function [lam, ssd, rv, sens, elas] = senstuff(mat);
%sensitivity, elasticity, lambda, rteigenvector, lfteigenvector

%call for all the output: 
%	[lam ssd rv sens elas] = senstuff(matrix)
%  these are the outputs             input

%call for lambda only:
%  senstuff(matrix)
%    will give only the first output variable, which is lambda1


%find the left eigenvector
[matlvec,matval] = eig(mat');
[maxmatval, loc] = max(abs(diag(matval)));
vvec=abs(matlvec(:,loc));

%find the right eigenvector
[matrvec,matval] = eig(mat);
[maxmatval, loc] = max(abs(diag(matval)));
uvec=abs(matrvec(:,loc));

%dom eigenvalue
lam = maxmatval;

uvec=uvec./sum(uvec);%rescales the rt eigenvector to sum to 1
vvec=vvec./(vvec'*uvec);%rescales the lft eigenvector to calc sens

sens=vvec*uvec';%gets the sensitivity matrix
elas=sens.*(mat./lam);%which scales each sij by each aij/lambda

ssd=uvec;%already normalized to sum to 1
rv=vvec;%normalized  so that its scalar product with ssd is 1, rv'*sd=1