%?
%???General?subspace?identification?
%???-------------------------------
%???
%???The?algorithm?‘subid‘?identifies?deterministic?stochastic?
%???as?well?as?combined?state?space?systems?from?IO?data.
%
%???????????[ABCDKR]?=?subid（yui）;
%?
%???Inputs:
%???????????y:?matrix?of?measured?outputs
%???????????u:?matrix?of?measured?inputs?
%??????????????for?stochastic?systems?u?=?[]
%???????????i:?number?of?block?rows?in?Hankel?matrices
%??????????????（i?*?#outputs）?is?the?max.?order?that?can?be?estimated?
%??????????????Typically:?i?=?2?*?（max?order）/（#outputs）
%???????????
%???Outputs:
%???????????ABCDKR:?combined?state?space?system
%???????????
%??????????????????x_{k+1）?=?A?x_k?+?B?u_k?+?K?e_k????????
%????????????????????y_k???=?C?x_k?+?D?u_k?+?e_k
%?????????????????cov（e_k）?=?R
%?????????????????
%???????????For?deterministic?systems:?K?=?R?=?[]
%???????????For?stochastic?systems:????B?=?D?=?[]
%
%???Optional:
%
%???????????[ABCDKRAUXss]?=?subid（yuinAUXWsil）;
%???
%???????????n:????optional?order?estimate?（default?[]）
%?????????????????if?not?given?the?user?is?prompted?for?the?order
%???????????AUX:??optional?auxilary?variable?to?increase?speed?（default?[]）
%???????????W:????optional?weighting?flag
%??????????????????????SV:????Singular?values?based?algorithm?
%?????????????????????????????（default?for?systems?with?input?u）
%??????????????????????CVA:???Canonical?variate?based?algorithm
%?????????????????????????????（default?for?systems?without?input?u）
%???????????ss:???column?vector?with?singular?values
%???????????sil:??when?equal?to?1?no?text?output?is?generated
%???????????
%???Example:
%???
%???????????[ABCDKRAUX]?=?subid（yu102）;
%???????????for?k=3:6
%??????????????[ABCD]?=?subid（yu10kAUX）;
%???????????end
%???????????
%???Reference:
%???
%???????????Subspace?Identification?for?Linear?Systems
%???????????Theory?-?Implementation?-?Applications
%???????????Peter?Van?Overschee?/?Bart?De?Moor
%???????????Kluwer?Academic?Publishers?1996
%???????????Stochastic?algorithm:???Figure?3.13?page?90?（positive）
%???????????Combined?algorithm:?????Figure?4.8?page?131?（robust）
%
%???Copyright:
%???
%???????????Peter?Van?Overschee?December?1995
%???????????peter.vanoverschee@esat.kuleuven.ac.be
%
%

function?[ABCDKRoAUXss]?=?subid（yuinAUXinWsil）;

if?（nargin?
mydisp（sil‘?‘）;
mydisp（sil‘???Subspace?Identification‘）;
mydisp（sil‘???-----------------------‘）;

%?Check?the?arguments
if?（nargin?if?（nargin?if?（nargin?
%?Check?if?its?deterministic?or?stochastic?ID
if?（u?==?[]）;???ds_flag?=?2;?		%?Stochastic
else;???????????ds_flag?=?1;?		%?Deterministic
end??

%?Give?W?its?default?value
if?（nargin?if?（W?==?[]）
??if?（ds_flag?==?1）;?W?=?‘SV‘;?		%?Deterministic:?default?to?SV
??else;????????????W?=?‘CVA‘;end?	%?Stochastic:?default?to?CVA
end


%?Turn?the?data?into?row?vectors?and?c