clc
clear
altura = [0.912; 0.986; 1.060; 1.130; 1.190; 1.260; 1.320; 1.380; 1.410; 1.490];
peso = [13.7; 15.9; 18.5; 21.3; 23.5; 27.2; 32.7; 36.0; 38.6; 43.7];
%p = @(h,c1,c2) c1.*h.^c2;
p = @(h,c1,c2) c1.*exp(c2.*log(h));
m = length(peso);

tol = 1e-9;
k = 0;
c = [2; .5];
%c = [1,.1];
d = inf;

while norm(d)>tol && k < 100
    r = -peso + p(altura, c(1), c(2));
    A = [exp(c(2).*log(altura)), c(1)*log(altura).*exp(c(2).*log(altura))];
    %cond(A'*A)
    %d = (A'*A)\(A'*r);

    %qr
    [Q,R] = qr(A);
    R = R(1:2,:);
    yy = transpose(Q)*r;
    yy = yy(1:2);
    d = R\yy;

    c = c - d;
    k = k+1;
end

vec = linspace(.8,1.6);
plot(altura, peso,'ok','LineWidth',2);
hold on
plot(vec, p(vec, c(1), c(2)), '-b', 'LineWidth', 2);
grid on
xlabel('t', 'FontSize',14)
ylabel('y', 'FontSize',14)

%% Parte b.
clc
log_peso = log(peso);
p_lin = @(h,a,b) a + b*log(h);
A = [ones(m,1), log(altura)];
%Ec normales.
yy = transpose(A)*log_peso;
AtA = transpose(A)*A;
x = AtA\yy;

cb = [exp(x(1));x(2)];

vec = linspace(.8,1.6);
plot(altura, peso,'ok','LineWidth',2);
hold on
plot(vec, p(vec, cb(1), cb(2)), '-b', 'LineWidth', 2);
grid on
xlabel('t', 'FontSize',14)
ylabel('y', 'FontSize',14)

%% Parte c.
vec = linspace(.8,1.6);
plot(altura, peso,'ok','LineWidth',2);
hold on
plot(vec, p(vec, cb(1), cb(2)), '-b', 'LineWidth', 2);
grid on
plot(vec, p(vec, c(1), c(2)), '-r', 'LineWidth', 2)