[x,A]=matrix_perimeter(A)

function [x,A]=matrix_perimeter(A)
% Function matrix_perimeter extracts the outer elements of 
% a matrix in a clockwise sense.
%
% INPUTS
% ------     
%         A     = An n x m matrix (real or imaginary)
%
% OUTPUTS
% -------
%         x     = Row vector of the elements of the matrix that exist
%                 in the perimeter, taken in a clockwise sense
%
%         A     = An (n-2)x(m-2) matrix, same as input matrix, without its elements 
%                 existed in the perimeter
%                 (The input matrix is decomposed within the function)
%
% COMPATIBILITY
% -------------
%                 Matlab 7.2 and later   
%                 
% EXAMPLE
% -------
% >> A=magic(4)
%
% A =
%
%     16     2     3    13
%      5    11    10     8
%      9     7     6    12
%      4    14    15     1
%
% >> [x,B]=matrix_perimeter(A)
%
% x =
%
%     16     2     3    13     8    12     1    15    14     4     9     5
%
%
% B =
%
%     11    10
%      7     6
% 
% Author  : Athanasios Makris
% Email   : [e-mail]
% Date    : 01.08.09 (dd/mm/yy)
% Version : 1.0

if nargin ~=1
    error('Function matrix_perimeter needs one argument')
end

if ~isempty(A)
    [n,m]=size(A);
    if ( (n~=1) && (m~=1) )
        x=[A(1,:) A(2:end,end)' A(end,[end-1:-1:1])  A(end-1:-1:2,1)' ] ;
        A=A(2:end-1,2:end-1);
    else
        x=A(:)';
        A=[];
    end
else
    x=[];
    A=[];
end

return;