function[b,c,s]=giv(a1,a2)
% This Matlab routine finds a 2*2 Givens rotation 
%[c,s\\-conj(s),c], where c is real and s is complex, 
% which transforms the vector [a1,a2]^T into the vector [b,0]
if (abs(a1)==0) 
    c=0.;s=1.;b=a2;
else
    if(abs(a2)==0)
        c=1.; s=0.; b=a1; 
    else
        %d=-(a2/a1)*abs(a1/a2);
        d=-(a2/abs(a2))*(abs(a1)/a1);
        if (abs(a2)>=abs(a1))
            e=abs(a1/a2);
            s=1/sqrt(1+e^2);
            c=e*s;
            s=d*s;
        else
            e=abs(a2/a1);
            c=1/sqrt(1+e^2);
            s=e*c;
            s=d*s;
        end
        s=-conj(s);
        b=c* a1+ s* a2;
    end
end