corrlin.m

krigging model for interpolating data

function  [r, dr] = corrlin(theta, d)
%CORRLIN  Linear correlation function,
%
%           n
%   r_i = prod max(0, 1 - theta_j * d_ij) ,  i = 1,...,m
%          j=1
%
% If length(theta) = 1, then the model is isotropic:
% all theta_j = theta .
%
% Call:    r = corrlin(theta, d)
%          [r, dr] = corrlin(theta, d)
%
% theta :  parameters in the correlation function
% d     :  m*n matrix with differences between given data points
% r     :  correlation
% dr    :  m*n matrix with the Jacobian of r at x. It is
%          assumed that x is given implicitly by d(i,:) = x - S(i,:), 
%          where S(i,:) is the i'th design site. 

% [e-mail]  
% Last update April 12, 2002

[m n] = size(d);  % number of differences and dimension of data
if  length(theta) == 1
  theta = repmat(theta,1,n);
elseif  length(theta) ~= n
  error(sprintf('Length of theta must be 1 or %d',n))
end

td = max(1 - abs(d) .* repmat(theta(:).',m,1), 0);
r = prod(td, 2);

if  nargout > 1
  dr = zeros(m,n);
  for  j = 1 : n
    dr(:,j) = prod(td(:,[1:j-1 j+1:n]),2) .* (-theta(j) * sign(d(:,j)));
  end
end