scm_online.m

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function scm_results = scm_online(mu, Theta_mu, scm_offline_data, M_alpha, M_plus, desired_constant)
%scm_results = scm_online(mu, Theta_mu, scm_offline_data, M_alpha, M_plus, desired_constant)
%
% function which computes the online-stage of the SCM including the
% computation of both a lower and an upper bound to the desired constant.
% See scm_offline.m for the description of the various model-fields
% controlling the SCM.
%
% The upper bound is computed as a simple search for a minimum, the lower
% bound is computed by solving a linear program.

% Dominik Garmatter 17.09 2012


warningstate = warning('off','MATLAB:rankDeficientMatrix');
%comment by Dominik Garmatter regarding this disable:
% the disabled warning occured sometimes in qpsub.m (lines 742 nd 632) when
% using a 'lin_evol' problem_type and the standard active-set algorithm (in
% the linear program - see scm_offline_data.Options). We couldn't find a
% reason why this warning should occur but neglected it because it didn't
% seem to be a huge problem (even if the 'lin_evol'-case isn't fully
% working yet - but in qpsub other warnings regarding singularity of
% matrices are also disabled for the respective lines)

% preparing the sets P_M_alpha and P_M_plus. But it is sufficient to have
% the indices of the selected parmeters!
[~, ind_alpha] = scm_get_neighbours(M_alpha, mu, scm_offline_data.C);
[~, ind_plus] = scm_get_neighbours(M_plus, mu, scm_offline_data.D);

%% computation of the lower bound

% if the offline-data is feasable we choose the upper end of the bounding
% box as starting vector.
if scm_offline_data.isfeasable == 1
    x0 = scm_offline_data.sigma_plus;
else
    warning('ONLINE:infeasable_data', 'offline_data can cause infeasable Problems. Check them!');
end

% now compute the lower bound via a linear program min_x (f'*x) with the
% inequality constriants A*x <= b
f = Theta_mu;
b = [scm_offline_data.sigma_plus; -scm_offline_data.sigma_minus; -scm_offline_data.alpha_C(ind_alpha); zeros(size(ind_plus,2),1)];
A = [eye(size(scm_offline_data.sigma_plus,1)); -eye(size(scm_offline_data.sigma_plus,1)); -scm_offline_data.Theta_C(:,ind_alpha)'; -scm_offline_data.Theta_D(:,ind_plus)'];

[~, fval, exitflag, ~] = linprog(f, A, b, [], [], [], [], x0, scm_offline_data.Options);

if exitflag < 0 % if you also want to include the case that the maximum number of iterations is reached choose if exitflag < 1 here
    warning('ONLINE:lin_prog', ['Optimization exited with exitflag = ' mat2str(exitflag)]);
    keyboard;
end

warning(warningstate) % reset the warning state of the above warning

%% inf-sup differntiation and computation of the upper bound

% get information about the parent-function using dbstack. In the coercive
% case or if the parenting function is the offline-phase never use sqrt. In
% other cases (online-phase of infsup) use sqrt!
% This solves the problem that the SCM for the inf-sup case (i.e.
% model.scm_desired_constant = 2) is cast for beta^2. But in an
% online-phase of such a SCM one wants beta as a result and not beta^2.
% This is solved with this block of code. 
% Also the upper bound is computed via a simple minimum search.
stack = dbstack;
if size(stack,1) > 1 && strcmp(stack(2,1).name,'scm_offline_new') == 1 || desired_constant == 1
    Lower_Bound = fval;
    Upper_Bound = min(scm_offline_data.ystern_C'*Theta_mu);
else
    Lower_Bound = sqrt(fval);
    Upper_Bound = sqrt(min(scm_offline_data.ystern_C'*Theta_mu));
end

%% output

scm_results.Upper_Bound = Upper_Bound;
scm_results.Lower_Bound = Lower_Bound;