using PyPlot
using NtToolBox

# SetAR = @(ar)set(gca, 'PlotBoxAspectRatio', [1 ar 1], 'FontSize', 10);
Xm = X -> X - repeat(mean(X,1), outer=(size(X,1), 1))
Cov = X -> Xm(X)'*Xm(X);

A = readdlm("NtToolBox/src/data/boston_house_prices.csv", ',');

A = A[randperm(size(A,1)),:];

X = A[:,1:end-1]
y = A[:,end];

n,p = size(X);

imshow(Cov(X), extent=[0, 1, 0, 1], cmap = get_cmap("jet"));

U,D,V = svd(Xm(X),thin=true)
Z = Xm(X) * V;

figure(figsize=(5,3))
plot(D, ".-", linewidth= 2, markersize= 20); axis("tight");

figure(figsize=(6,4))
plot_multiclasses(X,ones(n,1),disp_dim=3, ms=5);

col = ["blue" "green" "red" "cyan" "magenta" "yellow" "black"]
for i=1:min(p,3)
    subplot(3,1,i)
    plot(Z[:,i], y, ".", c=col[i], ms=10)
    axis("tight")
end
tight_layout()

n0 = Int(round(.5*n)); n1 = n-n0
X0 = X[1:n0,:];     y0 = y[1:n0]
X1 = X[n0+1:end,:]; y1 = y[n0+1:end];

w = (X0'*X0) \ (X0'*y0);

E = sqrt( sum( (X1*w-y1).^2 ) / n1 );

lambda = .1;
w = (X0'*X0+lambda*eye(p)) \ (X0'*y0);
w1 = X0'*( (X0*X0'+lambda*eye(n0)) \ y0 );
@printf "Error (should be 0): %.4f\n" norm(w-w1)/norm(w)

include("NtSolutions/ml_2_regression/exo1.jl");

# Insert your code here.

include("NtSolutions/ml_2_regression/exo2.jl");

# Insert your code here.

include("NtSolutions/ml_2_regression/exo3.jl");

# Insert your code here.

B = 3
n = 500; p = 2
# X = 2*B*rand(n,2)-B
# rho = .5; # noise level
# y = peaks(X[:,1], X[:,2]) + randn(n,1)*rho;
X = readdlm("NtToolBox/src/data/peaks_X.csv", ',')
y = readdlm("NtToolBox/src/data/peaks_y.csv", ',');

scatter(X[:,1], X[:,2], ones(n,1)*20, y, cmap = get_cmap("jet"))
axis([-B B -B B]'); box("on");

distmat = (X,Z) -> broadcast(+,sum(X'.*X',1)',sum(Z'.*Z',1))-2*(X*Z');

sigma = .3
kappa = (X,Z) -> exp( -distmat(X,Z)/(2*sigma^2) );

K = kappa(X,X);

lambda = 0.01
h = (K+lambda*eye(n))\y;

Y = x-> kappa(x,X)*h;

q = 101;
t = linspace(-B,B,q);
v,u = meshgrid(t,t);
Xn = [u[:] v[:]];

yn = reshape(Y(Xn),q,q)
imshow(yn, extent=[0,1, 0,1], cmap = get_cmap("jet"))
axis("image"); axis("off"); 

include("NtSolutions/ml_2_regression/exo4.jl");

# Insert your code here.

include("NtSolutions/ml_2_regression/exo5.jl");

# Insert your code here.