%% Annotated Matlab transcript -- 2/27
%% CS 323 - Doug DeCarlo

% Here are the fixed point example functions, evaluated
% at their fixed points:
1 + 0.5*sin(1.4987)
3 + 2*sin(3.0944)

% Here are plots - note how fixed points are where y=x intersects y=g(x)
x = -1:0.01:4;
plot(x,1+0.5*sin(x), x,3+2*sin(x), x,x)

% We can take a wider view to see that these are the only fixed points...
x = -20:0.01:20;
plot(x,1+0.5*sin(x), x,3+2*sin(x), x,x)

% Lets see if the first one converges...
x = 0;
for i=1:20
x = 1 + 0.5*sin(x);
r(i) = x;
end
plot(1:length(r),r,'.-')
% it does!

% and how about the second one?
x = 0;
for i=1:20
x = 3+2*sin(x);
r(i) = x;
end
plot(1:length(r),r,'.-')
% no luck there..  it doesn't converge