clear all
% these are the values in the3 notes x(1), y(1)
x_input = -5:1:10;
y_input = 5*x_input.*x_input + 7*x_input + sqrt(13);
% column vector
y_input=y_input';
x_input=x_input';
M = length(x_input); % data pairs
%    x|y
%   ------
% x(1)|(y1)



x = -10:0.1:10;

% see notes why
w1_11 = 1;
b1_1 = 2.5;

w1_12 = 1;
b1_2 = -2.5;


w1_13 = 1;
b1_3 = -7.5;

% we're going to solve for these
% w_11 = 600;
% w_21 = -600;
% b_1 = 600;

for i=1:M
    phi(:,i) = [1/(1+exp(-(x_input(i)*w1_11+b1_1)));...
        1/(1+exp(-(x_input(i)*w1_12+b1_2)));...
        1/(1+exp(-(x_input(i)*w1_13+b1_3)));...
        1];
end

Phi=phi'
theta = Phi\y_input;

w_11 = theta(1);
w_21 = theta(2);
w_31 = theta(3);
b_1 =  theta(4);

y1 = Phi*theta;

xbar1_1 = w1_11*x + b1_1;
y1_1 = 1./(1+ exp(-xbar1_1));

xbar1_2 = w1_12*x + b1_2;
y1_2 = 1./(1+ exp(-xbar1_2));

xbar1 = y1_1*w_11 + y1_2*w_21 + b_1;
%y1 = xbar1;

grid on;

figure (2)
plot(x_input,y_input,'r.-');
hold on;
plot(x_input,y1,'b.-');
hold off;
grid on