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function k = svkernel(ker,u,v) 
%SVKERNEL kernel for Support Vector Methods 
% 
%  Usage: k = svkernel(ker,u,v) 
% 
%  Parameters: ker - kernel type 
%              u,v - kernel arguments 
% 
%  Values for ker: 'linear'  - 
%                  'poly'    - p1 is degree of polynomial 
%                  'rbf'     - p1 is width of rbfs (sigma) 
%                  'sigmoid' - p1 is scale, p2 is offset 
%                  'spline'  - 
%                  'bspline' - p1 is degree of bspline 
%                  'fourier' - p1 is degree 
%                  'erfb'    - p1 is width of rbfs (sigma) 
%                  'anova'   - p1 is max order of terms 
%               
%  Author: Steve Gunn (srg@ecs.soton.ac.uk) 
 
  if (nargin < 1) % check correct number of arguments 
     help svkernel 
  else 
      
    global p1 p2; 
 
    % could check for correct number of args in here 
    % but will slow things down further 
    switch lower(ker) 
      case 'linear' 
        k = u*v'; 
      case 'poly' 
        k = (u*v' + 1)^p1; 
      case 'rbf' 
        k = exp(-(u-v)*(u-v)'/(2*p1^2)); 
      case 'erbf' 
        k = exp(-sqrt((u-v)*(u-v)')/(2*p1^2)); 
      case 'sigmoid' 
        k = tanh(p1*u*v'/length(u) + p2); 
      case 'fourier' 
        z = sin(p1 + 1/2)*2*ones(length(u),1); 
        i = find(u-v); 
        z(i) = sin(p1 + 1/2)*(u(i)-v(i))./sin((u(i)-v(i))/2); 
        k = prod(z); 
      case 'spline' 
        z = 1 + u.*v + u.*v.*min(u,v) - ((u+v)/2).*(min(u,v)).^2 + (1/3)*(min(u,v)).^3; 
        k = prod(z); 
      case {'curvspline','anova'} 
        z = 1 + u.*v + (1/2)*u.*v.*min(u,v) - (1/6)*(min(u,v)).^3; 
        k = prod(z); 
 
% - sum(u.*v) - 1;  
%        z = 1 + u.*v + (1/2)*u.*v.*min(u,v) - (1/6)*(min(u,v)).^3; 
%        k = prod(z);  
%        z = (1/2)*u.*v.*min(u,v) - (1/6)*(min(u,v)).^3; 
%        k = prod(z);  
 
      case 'bspline' 
        z = 0; 
        for r = 0: 2*(p1+1) 
          z = z + (-1)^r*binomial(2*(p1+1),r)*(max(0,u-v + p1+1 - r)).^(2*p1 + 1); 
        end 
        k = prod(z); 
      case 'anovaspline1' 
        z = 1 + u.*v + u.*v.*min(u,v) - ((u+v)/2).*(min(u,v)).^2 + (1/3)*(min(u,v)).^3; 
        k = prod(z);  
      case 'anovaspline2' 
        z = 1 + u.*v + (u.*v).^2 + (u.*v).^2.*min(u,v) - u.*v.*(u+v).*(min(u,v)).^2 + (1/3)*(u.^2 + 4*u.*v + v.^2).*(min(u,v)).^3 - (1/2)*(u+v).*(min(u,v)).^4 + (1/5)*(min(u,v)).^5; 
        k = prod(z); 
      case 'anovaspline3' 
        z = 1 + u.*v + (u.*v).^2 + (u.*v).^3 + (u.*v).^3.*min(u,v) - (3/2)*(u.*v).^2.*(u+v).*(min(u,v)).^2 + u.*v.*(u.^2 + 3*u.*v + v.^2).*(min(u,v)).^3 - (1/4)*(u.^3 + 9*u.^2.*v + 9*u.*v.^2 + v.^3).*(min(u,v)).^4 + (3/5)*(u.^2 + 3*u.*v + v.^2).*(min(u,v)).^5 - (1/2)*(u+v).*(min(u,v)).^6 + (1/7)*(min(u,v)).^7; 
        k = prod(z); 
      case 'anovabspline' 
        z = 0; 
        for r = 0: 2*(p1+1) 
          z = z + (-1)^r*binomial(2*(p1+1),r)*(max(0,u-v + p1+1 - r)).^(2*p1 + 1); 
        end 
        k = prod(1 + z); 
      otherwise 
        k = u*v'; 
    end 
 
  end