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% Performs a local 4D-optimal interpolation (objective analysis).


function [fi,vari] = optiminterp4(x,y,z,t,f,var,lenx,leny,lenz,lent,m,xi,yi,zi,ti)


% -*- texinfo -*-
% @deftypefn {Loadable Function} {[@var{fi},@var{vari}] = } optiminterp4(@var{x},@var{y},@var{z},@var{t},@var{f},@var{var},@var{lenx},@var{leny},@var{lenz},@var{lent},@var{m},@var{xi},@var{yi},@var{zi},@var{ti})
% Performs a local 4D-optimal interpolation (objective analysis).
% Every elements in @var{f} corresponds to a data point (observation)
% at location  @var{x}, @var{y}, @var{z}, @var{t} with the error variance var
% @var{lenx},@var{leny},@var{lenz} and @var{lent} are correlation length in x-,y-,z-direction and time,
% respectively. 
% @var{m} represents the number of influential points.
% @var{xi},@var{yi},@var{zi} and @var{ti} are the data points where the field is
% interpolated. @var{fi} is the interpolated field and @var{vari} is 
% its error variance.
% The background field of the optimal interpolation is zero.
% For a different background field, the background field
% must be subtracted from the observation, the difference 
% is mapped by OI onto the background grid and finally the
% background is added back to the interpolated field.
% The error variance of the background field is assumed to 
% have a error variance of one. 
% @end deftypefn


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