function [K] = kernel(ker,x,y)
% Calculate kernel function.   
% x: 輸入樣本,n1×d的矩陣,n1為樣本個數,d為樣本維數
% y: 輸入樣本,n2×d的矩陣,n2為樣本個數,d為樣本維數
% 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)  
%                                        % norm命令計算矩陣或向量(x-y)的2-范數
%            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).
% ker = struct('type','linear');
% ker = struct('type','ploy','degree',d,'offset',c);
% ker = struct('type','gauss','width',s);
% ker = struct('type','tanh','gamma',g,'offset',c);
% K: 輸出核參數,n1×n2的矩陣
%-------------------------------------------------------------%
switch ker.type
    case 'linear'
        K = x*y';         % n*n的矩陣
    case 'ploy'
        d = ker.degree;
        c = ker.offset;
        K = (x*y'+c).^d;
    case 'gauss'
        s = ker.width;
        rows = size(x,1);
        cols = size(y,1);   
        tmp = zeros(rows,cols);
        for i = 1:rows
            for j = 1:cols
                tmp(i,j) = norm(x(i,:)-y(j,:));
            end
        end        
        K = exp(-0.5*(tmp/s).^2);
    case 'tanh'
        g = ker.gamma;
        c = ker.offset;
        K = tanh(g*x*y'+c);
    otherwise
        K = 0;
end