function [a,c,s]=rotg(a,b)
% Input:  a,b
% Output: a,c,s
% Function rotg.m applies Givens rotation matrix [c s;-s c] to vector [a;b]
%  |a~|   | c  s| |a|
%  |  |<--|     | | |
%  |0 |   |-s  c| |b|
% where a~ modified top element in vector and c, s elements of Given matrix.
% Used with a version of GMRES (gmres.m) organized as suggested by
% R.J. Hanson and D.R. Kincaid,"Notes on GMRES Algorithm Organization",
% Technical Report TR-05-05, March 2005,
% Computer Sciences Department, University of Texas at Austin.
% Date = 5 March 2005.

     t = b;
     if(abs(a) > abs(b))
         t = a;
     end
     scale = abs(a)+abs(b);
     if(scale <= 0)
         c=1;
         s=0;
         return
     end
     r=scale*sqrt((a/scale)^2 + (b/scale)^2);
     if(t < 0)
         r=-r;
     end
     c = a/r;
     s = b/r;
     a=r;
end