function [beta, bias] = smo1forsvr(X,Y,ker,C,loss,e,tau)%SVR Support Vector Regression%%  Usage: [nsv beta bias] = svr(X,Y,ker,C,loss,e)%%  Parameters: X      - Training inputs%              Y      - Training targets%              ker    - kernel function%              C      - upper bound (non-separable case)%              loss   - loss function%              e      - insensitivity%              nsv    - number of support vectors%              beta   - Difference of Lagrange Multipliers%              bias   - bias term%              tau    - violating pair's tolerance parameter%  Author: Steve Gunn (srg@ecs.soton.ac.uk)  %if (nargin < 3 | nargin > 7) % check correct number of arguments    %help svr%  else    fprintf('Sequence Minimization Optimization for SVR ....\n')    fprintf('______________________________\n')        %if (nargin<6) e=0.0;, end    %if (nargin<5) loss='eInsensitive';, end    %if (nargin<4) C=Inf;, end    %if (nargin<3) ker='linear';, end      % tolerance for Support Vector Detection    epsilon = svtol(C);    % Construct the Kernel matrix            %fprintf('Constructing ...\n');        n = size(X,1);    H = zeros(n,n);      for i=1:n       for j=1:n          H(i,j) = svkernel(ker,X(i,:),X(j,:));       end    end    beta=zeros(n, 1);    k=0;    HH=zeros(n, 1);            for i=1:n        HH(i)=-Y(i)+H(i,:)*beta;    end        hplus=HH+e;    hminus=HH-e;        if size(find(beta>0 & beta<=C), 1)==0       Max=max(hminus(find(beta>-C & beta<=0)));    elseif size(find(beta>-C & beta<=0), 1)==0       Max=max(hplus(find(beta>0 & beta<=C)));    elseif size(find(beta>0 & beta<=C), 1)~=0 & size(find(beta>-C & beta<=0), 1)~=0       Max=max(max(hplus(find(beta>0 & beta<=C))), max(hminus(find(beta>-C & beta<=0))));    end        if size(find(beta>=0 & beta<C), 1)==0       Min=min(hminus(find(beta>=-C & beta<0)));    elseif size(find(beta>=-C & beta<0), 1)==0       Min=min(hplus(find(beta>=0 & beta<C)));    elseif size(find(beta>=0 & beta<C), 1)~=0 & size(find(beta>=-C & beta<0), 1)~=0       Min=min(min(hplus(find(beta>=0 & beta<C))), min(hminus(find(beta>=-C & beta<0))));    end               while Max-tau > Min;        Max        Min        for i=1:n            for j=[i+1:n 1:i-1]                 flag=0;                eta=H(i,i)+H(j,j)-2*H(i,j);            if beta(i)>-C & beta(i)<=C & beta(j)>=-C & beta(j)<C                if beta(i)>-C & beta(i)<=0                    hup=hminus(i);                else                    hup=hplus(i);                end                if beta(j)>=-C & beta(j)<0                    hlow=hminus(j);                else                    hlow=hplus(j);                end                hup                hlow                if hup > hlow+tau                        fprintf('found a violating pair...........\n')                        [beta(i), beta(j)] = ntonplusone(beta(i),beta(j),HH(i), HH(j), eta,e,tau,C); %beta(k+1)=...beta(k)                        beta                        flag=1;                end            end            if flag==0               if beta(i)>=-C & beta(i)<C & beta(j)>-C & beta(j)<=C                         if beta(i)>=-C & beta(i)<0                     hlow=hminus(i);                  else                     hlow=hplus(i);                  end                  if beta(j)>-C & beta(j)<=0                    hup=hminus(j);                  else                    hup=hplus(j);                  end                  hlow                  hup                  if hlow < hup-tau                          fprintf('found a violating pair...........\n')                          [beta(i), beta(j)] = ntonplusone(beta(i),beta(j),HH(i), HH(j), eta,e,tau,C); %beta(k+1)=...beta(k)                          beta                          flag=1;                          %break;                  end               end            end                         for i=1:n                 HH(i)=-Y(i)+H(i,:)*beta;              end                  hplus=HH+e;              hminus=HH-e;                  if size(find(beta>0 & beta<=C), 1)==0                 Max=max(hminus(find(beta>-C & beta<=0)));              elseif size(find(beta>-C & beta<=0), 1)==0                 Max=max(hplus(find(beta>0 & beta<=C)));              elseif size(find(beta>0 & beta<=C), 1)~=0 & size(find(beta>-C & beta<=0), 1)~=0                 Max=max(max(hplus(find(beta>0 & beta<=C))), max(hminus(find(beta>-C & beta<=0))));              end                   if size(find(beta>=0 & beta<C), 1)==0                 Min=min(hminus(find(beta>=-C & beta<0)));              elseif size(find(beta>=-C & beta<0), 1)==0                 Min=min(hplus(find(beta>=0 & beta<C)));              elseif size(find(beta>=0 & beta<C), 1)~=0 & size(find(beta>=-C & beta<0), 1)~=0                 Min=min(min(hplus(find(beta>=0 & beta<C))), min(hminus(find(beta>=-C & beta<0))));              end                            Max              Min                            if Max-tau <= Min                  break;              end                          end    %j                        if Max-tau <= Min                break;            end           % break;                                                end    %i                                  %break;       end        %while                % Implicit bias, b0    bias = 0;    % Explicit bias, b0     if nobias(ker) ~= 0      switch lower(loss)        case 'einsensitive',          % find bias from average of support vectors with interpolation error e          % SVs with interpolation error e have alphas: 0 < alpha < C          svii = find( abs(beta) > epsilon & abs(beta) < (C - epsilon));          if length(svii) > 0            bias = (1/length(svii))*sum(Y(svii) - e*sign(beta(svii)) - H(svii,svi)*beta(svi));          else             fprintf('No support vectors with interpolation error e - cannot compute bias.\n');            bias = (max(Y)+min(Y))/2;          end        case 'quadratic',            bias = mean(Y - H*beta);      end     end  end