function cost = costwfixed(StepSigma,DirSigma,Sigma,indsup,Alpsup,C,Sigmaold,Xapp,yapp,pow);%COSTWFIXED Computes an upper bound on SVM loss %  COST = COSTWFIXED(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 weight%  parameters 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);% I) update bandwidthsSigmaP = Sigma.^pow + StepSigma * DirSigma;Sigma  = abs(real(SigmaP.^(1/pow)));% II) compute cost % II.1) slack variables, old Sigma old on support, new Sigma on data pointsindpos = find(yapp== 1);indneg = find(yapp==-1);npos = length(indpos) ;nneg = length(indneg) ;n    = npos + nneg ;nmin = min(npos,nneg);Xsup = Xapp(indsup,:).*repmat(Sigmaold,nsup,1);Xapp = Xapp.*repmat(Sigma,n,1);Dist = Xsup*Xapp';Dist = Dist - repmat(0.5*sum(Xsup.^2,2),1,n) - repmat(0.5*sum(Xapp.^2,2)',nsup,1) ; % - 1/2 ||Sigma . xi - Sigmaold . xj||^2Dist = exp(Dist) ;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.2) norm of classifier, w fixed (Sigma old)Dist = Xsup*Xsup';dist = 0.5*diag(Dist);Dist = Dist - repmat(dist,1,nsup) - repmat(dist',nsup,1) ; % -1/2 (xi-xj)T Sigmaold^2 (xi-xj)Dist = exp(Dist) ;costw = 0.5 * (Alpsup' * Dist * Alpsup) ;% II.3) end: total costcost = costw + costxi ;