function R=cholesky(K,eta)



%function R=cholesky(K,eta)

%

% Performs inncomplete cholesky of the kernel matrix K

%

%INPUTS

% K = the kernel matrix (ell x ell matrix)

% eta = tolerance parameter

%

%OUTPUTS

% R = the T first cholesky components of K (R is ell x T)

%

%

%For more info, see www.kernel-methods.net





% original kernel matrix stored in variable K

% of size ell x ell.

% new features stored in matrix R of size T x ell 

% eta gives threshold residual cutoff

ell=size(K,1);

j = 0;

R = zeros(ell,ell);

d = diag(K);

[a,I(j+1)] = max(d);

while a > eta

  j = j + 1;

  nu(j) = sqrt(a);

  for i = 1:ell

    R(j,i) = (K(I(j),i) - R(:,i)'*R(:,I(j)))/nu(j);

    d(i) = d(i) - R(j,i)^2;

  end

  [a,I(j+1)] = max(d);

end

T = j;

R = R(1:T,:);