scm_coercive_lb.m

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function alpha_LB = scm_coercive_lb(mu,model,operator,SCM_data)
%alpha_LB = scm_lb(mu,model,model_data)
% computation of the lowerbound of the coercive constant 
% equal to the coercive constant computet via SCM
%
% mu         : parameter which lower bound value is desired
% model      : standart model 
% model_data : standart model_data
% SCM_data   : precomputed offline SCM data (e.g. via scm_coercive_greedy)

% David Kreplin 01.12 2014

if isfield(SCM_data,'C') == 0
    error('SCM Greedy computation is required first')
end

[~,Ind_PMa]   = scm_get_neighbours(SCM_data.params.Ma, mu, SCM_data.C.Set);
[PMp,Ind_PMp] = scm_get_neighbours(SCM_data.params.Mp, mu, SCM_data.params.ParameterSet);
Ma = length(Ind_PMa);
Mp = length(Ind_PMp);
b_lp= zeros(Ma+Mp,1);
A_lp= zeros(Ma+Mp,SCM_data.params.Q);
 
b_lp(1:Ma) = -1*SCM_data.C.coercivity(Ind_PMa(1:Ma));
A_lp(1:Ma,:) = -1*SCM_data.C.ParameterVector(Ind_PMa(:,1:Ma),:);

for i = 1:Mp
    model = set_mu(model,PMp(:,i));
    model.decomp_mode=2;
    [A,~] =  operator(model);
    A_lp(i+Ma,:) = -1*A';
end

model = set_mu(model,mu);
model.decomp_mode=2;
[A,~] =  operator(model);
f_lp = A;
Options = optimset('Display','off');
[~,alpha_LB]=linprog(f_lp,A_lp,b_lp,[],[],SCM_data.lower_bound_coercivity,...
    SCM_data.upper_bound_coercivity,SCM_data.upper_bound_coercivity,Options);
%keyboard;
end