function?res=exi2d（Prmus）
%?P:?approximation?set?2xK?r:?reference?point?mu:?mean?vector?s:stdev
%?vector
%?Example:?exi2d（[02;11;20][33][00][0.10.1]）?should?approximately
%?result?in?3
%?
%?determine?all?lower?left?corner?cell?coordinates
S=sortrows（P）;
k=length（S）;

c2?=?sort（S（:2））;
c1?=?sort（S（:1））;

for?i=0:k?????%?hoogte?van?beneden?naar?boven;?hight?from?below?to?above
????for?j=0:（k-i）?%?first?coordinate?（length）?of?cell?grid
????????%?c1（i）?c2（j）?are?now?the?cell?coordinates?according?Fig.?2???
????????%?For?coordinate?j?determine?hight?fMax2?
????????if?（j==0）?fMax2=r（2）;?else?fMax2?=?c2（k+1-j）;?end;
????????%?For?coordinate?i?determine?the?width?of?the?staircase?fMax1?
????????if?（i==0）?fMax1=r（1）;?else?fMax1?=?c1（k+1-i）;?end;
????????%?get?cell?coordinates
????????if?（j==0）?cL1=?-inf;?else?cL1?=?c1（j）;?end;?
????????if?（i==0）?cL2=?-inf;?else?cL2?=?c2（i）;?end;
????????if?（j==k）?cU1?=?r（1）;?else?cU1?=?c1（j+1）;?end;
????????if?（i==k）?cU2?=?r（2）;?else?cU2?=?c2（i+1）;?end;
????????%?SM?=?points?that?are?dominated?or?equal?to?upper?cell?bound??
????????SM=[;];?
????????for?m=1:k
????????????if?（cU1?<=?S（m1）?&&?cU2?<=?S（m2））
????????????????SM=[[S（m1）S（m2）];SM];
????????????end?????????????
????????end
????????sPlus?=?hvolume2d（SM?[fMax1fMax2]）;
????????%Marginal?integration?over?the?length?of?a?cell
????????Psi1?=?exipsi（fMax1cU1mu（1）s（1））?-?exipsi（fMax1cL1mu（1）s（1））;
????????%Marginal?integration?over?the?height?of?a?cell
????????Psi2?=?exipsi（fMax2cU2mu（2）s（2））?-?exipsi（fMax2cL2mu（2）s（2））;
????????%Cumulative?Gaussian?over?length?for?correction?constant
????????GaussCDF1?=?gausscdf（（cU1-mu（1））/s（1））?-?gausscdf（（cL1-mu（1））/s（1））;
????????%Cumulative?Gaussian?over?length?for?correction?constant
????????GaussCDF2?=?gausscdf（（cU2-mu（2））/s（2））?-?gausscdf（（cL2-mu（2））/s（2））;
????????%ExI?Kontribution?fuer?die?aktuelle?Zelle
????????c（i+1j+1）=?Psi1*Psi2-sPlus*GaussCDF1*GaussCDF2;
????end
end

res=sum（sum（max（c0）））;

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2010-04-28?15:05??HV_based_expected_improvement\
?????文件????????2033??2010-04-27?19:14??HV_based_expected_improvement\exi2d.m
?????文件??????????80??2010-04-26?22:21??HV_based_expected_improvement\exipsi.m
?????文件??????????51??2010-04-27?18:50??HV_based_expected_improvement\gausscdf.m
?????文件??????????59??2010-04-27?18:46??HV_based_expected_improvement\gausspdf.m
?????文件?????????339??2010-04-26?22:21??HV_based_expected_improvement\hvolume2d.m
?????文件????????1283??2010-04-27?19:29??HV_based_expected_improvement\README.txt