rls_fista_driver.m

function w=rls_fista_driver( XtX, Xty, n, lambda,inst_alpha,Niter,relthre,verbose)
% rls_ista_driver( XtX, Xty, n, lambda,alpha,Niter,reltol,verbose)
% Utility function used by rls_ista
% 
% INPUTS:
% -XtX: symmetric dxd square matrix
% -Xty: dxT matrix
% -n: number of training samples
% -lambda: regularization parameter
% -alpha: l1 norm l2 norm weight parameter
% -Niter: maximum number of iteration
% -retol: relative tolernce for convergence
% -verbose: output option
%
% OUTPUTS:
% -W: matrix of coefficient vector for linear RLS classifier

    gamma = n/(2*eigs(XtX,1)+lambda*(1-inst_alpha)); %Step size
    
    % make sure Niter, retol are proper
    if (Niter-round(Niter))~=0 && ~isinf(Niter)
        if verbose
        fprintf('\t...Interation number must be integer. Rounding opt.paramsel.niter\n');
        end
        Niter = ceil(Niter);
    end
    if Niter<=0 && relthre<0
        if verbose
            fprintf(['\t...Unvalid stopping rule for ISTA.',...
            'Using default relative tolerance = 1e-4\n']);
        end
        Niter = -1;
        relthre=1e-4;      
    end
    
    % start ista
    t0=1;t1=1;
    w2=rls_primal_driver(XtX, Xty, n, 0);
    w2(abs(w2)<lambda*inst_alpha*gamma)=0;
    w2=w2-sign(w2)*lambda*inst_alpha*gamma;
    w1=0*w2;
    %dw = mean(abs(w1-w2));
    k=0;

    while mean(abs(w1-w2))>relthre*max([mean(abs(w1)),mean(abs(w2))])
        yk=w2+(t0-1)*(w2-w1)/t1;
        w1=w2;
        w2=(1-lambda*gamma*(1-inst_alpha))*yk+2*gamma*(Xty-XtX*yk)/n;
        w2(abs(w2)<lambda*inst_alpha*gamma)=0;
 %       plot(w2)
        w2=w2-sign(w2)*lambda*inst_alpha*gamma;
        t0=t1;
        t1=(1+(1+4*t1^2)^0.5)/2;
        k=k+1;
        if k==Niter
            break;
        end

    end

    w=w2;
end