clc
clear all 
close all

%% EXERCISE 1
A = [1 0 3 0; 0 2 0 5; 3 0 4 0; 0 5 0 6]
eig(A)

%% EXERCISE 3
z = @(x, y) x.*y.^2 + x.^3.*y - x.*y;
I = [-7 7 -7 7];
fsurf(z, I)

% D is a local maximum
D = [-1/sqrt(5), 2/5]

% I prepare a function for the fminsearch procedure
z2 = @(x) -(x(1)*x(2)^2 + x(1)^3*x(2) - x(1)*x(2));

% I start near D
D1 = D + [.1, .1];
[D2, fval] = fminsearch(z2, D1)

% E is a local minimum
E = [1/sqrt(5), 2/5]

% I prepare a function for the fminsearch procedure
z3 = @(x) x(1)*x(2)^2 + x(1)^3*x(2) - x(1)*x(2);

% I start near E
E1 = E + [.1, .1];
[E2, fval] = fminsearch(z3, D1)


%% EXERCISE 4
cf = [-100 30 80];
cfd = ["01/01/2023", "01/01/2025", "01/01/2027"];
ii = xirr(cf, cfd)