    are already existing in the code should be first discussed with the
%    authors.
%   
% This code and subroutines are part of a continuous development, they 
%    are provided “as they are” without guarantees or liability on part
%    of PSI or the authors. It is the user responsibility to ensure its 
%    proper use and the correctness of the results.

function A = imgaussfilt3_fft(A,sigma, split)
    % gaussian blurring in 3D 
    import math.*

    if sigma == 0
        return
    end
    if nargin < 3
        split = 1; 
    end

    Npx = size(A);
    isReal = isreal(A);
    
    A = fftn_partial(A, split);

    for dim=1:3
        grid = single((-Npx(dim)/2:Npx(dim)/2-1));
        ker = exp(-grid.^2/ sigma^2)';
        ker = ker / sum(ker);
        ker = fft(ker,[],1);

        ker_shape = ones(1,3);
        ker_shape(dim) = Npx(dim);
        B{dim} = reshape(ker,ker_shape);
    end
    if isa(A, 'gpuArray')
        A = arrayfun(@prod3,A,B{:});
    else
        A = prod3(A,B{:});
    end

    
    A = ifftn_partial(A, split);
    if isReal
        A = real(A);
    end
    
    % Im not sure why, but the output needs to be fftshifted

    for dim = 1:3
        m = size(A, dim);
        p = ceil(m/2);
        idx{dim} = [p+1:m 1:p];
    end

    % Use comma-separated list syntax for N-D indexing.
    A = A(idx{:});

end

function A = prod3(A,k1,k2,k3)
    A = A .* k1 .* k2 .* k3;
end