function [ nsv , beta , bias ] = svr (X,Y,ker ,C, loss ,e)

%Note: As of 7/17/2013 this code is broken and has not be used once - ES

% 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

%

% Author : Steve Gunn ( srg@ecs . soton .ac .uk )

if ( nargin < 3 | nargin > 6) % check correct number of arguments

    help svr

else

    fprintf ('Support Vector Regressing ....\ n')

    fprintf (' ______________________________ \n')

    n = size (X ,1);

    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

    % Construct the Kernel matrix

    fprintf (' Constructing ...\ n');

    H = zeros (n,n);

    for i =1: n

        for j =1: n

            H(i,j ) = svkernel (ker ,X(i ,:) ,X(j ,:));

        end

    end

    % Set up the parameters for the Optimisation problem

    switch lower ( loss )

        case ' einsensitive ',

            Hb = [ H -H; -H H];

            c = [( e* ones (n ,1) - Y ); ( e* ones (n ,1) + Y )];

            vlb = zeros (2*n ,1); % Set the bounds : alphas >= 0

            vub = C* ones (2*n ,1); % alphas <= C

            x0 = zeros (2*n ,1); % The starting point is [0 0 0 0]

            neqcstr = nobias ( ker ); % Set the number of equality constraints (1 or 0)

            if neqcstr

                A = [ ones (1,n) - ones (1,n)]; , b = 0; % Set the constraint Ax = b

            else

                A = []; , b = [];

            end

        case 'quadratic ',

            Hb = H + eye (n )/(2* C);

            c = -Y;

            vlb = -1 e30 * ones (n ,1);

            vub = 1 e30 * ones (n ,1);

            x0 = zeros (n ,1); % The starting point is [0 0 0 0]

            neqcstr = nobias ( ker ); % Set the number of equality constraints (1 or 0)

            if neqcstr

                A = ones (1,n); , b = 0; % Set the constraint Ax = b

            else

                A = []; , b = [];

            end

        otherwise , disp ('Error : Unknown Loss Function \n');

end

% Add small amount of zero order regularisation to

% avoid problems when Hessian is badly conditioned .

% Rank is always less than or equal to n.

% Note that adding to much reg will peturb solution

Hb = Hb + 1e -10 * eye ( size (Hb ));

% Solve the Optimisation Problem

fprintf ('Optimising ...\ n');

st = cputime ;

[ alpha lambda how ] = qp(Hb , c , A , b , vlb , vub , x0 , neqcstr );

fprintf ('Execution time : %4.1 f seconds \n',cputime - st );

fprintf ('Status : % s\n',how );

switch lower ( loss )

    case ' einsensitive ',

        beta = alpha (1: n) - alpha (n +1:2* n);

    case 'quadratic ',

        beta = alpha ;

end

fprintf ('|w0 |^2 : % f\n',beta '*H* beta );

fprintf ('Sum beta : % f\n',sum ( beta ));

% Compute the number of Support Vectors

epsilon = svtol ( abs ( beta ));

svi = find ( abs ( beta ) > epsilon );

nsv = length ( svi );

fprintf ('Support Vectors : % d (%3.1 f %%)\ n',nsv ,100* nsv /n);

% 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