fibonacci(n)

% Given a matrix of integers n, compute the nth Fibonacci numbers.
% Example:
%
%   fibonacci(magic(3))
%   ans =
%
%       21     1     8
%        2     5    13
%        3    34     1

% Fibonacci.m by David Terr, Raytheon, 5-11-04
% vectorized by Michael Völker, 07-Jan-2011

function fibs = fibonacci(n)

    % Make sure input is sane
    if any( ~isreal(n(:)) )
        error('Argument must be real.')
    end
    if any( n(:) ~= floor(n(:)) )
        error('Argument must be integers.')
    end

    alpha = (1 + sqrt(5))/2;                % alpha = 1.618... is the golden ratio
    fibs  = round( alpha.^n ./ sqrt(5) );

    neg = n(:) < 0;                         % negative input is treated separately

    % without this if, MATLAB recurses forever
    if any( neg )
        fibs( neg ) = (-1).^(n(neg)+1) .* fibonacci( -n(neg) );
    end

end