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%%% REGRESION representa las curvas de regresion de diferentes ordenes a
%%%           partir de un conjunto de datos.
%%%
%%% AUTOR:   Jesus Cid Sueiro.
%%% VERSION: 2.1 (01/03/2010)
%%% CHANGES: wrt v1.0: visualiza las curvas de regresi?n progresivamente,
%%%                    cada vez que se a?ade una observacion. 
%%%          wrt v1.1: Splits observations in training and test
%%%                    Starts commenting code in English.
%%%                    Changes inverse computation by the '\' matlab
%%%                    operator, which is much more robust.
%%%                    Removes sample-by-sample regression and
%%%                    visualization.
%%%          wrt v2.0: Includes train and test data labels in legend plot.
%%% Asignatura:          Teoría Moderna de la Detección y la Estimación
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% Borra todo
clear all; close all; format compact

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%%% Parametros ajustables
N        = 10;          %%% No. of training samples (and same amount for testing)
orden    = [1 2 N-1]; %%% Models to visualize
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% Inicializa figura
figure
tipolinea = 'b- b--b: b-.r- r--r: r-.g- g--g: g-.';

%%% Inicializa vectores de observaciones
x = zeros(2*N,1);
s = zeros(2*N,1);

%%% Determina y representa las observaciones
for i=1:2*N
    subplot(121)
    axis([0 1 0 2]);
    [x(i,1),s(i,1)]  = ginput(1);  % Selecciona observacion con el raton
    plot(x,s,'+');                 % Pinta todas las observaciones
end
axis([0 1 0 2]);
drawnow

%%% Calcula matriz de features extendidas con potencias de hasta orden 'OrdenMax'.
OrdenMax = N-1;       %%% Maximum model order
Xe       = repmat(x,1,OrdenMax+1).^repmat(0:OrdenMax,2*N,1);   

%%% Split for training and test.
ind     = randperm(2*N);
iTrain  = ind(1:N);
iTest   = ind(N+1:2*N);
xTrain  = x(iTrain);
sTrain  = s(iTrain);
XeTrain = Xe(iTrain,:);
xTest   = x(iTest);
sTest   = s(iTest);
XeTest  = Xe(iTest,:);

%%% Plot training and test points
subplot(121)
axis([0 1 0 2]);
hplot(1) = plot(xTrain,sTrain,'+b'); hold on;
hplot(2) = plot(xTest,sTest,'*r');   
leyenda{1} = 'Datos entren.';
leyenda{2} = 'Datos test';

% Compute feature vector from a uniform grid of the input line.
xgrid  = (0:0.01:1)';
xegrid = repmat(xgrid,1,OrdenMax+1).^repmat(0:OrdenMax,length(xgrid),1);

%%% Determina las curvas de regresion
eTrain = zeros(OrdenMax,1);
eTest  = zeros(OrdenMax,1);
for j=1:N-1;                       % Por cada valor de j, una curva de
    % regresion de orden j
    Xej = XeTrain(:,1:j+1);             % Selecciona las variables hasta orden j
    we = Xej\sTrain;   % Calcula los coeficientes

    % Calcula errores cuadraticos medios
    yTrain   = Xej*we;
    eTrain(j)= sum((sTrain-yTrain).^2);
    yTest    = XeTest(:,1:j+1)*we;
    eTest(j) = sum((sTest-yTest).^2);

    % Compute estimates from the grid samples
    ygrid  = we'*xegrid(:,1:j+1)';

    % Representa graficamente las curvas de regresion
    [tf,loc] = ismember(j,orden);
    if (loc>0), %||((loc==0)&&(j==N-1)),
        if loc==0,
            loc = loc_old + 1;
        else
            loc_old = loc;
        end
        subplot(121);
        hold on
        hplot(loc+2) = plot(xgrid,ygrid,tipolinea(3*(loc-1)+1:3*loc));
        title('Curvas de regresi?n');
        xlabel('x');
        ylabel('s')
        leyenda{loc+2} = ['Grado ' num2str(j)];
    end
end

%%% Escribe la leyenda, y la grafica de errores
subplot(121)
axis([0 1 0 2]);
legend(hplot,leyenda)
drawnow

% Dibuja la curva de errores
subplot(122)
iOrden = 1:OrdenMax;
stem(iOrden,eTest,'--r','filled');
axis([0 OrdenMax 0 1.5*max(eTrain(1),eTest(1))]);
hold on
stem(iOrden,eTrain,'filled');
title('Errores cuadraticos de entrenamiento y test');
xlabel('Grado del polinomio de regresion')
ylabel('Suma de errores cuadraticos')
legend('Errores de test','Errores de entrenamiento');
drawnow

hold off