isrotm2d.m

%ISROTM2D Test if value is SO(2) rotation matrix
%
% ISROTM2D(R) is true (1) if the argument is of dimension 2x2 or 2x2xN,
% else false (0).
%
% ISROTM2D(R, check=true) as above, but also checks the validity of the
% rotation matrix.
%
% Notes:
% - A valid rotation matrix R has R'*R = I and det(R)=1.
% - The first form is a fast, but incomplete, test that a matrix belong
%   to SO(2).
%
% See also ISROTM, ISTFORM2D, ISVEC.

% Copyright 2022-2023 Peter Corke, Witold Jachimczyk, Remo Pillat 

function h = isrotm2d(R, options)
    arguments
        R
        options.check (1,1) logical = false
    end

    h = false;
    if ~isnumeric(R)
        return
    end

    d = size(R);
    if ~(all(d(1:2) == [2 2]))
        return %false
    end
        
    if options.check
        for i = 1:size(R,3)
            RR = R(:,:,i);
            % check transpose is inverse
            e = RR'*RR - eye(2,2);
            if norm(e) > 10*eps
                return %false
            end
            % check determinant is +1
            e = abs(det(RR) - 1);
            if norm(e) > 10*eps
                return %false
            end
        end
    end
    
    h = true;

end