function g = tensorKernGradient(kern, x, varargin)

% TENSORKERNGRADIENT Gradient of TENSOR kernel's parameters.
%
%	Description:
%
%	G = TENSORKERNGRADIENT(KERN, X, PARTIAL) computes the gradient of
%	functions with respect to the tensor product kernel's parameters. As
%	well as the kernel structure and the input positions, the user
%	provides a matrix PARTIAL which gives the partial derivatives of the
%	function with respect to the relevant elements of the kernel matrix.
%	 Returns:
%	  G - gradients of the function of interest with respect to the
%	   kernel parameters. The ordering of the vector should match that
%	   provided by the function kernExtractParam.
%	 Arguments:
%	  KERN - the kernel structure for which the gradients are being
%	   computed.
%	  X - the input locations for which the gradients are being
%	   computed.
%	  PARTIAL - matrix of partial derivatives of the function of
%	   interest with respect to the kernel matrix. The argument takes the
%	   form of a square matrix of dimension  numData, where numData is
%	   the number of rows in X.
%
%	G = TENSORKERNGRADIENT(KERN, X1, X2, PARTIAL) computes the
%	derivatives as above, but input locations are now provided in two
%	matrices associated with rows and columns of the kernel matrix.
%	 Returns:
%	  G - gradients of the function of interest with respect to the
%	   kernel parameters.
%	 Arguments:
%	  KERN - the kernel structure for which the gradients are being
%	   computed.
%	  X1 - the input locations associated with the rows of the kernel
%	   matrix.
%	  X2 - the input locations associated with the columns of the kernel
%	   matrix.
%	  PARTIAL - matrix of partial derivatives of the function of
%	   interest with respect to the kernel matrix. The matrix should have
%	   the same number of rows as X1 and the same number of columns as X2
%	   has rows.
%	
%
%	See also
%	% SEEALSO TENSORKERNPARAMINIT, KERNGRADIENT, TENSORKERNDIAGGRADIENT, KERNGRADX


%	Copyright (c) 2006 Neil D. Lawrence
% 	tensorKernGradient.m CVS version 1.2
% 	tensorKernGradient.m SVN version 328
% 	last update 2011-06-16T07:23:44.000000Z

  
% Last of varargin is covGrad.
  g = zeros(1, kern.nParams);
  startVal = 1;
  endVal = 0;
  twoXin = 0;
  if length(varargin) > 1
    twoXin = 1;
    x2 = varargin{1};
    covGrad = varargin{end};
  else
    covGrad = varargin{end};
  end
  
  for i = 1:length(kern.comp)
    tempKern = tensorKernSlash(kern, i);
    if twoXin
      tempCovGrad = covGrad.*kernCompute(tempKern, x, x2);
    else
      tempCovGrad = covGrad.*kernCompute(tempKern, x);
  end
  endVal = endVal + kern.comp{i}.nParams;
  if ~isempty(kern.comp{i}.index)
    % only part of the data is involved in the kernel.
    if ~twoXin
      g(1, startVal:endVal)  = kernGradient(kern.comp{i}, ...
                                            x(:, kern.comp{i}.index), ...
                                            tempCovGrad);
    else
      g(1, startVal:endVal) = kernGradient(kern.comp{i}, ...
                                           x(:, kern.comp{i}.index), ...
                                           x2(:, kern.comp{i}.index), ...
                                           tempCovGrad);
    end
  else
    if ~twoXin
      % all the data is involved with the kernel.
      g(1, startVal:endVal)  = kernGradient(kern.comp{i}, x, ...
                                            tempCovGrad);
    else
      g(1, startVal:endVal) = kernGradient(kern.comp{i}, x, x2, ...
                                           tempCovGrad);
    end
  end
  startVal = endVal + 1;
end
g = g*kern.paramGroups;