stepsize_dichotomie.m

function [model,t_opt,nr_fct,output]=stepsize_dichotomie(model, model_data, output, x, d);
%function [model,t_opt,nr_fct,output]=stepsize_dichotomie(model, model_data, output, x, d)
%
% Function calculating a stepsize following a Dichotomie-algorithm
%
%Required fields of model:
% model.optimization.objective_function: function to be optimized
% model.optimization.tol: tolerance for exactness of the stepsize
% x: initial value
% d: search direction
%
%
%Output variables
% t_opt: optimal value for stepsize t
% nr_fct: number of function calls needed during process
%
%
% Oliver Zeeb 25.05.2010%

if(model.verbose>=8)
    disp('entered stepsize_dichotomie')
end

if model.optimization.min_or_max == 'min'
    min_or_max=1;
elseif model.optimization.min_or_max == 'max'
    min_or_max=-1;
else disp('maximize or minimize? model.optimization.min_or_max not properly defined')
    return
end


% Initializing
tol = model.optimization.tol;
nr_fct = 0; %counter for the number of function calls
t = 1;      %Initial stepsize


h_t = calc_h(model,model_data,x,t,d)*min_or_max; nr_fct=nr_fct+1; 
h_2_t = calc_h(model,model_data,x,2*t,d)*min_or_max; nr_fct=nr_fct+1; 
h_0 = calc_h(model,model_data,x,0,d)*min_or_max; nr_fct=nr_fct+1; 

if isempty(output) %first component, before mu is changed. i.e. value of the functional with init_params, saves one simulation in gradient_opt
    output=[output,h_0];
end

%
% Phase 1
% Surrounding the minimum
%
if(model.verbose>=8)
    disp('in stepsize_dichotomie, Phase 1')
end

%debug
max_iter_phase_1=20;
iter_phase_1=0;
%end debug


if h_t >= h_0           
    while (h_t >= h_0) 
        t = t/2;
        h_t = calc_h(model,model_data,x,t,d)*min_or_max; 
        nr_fct=nr_fct+1;
            %debug
            iter_phase_1=iter_phase_1+1
            if iter_phase_1 == max_iter_phase_1
                break
            end
            %end debug
    end
    a=0;
    b=t;
    c=2*t;
else        %h(t) < h_0
    while (h_2_t <= h_t) 
        h_t = h_2_t;
        t = 2*t;
        h_2_t = calc_h(model,model_data,x,t,d)*min_or_max; 
        nr_fct=nr_fct+1;
            %debug
            %iter_phase_1=iter_phase_1+1
            %if iter_phase_1 == max_iter_phase_1
            %    break
            %end
            %end debug
        
        
    end
    a=0;
    b=t/2;
    c=t;
end

%
% Phase2
% Finding the minimum
%
if(model.verbose>=8)
    disp('in stepsize_dichotomie, Phase 2')
end


%debug
iter_phase_2=0;
%end debug

h_b = calc_h(model,model_data,x,b,d)*min_or_max; nr_fct=nr_fct+1; 
while (c-a) >= tol
    nr_fct=nr_fct+1; %checking the following if condition needs a function call
    if calc_h(model,model_data,x,(a+b)/2,d)*min_or_max < h_b 
        c=b;
        b=(a+b)/2;
        h_b=calc_h(model,model_data,x,b,d)*min_or_max; nr_fct=nr_fct+1; 
    elseif calc_h(model,model_data,x,(b+c)/2,d)*min_or_max < h_b 
        nr_fct=nr_fct+1; % elseif-condition was just checked, that needed a function call
        a=b;
        b=(b+c)/2;
        h_b=calc_h(model,model_data,x,b,d)*min_or_max; nr_fct=nr_fct+1;
    else % h(b) <= min{h((a+b)/2), h((b+c)/2)}
        nr_fct=nr_fct+1; % elseif-condition was just checked, that needed a function call
        a=(a+b)/2;
        c=(b+c)/2;
    end
    
            %debug
            iter_phase_2=iter_phase_2+1
            if mod(iter_phase_2,50) == 0
                zeit_vergangen_phase_2=toc;
                keyboard
            end
            %end debug    
    
    
end

%setting output data
t_opt=(a+c)/2;
func_t_opt=calc_h(model,model_data,x,t_opt,d)*min_or_max;
output=[output;func_t_opt];
model=set_mu_to_optimize(model,x,t_opt,d);

if(model.verbose>=8)
    disp('leaving stepsize_dichotomie')
end

        
%calculation of function h(t), i.e. function f(x+t*d)
function h_t=calc_h(model,model_data,x,t,d)
model_t_d=set_mu_to_optimize(model,x,t,d);
h_t=model.optimization.objective_function(model_t_d,model_data);