function M = smat(v)

%Generate a symmetrix matrix with size n from the column vector of size
%n(n+1)/2.

[ntilde,m]=size(v);
counter=0;

n=round((-1+sqrt(1+8*ntilde))/2);

for j=1:n
    for i=j:n
        if (i==j)
            M(i,j)=v(counter+i-j+1);
        else
            M(i,j)=v(counter+i-j+1)/sqrt(2);
        end
        M(j,i)=M(i,j);
    end
    counter=counter+n-j+1;
end