%GET_GOLDEN_RATIO_GROUPS use the provided angle to select Ngroups groups containing
%the most orthogonal set of projections 
%
% group_ind = get_golden_ratio_groups(theta_all, Ngroups)
% 
%  Inputs: 
%   **theta_all    - list of angles in degrees 
%   **Ngroups      - number of sets to split the angles 
%  *returns*
%   ++group_ind    - cells containing indices for each set 


% Academic License Agreement
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% Source Code
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% Introduction 
% •	This license agreement sets forth the terms and conditions under which the PAUL SCHERRER INSTITUT (PSI), CH-5232 Villigen-PSI, Switzerland (hereafter "LICENSOR") 
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% Additionally, any publication using the package, or any translation of the code into another computing language should cite 
% K. Wakonig, H.-C. Stadler, M. Odstrčil, E.H.R. Tsai, A. Diaz, M. Holler, I. Usov, J. Raabe, A. Menzel, M. Guizar-Sicairos, PtychoShelves, a versatile 
% high-level framework for high-performance analysis of ptychographic data, J. Appl. Cryst. 53(2) (2020). (doi: 10.1107/S1600576720001776)
% and for difference map:
% P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, High-resolution scanning X-ray diffraction microscopy, Science 321, 379–382 (2008). 
%   (doi: 10.1126/science.1158573),
% for maximum likelihood:
% P. Thibault and M. Guizar-Sicairos, Maximum-likelihood refinement for coherent diffractive imaging, New J. Phys. 14, 063004 (2012). 
%   (doi: 10.1088/1367-2630/14/6/063004),
% for LSQ-ML:
% M. Odstrčil, A. Menzel, and M. Guizar-Sicairos, Iterative least-squares solver for generalized maximum-likelihood ptychography, Opt. Express 26(3), 3108 (2018). 
%   (doi: 10.1364/OE.26.003108),
% for mixed coherent modes:
% P. Thibault and A. Menzel, Reconstructing state mixtures from diffraction measurements, Nature 494, 68–71 (2013). (doi: 10.1038/nature11806),
% and/or for multislice:
% E. H. R. Tsai, I. Usov, A. Diaz, A. Menzel, and M. Guizar-Sicairos, X-ray ptychography with extended depth of field, Opt. Express 24, 29089–29108 (2016). 
%   (doi: 10.1364/OE.24.029089),
% and/or for OPRP:
% M. Odstrcil, P. Baksh, S. A. Boden, R. Card, J. E. Chad, J. G. Frey, W. S. Brocklesby,  Ptychographic coherent diffractive imaging with orthogonal probe relaxation. 
% Opt. Express 24.8 (8360-8369) 2016. (doi: 10.1364/OE.24.008360).
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% 10.	This Agreement shall be governed by the material laws of Switzerland and any dispute arising out of this Agreement or use of the PROGRAM shall be brought before 
%       the courts of Zürich, Switzerland.


function group_ind = get_golden_ratio_groups(theta_all, Ngroups)
    Nangles = length(theta_all); 

    if all(theta_all == theta_all(1))
       group_ind = {}; 
        for ll  = 1:Ngroups
            ind = 1+(ll-1)*ceil(Nangles/Ngroups):min(Nangles, (ll)*ceil(Nangles/Ngroups));
            group_ind{end+1} = (ind);
        end
        return
    end

    theta_aux = theta_all; 
    Nangles = length(theta_all); 
    start_index = 200; 

    for ll = 1:Nangles
        % golden ratio angle selector 
        gold_angle = mod((ll + start_index) * (1+sqrt(5))/2* 360,  360);
        theta = theta_aux(math.argmin(abs(theta_aux-gold_angle)));
        theta_aux = setdiff(theta_aux, theta); 
        index(ll) = find(theta_all== theta); 
    end

    group_ind = {}; 
    for ll  = 1:Ngroups
        ind = 1+(ll-1)*ceil(Nangles/Ngroups):min(Nangles, (ll)*ceil(Nangles/Ngroups));
        group_ind{end+1} = index(ind);
    end
end