function [Y,Z]=schurlog(A,p,q,v)
% Y=SCHURLOG(A,p) computes A^(1/p) using a binary powering technique.
% Y=SCHURLOG(A,p,q) computes A^(q/p)=(A^(1/p))^q using a 
%   binary powering technique. 
% Y=SCHURLOG(A,p,q,v) computes A^(q/p) where the determinations of
%   the p-th roots are chosen according to the vector v(1),...,v(s)
%   where s is the number of diagonal blocks in the real Schur form
%   of A and v(i) is the determination of the p-th root of one  
%   eigenvalue on the i-th block obtained by schur(A), in the complex
%   conjugate case two conjugate determinations are chosen in order
%   to get real roots and fractional powers
%   v(i)=0 for the principal determination
%   v(i)=1,...,p-1, for the other determinations.
%
% Reference.
% B. Iannazzo and C. Manasse, "A Schur logarithmic algorithm for
% fractional powers of a matrix", SIAM J. Matrix Anal. Appl, 34-2,
% pp. 794-813, 2013.
%
% Warning! This is just a straightforwad implementation. 
% The code is not optimized.
% works for real matrices