function svm = Epsilon_SVR_Train(X,Y,C,e,ker)

% 輸入參數:
% X 訓練樣本,n×d的矩陣,n為樣本個數,d為樣本維數
% Y 訓練目標,n×1的矩陣,n為樣本個數,值為期望輸出
% C 拉格朗日乘子上界
% e 不敏感損失函數的參數，Epsilon越大，支持向量越少
% ker 核參數(結構體變量)
% the following fields:
% type - linear : k(x,y) = x'*y
% poly : k(x,y) = (x'*y+c)^d
% gauss : k(x,y) = exp(-0.5*(norm(x-y)/s)^2)
% tanh : k(x,y) = tanh(g*x'*y+c)
% degree - Degree d of polynomial kernel (positive scalar).
% offset - Offset c of polynomial and tanh kernel (scalar, negative for tanh).
% width - Width s of Gauss kernel (positive scalar).
% gamma - Slope g of the tanh kernel (positive scalar).

% 輸出參數:
% svm 支持向量機(結構體變量)
% the following fields:
% ker - 核參數
% x - 訓練樣本
% y - 訓練目標;
% a - 拉格朗日乘子

% ------------------------------------------------------------%
% 解二次優化

n = length(Y);
Q = Calckernel(ker,X,X);
H = [Q,-Q;-Q,Q];
f = [e*ones(n,1)-Y;e*ones(n,1)+Y]; % 符號不一樣,決策函數就不一樣,實際上是一回事!見文件"Epsilon_SVR_Sim.m"第37,45行
%f = [e*ones(n,1)+Y;e*ones(n,1)-Y];
A = [];
b = [];
Aeq = [ones(1,n),-ones(1,n)];
beq = 0;
lb = zeros(2*n,1); 
ub = C*ones(2*n,1);
a0 = zeros(2*n,1);

%第三步：調用優化工具箱quadprog函數求解二次規劃
options = optimset;
options.LargeScale = 'off';
options.Display = 'off';

[a,fval,eXitflag,output,lambda] = quadprog(H,f,A,b,Aeq,beq,lb,ub,a0,options);
eXitflag

% ------------------------------------------------------------%
% 輸出 svm
svm.ker = ker;
svm.x = X;
svm.y = Y;
svm.a = a(1:n)-a(n+1:end);