%% Annotated Matlab transcript -- 3/6
%% CS 323 - Doug DeCarlo

% Perturbation analysis

% Let's plot example 3.5.4 on page 112 of the text
x = 0.9:0.01:7.3;
f = (x-1).*(x-2).*(x-3).*(x-4).*(x-5).*(x-6).*(x-7);
plot(x,f,x,0);

% Here is the perturbed version, too
F = f - 0.002*x.^6;
plot(x,f,x,F,x,0);

% We can see that the perturbed term does get quite big
plot(x,f,x,F,x,0,x,0.002*x.^6);

% - - -

% after class, I also decided to plot the predicted scale of the
% perturbation:  -g/f'  (you just do this at the roots...)
r = 1:7;
% I did this in maple.. :)
dF = 7*r.^6-168*r.^5+1610*r.^4-7840*r.^3+20307*r.^2-26264*r+13068;
% and now plot the size of the perturbation as a red dot
plot(x,f,x,F,x,0,r,-r.^6./dF,'.r')