function [cost] = costlfixed(StepSigma,DirSigma,Sigma,indsup,Alpsup,C,Xapp,yapp,pow);%COSTLFIXED Computes an upper bound on SVM loss %  COST = COSTLFIXED(STEPSIGMA,DIRSIGMA,SIGMA,INDSUP,ALPSUP,C,XAPP,YAPP,POW) %  is the upper bound on the SVM loss for updated scale parameters  %  (SIGMA.^POW + STEPSIGMA * DIRSIGMA)^(1/POW), %  when the Lagrange multipliers are considered unaffected by the SIGMA update %  %  STEPSIGMA is the stepsize of SIGMA update%  DIRSIGMA is the direction of SIGMA update%  SIGMA is the current SIGMA value%  INDSUP is the (nsup,1) index of current support vectors %  ALPSUP is the (nsup,1) vector of non-zero Lagrange multipliers%  C is the error penalty hyper-aparameter%  XAPP,YAPP are the learning examples%  27/01/03 Y. Grandvalet% initializationnsup    = length(indsup);[n,dim] = size(Xapp);% I) update bandwidthsSigmaP = Sigma.^pow + StepSigma * DirSigma;Sigma  = abs(real(SigmaP.^(1/pow)));% II) compute cost % II.1) distancesXapp = Xapp.*repmat(Sigma,n,1);Xsup = Xapp(indsup,:);Dist = Xsup*Xapp';dist = 0.5*sum(Xapp.^2,2) ;Dist = Dist - repmat(dist(indsup),1,n) - repmat(dist',nsup,1) ; % -1/2 (xi-xj)T Sigma^2 (xi-xj)Dist = exp(Dist) ;% II.2) slack variablesindpos = find(yapp== 1);indneg = find(yapp==-1);npos = length(indpos) ;nneg = length(indneg) ;nmin = min(npos,nneg);xipos = -sort(-(1 - Alpsup'*Dist(:,indpos))); xineg = -sort(-(1 + Alpsup'*Dist(:,indneg))); xi = sum([xineg(1:nmin) ; xipos(1:nmin)],1);costxi = C*sum(xi(xi>0));% II.3) norm of classifiercostw = 0.5 * (Alpsup' * Dist(:,indsup) * Alpsup) ;% II.4) end: total costcost = costw + costxi ;