clear all;
fxy = @(x) x(1)*exp(-x(1)^2-x(2)^2)

fc = fxy([1; 1])
df = fdjac(fxy,[1; 1])
fx = df(1)
fy = df(2)

fxyaprox = @(x) fc - fx - fy + fx*x(1) + fy*x(2)

x=[1; 2];
fxy(x)
fxyaprox(x)

x = 0.5:0.1:1.5;
n = length(x);

forig = zeros(n,n);
faprox = zeros(n,n);
X = zeros(n,n);

for i = 1:n;
    for j=1:n;
        forig(i,j) = fxy([x(i);x(j)]);
        faprox(i,j) = fxyaprox([x(i);x(j)]);
        X(i,j) = x(j);
    end;
end;

surf(x,x,forig);
view(40, 10); 

surf(x,x,faprox);
view(30, 10);

Ex = integral(@(x) integrando(x,3,2),-Inf,Inf)

intf = @(x,mu,sigma) x.*normpdf(x,mu,sigma)
integral(@(x) intf(x,3,2),-Inf,Inf)

Ex2 = integral(@(x) integrando2(x,3,2),-Inf,Inf)

Vx = Ex2 - Ex^2

clear all;
c = [0.6; 0.6];
eta = 1.2;

q0 = [0.2; 0.2];
qstar = fsolve(@(x) cournot(x,c,eta),q0)

clear all;
warning('off');
impdata = importdata('DatosMCO.txt');
[N, K]= size(impdata);
y = impdata(:,1);
X1 = impdata(:,2);
X2 = impdata(:,3);

X = [X1 X2];

par0 = [2 0.1 0.1 log(2)];
par = fminunc(@(x) loglike(x,y,X),par0);
disp(par)

sig = exp(par(4))

clear all;
alpha = [0.2 0.4 0.1 0.3]';
p = [2 3 4 5];
m = 100;

AI = p;
bI = m;
lb = [0 0 0 0]';
ub = [Inf Inf Inf Inf]';

x0 = [1 1 1 1]';
x = fmincon(@(x) utility(x,alpha),x0,AI,bI,[],[],lb,ub);
disp(x);

p*x