%?function?[dx?A]?=?assimilate（prm?A?HA?pos?dy?stats）
%
%?Calculates?correction?of?the?ensemble?mean?and?updates?the?ensemble?anomalies.
%
%?@param?prm?-?system?parameters
%?@param?A?-?ensemble?anomalies?（n?x?m）
%?@param?HA?-?ensemble?observations?（p?x?m）
%?@param?pos?-?coordinates?of?observations?（p?x?1）
%?@param?dy?-?vector?of?increments?dy?=?y?-?Hx?（p?x?1）
%?@param?stats?-?system?statistics
%?@return?dx?-?correction?of?the?mean?dx?=?K?dy
%?@return?A?-?updated?ensemble?anomalies

%?File:???????????assimilate.m
%
%?Created:????????23/03/2009
%
%?Last?modified:??19/11/2009
%
%?Author:?????????Pavel?Sakov
%?????????????????NERSC
%
%?Purpose:????????Contains?core?code?for?asynchronous?data?assimilation?with?the
%?????????????????EnKF.
%
%?Description:????This?procedure?calculates?the?analysis?correction?and?updates
%?????????????????the?ensemble?by?applying?scheme?specified?by?prm.method.
%?????????????????It?assumes?that?the?system?runs?in?the?asynchronous?regime
%?????????????????i.e.?that?both?increments?‘dy‘?and?ensemble?observations?‘HA‘
%?????????????????contain?values?recorded?at?the?time?of?observations.
%?????????????????There?are?some?differences?with?the?assimilate.m?that?handles
%?????????????????synchronous?observations:
%?????????????????（i）?There?are?no?batches?of?observations?anymore.?If?there
%?????????????????????are?too?many?observations?-?one?can?always?use?LA?
%?????????????????????localisation?and?conduct?analysis?in?the?ensemble?space
%?????????????????（ii）?Not?all?schemes?are?available?for?every?localisation
%?????????????????????method.?Following?are?the?lists?of?available?schemes?for?
%?????????????????????each?method.
%?????????????????????*?With?no?localisation?or?with?LA:
%???????????????????????EnKF
%???????????????????????DEnKF
%???????????????????????ETKF
%???????????????????????Potter
%???????????????????????EnOI
%?????????????????????*?With?CF:
%???????????????????????EnKF
%???????????????????????DEnKF
%???????????????????????EnOI
%
%?Revisions:

%?????????????????1.10.2009?PS:
%???????????????????--?Fixed?a?defect?in?the?EnKF?scheme?（an?extra?division?by
%??????????????????????sqrt（r）?for?D）
%???????????????????--?Introduced?CF?localisation?with?only?three?schemes?at
%??????????????????????the?moment:?EnKF?DEnKF?and?EnOI
%?????????????????19.11.2009?PS:
%???????????????????--?Updated?description?in?the?file?header
%?????????????????5.8.2010?PS:
%???????????????????--?Modified?LA?part?to?accommodate?“rfactor“
%?????????????????25/08/2010?PS:
%???????????????????-?This?file?formerly?known?as?assimilate_a.m?now?replaced
%?????????????????????the?previous?（synchronous）?version?of?assimilate.m

%%?Copyright?（C）?2009?Pavel?Sakov
%%?
%%?This?file?is?part?of?EnKF-Matlab.?EnKF-Matlab?is?a?free?software.?See?
%%?LICENSE?for?details.

function?[dx?A]?=?assimilate（prm?A?HA?pos?dy?stats）
????
????m?=?prm.m;
????n?=?prm.n;
????r?=?prm.obs_variance;
????rfactor?=?prm.rfactor;
????p?=?size（HA?1）;
????np?=?prm.n