function [l X Y w b J0 rho] = svmQP(yx,toler)
###########################################################
#
# USAGE:
#          [l x y w b J0 rho] = svmQP(yx,toler)
#
# INPUT:
#       yx  = matrix with N examples. Each line: y x
#       toler = tolerance for QPsolver. e.g. 1.0e-5
###########################################################
# OUTPUT:
#
#    l   The vector of lambdas
#    x   matrix [x1,x2,...,xn]'
#    y   vector of labels
#    w   normal vector of optimal hyperplane
#    b   location scalar optimal hypp  <w,x>+b = 0
#    J0  list of indices of support vectors
#    rho margin 1/|w|
#
###########################################################

[d,dimyx] = size(yx);

[Q,A,b,c] = setQP(yx,d);

YesQPsolver;       ## sets x,y,obhis

l = x;
b = y;
l(find(x <= 10*toler)) = 0;
J0 = find(l > 10*toler);
X = yx(:,2:dimyx);
Y = yx(:,1);
w = (l.*Y)'*X;
rho = 1/norm(w);

endfunction


function [Q,A,b,c] = setQP(yx,d)
     [n,cc] = size(yx);
     d = d+1;
     Q = zeros(n,n);
     A = yx(:,1)';
     b = 0;
     c = (-1)*ones(n,1);
     for i = 1:n
       Q(i,i) = A(i)*A(i)*dot(yx(i,2:d),yx(i,2:d));
       for j = i:n
	 Q(i,j) = A(i)*A(j)*dot(yx(i,2:d),yx(j,2:d));
	 Q(j,i) = Q(i,j);
       endfor
     endfor
endfunction