function Ainv = pseudinv(A, r)%PSEUDINV   Pseudo-inverse of rank r.%--------%   Usage:    Ainv = pseudinv(A, r)%%      produces the rank-r inverse of A, from the SVD of A.%      Only r singular values are retained for the inverse%      with the exception that singular values less than%      MAX(SIZE(A)) * S(1) * EPS are discarded.%      Ainv = pseudinv(A) uses all possible singular values.%% See also  SVD and PINV%---------------------------------------------------------------% copyright 1994, by C.S. Burrus, J.H. McClellan, A.V. Oppenheim,% T.W. Parks, R.W. Schafer, & H.W. Schussler.  For use with the book% "Computer-Based Exercises for Signal Processing Using MATLAB"% (Prentice-Hall, 1994).%---------------------------------------------------------------[U,S,V] = svd(A);S = diag(S);keep = sum( S > (max(size(A)) * S(1) * eps) );if (nargin == 1)   r = keep;else   r = min( r, keep );endS = diag( ones(r,1) ./ S(1:r) );Ainv = V(:,1:r) * S * U(:,1:r)';