%%========== λₙ λ₁   λ₂
ln = 0;  l1 = 5;   l2 = 4.5;
%%========== M and σ₀ 
M = .5*(l1+ln);  so = .5*(l2+ln);
%%========== function for σ<σ₀ 
f1 = @(t) ( (l2-t) ./ (l1 -t) );
%%========== function for σ≥σ₀ 
f2 = @(t) ( (t-ln) ./ (l1-t)) ; 
%%========== plotting
x1 = linspace(ln,so,100);
y1 = f1(x1);
x2 = linspace(so,M,50);
y2 = f2(x2);
plot([x1,x2],[y1,y2],'linewidth',2)
hold on
plot([so,so],[0.8,1],'r--','linewidth',2)
xlabel('\sigma')
ylabel('\rho')

