%% Annotated Matlab transcript -- 4/12
%% CS 323 - Doug DeCarlo

% Matlab integration example using code from book

[i,d,r] = simpson(0,pi/2,2,0);
i
d
r
es = 1 - i;
% ratio of simpson error is 16
es(1:end-1) ./ es(2:end)

trapezoidal(0,pi/2,2,0)
et = 1 - trapezoidal(0,pi/2,2,0)
plot(1:length(et),et,'.-')
semilogy(1:length(et),abs(et),'.-')
% ratio of trapezoid error is 4
et(1:end-1) ./ et(2:end)

% plotting both errors...

plot(1:length(et),et,'.-',1:length(es),es,'.-r');
semilogy(1:length(et),abs(et),'.-',1:length(es),abs(es),'.-r');