function K = kernel(varargin)% KERNEL Evaluates kernel function.%% Synopsis:%  K = kernel(X,ker,arg)%  K = kernel(X1,X2,ker,arg)%% Description:%  K = kernel( X, ker, arg ) returns kernel matrix K [n x n] %%    K(i,j) = k(X(:,i),X(:,j))  for all i=1..n, j=1..n,%%   where k: a x b -> R is a kernel function given by %   identifier ker and argument arg:%     %   Identifier    Name           Definition%   'linear'  ... linear kernel  k(a,b) = a'*b%   'poly'    ... polynomial     k(a,b) = (a'*b+arg[2])^arg[1]%   'rbf'     ... RBF (Gaussian) k(a,b) = exp(-0.5*||a-b||^2/arg[1]^2)%   'sigmoid' ... Sigmoidal      k(a,b) = tanh(arg[1]*(a'*b)+arg[2])%%  K = kernel( X1, X2, ker, arg ) returns kernel matrix K [n1 x n2]% %    K(i,j) = k(X1(:,i),X2(:,j))  for all i=1..n1, j=1..n2,%% Input:%  X [dim x n] Single matrix of input vectors.%  X1 [dim x n1], X2 [dim x n2] Pair of input matrices.%  ker [string] Kernel identifier.%  arg [1 x  narg] Kernel argument.%% Output:%  K [n1 x n1] or K [n1 x n2] Kernel matrix.% % Example:%  X = rand(2,50);%  K = kernel( X, 'rbf', 1);%  figure; pcolor( K );               which pcolor%% See also:%  DIAGKER, KERNELPROJ.%% About: Statistical Pattern Recognition Toolbox% (C) 1999-2003, Written by Vojtech Franc and Vaclav Hlavac% <a href="http://www.cvut.cz">Czech Technical University Prague</a>% <a href="http://www.feld.cvut.cz">Faculty of Electrical Engineering</a>% <a href="http://cmp.felk.cvut.cz">Center for Machine Perception</a>% Modifications:% 19-sep-2004, VF% 5-may-2004, VF% MEX-File function.