function [cost] = costlbfixed(StepSigma,DirSigma,Sigma,indsup,Alpsup,w0,C,Xapp,yapp,pow);%COSTLBFIXED Computes an upper bound on SVM loss %  COST = COSTLBFIXED(STEPSIGMA,DIRSIGMA,SIGMA,INDSUP,ALPSUP,W0,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 %  and the bias parameter 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%  W0 is the bias parameter%  C is the error penalty hyper-aparameter%  XAPP,YAPP are the learning examples%  27/01/03 Y. Grandvalet% initializationnsup = length(indsup);n    = size(Xapp,1);% 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 variablesxi = 1 - yapp.*((Dist'*Alpsup) + w0); costxi = C*sum(xi(xi>0));% II.3) norm of classifiercostw = 0.5 * (Alpsup' * Dist(:,indsup) * Alpsup) ;% II.4) end: total costcost = costw + costxi ;