%SCRIPT FOR RUNNING THE CRA TOOLBOX WITHOUT USING THE GUI
%The model is written as a Matlab function.

%%%% THE FIRST THING TO DO FOR RUNNING THE SCRIPT IS TO ADD THE FOLDER
%%%% CLASSES AND THE FOLDER Examples TO THE PATH %%%%

%Parameters to be set by the user are:
% 1-model_name: name of the model in .xml format. A struct is created to
% store the following characteristics of an ODE model: nominal values and
% names of the parameters, initial conditions and names of variables, input
% values.
% 2-stop_time: final time point for the model simulation
% 3-step_size: time interval for the vector of time points
% 4- ode_solver: type of ode_solver for simulating the model (possible
% choices are: ode45, ode15s, ode23t, sundials, stochastic, explicit tau
% and implicit tau
% 5- Nr: number of independent realizations to perform 
% 6- LBpi: lower boundary of the Latin Hypercube Sampling for perturbation
% of the model parameter space
% 7- UBpi: upper boundary of the Latin Hypercube Sampling
% 8- Ns: number of samples of the Latin Hypercube (parameters n of the
% lhsdesign function)
% 9- variable_name: variable of the model to set as reference node to be
% measured
% 10- current_func: is the type of evaluation function. Currently, it is
% possible to choose among
% three evaluation functions: area under the curve, maximum value and time
% of maximum for the time behavior of the selected variables. The user can
% also define his evaluation function in a .m file by extending the
% abstract class EvaluationFunction
% 11- tail_size: number of samples to include in the upper and lower tail
% when computing the probability density function of the evaluation
% function
% 12- current_tm: is the method for computing the tails of the pdf of the
% evaluation function. Right now, it is possible to choose between two
% methods: sorted() which sorts the values of the evaluation function and
% selects the first and last samples according to tail_size; tmp_sum()
% computes the tails by selecting the upper and lower quartile. When using
% tmp_sum(), the parameter step_size needs also to be specified. Step_size
% is the step for computing the lower and upper quartile of the pdf in an
% iterative way, i.e. when the upper and lower tails do not have the number of
% samples specified by the user, the threshold is increased of a quantity
% equal to step_size and the calculation of the tails is repeated. 
% The user can also define his own method for the tails computation by
% extending the abstract class TailMethod().
% 13- folder: name of the folder to create where the results are saved

tic;

model_name='ode_covid19_v2';

stop_time=80;
step_size=1;
ode_solver='ode15s';

%time axis for model simulation
time_axis=[0:step_size:stop_time]';

%parameters and initial conditions of the model

N = 882000;         
InitInf=1;

E00 = InitInf;
S0 = N-E00;
x0 = [S0 E00 0 0 0 0 0 0 0];

load('Examples/moda_parametri_inizio14step_LOG_100000_UMBRIA_I2I3DE.mat');
nominal_parameters=moda_parametri_inizio14step_LOG(1:15);
s01=moda_parametri_inizio14step_LOG(16);
s11=moda_parametri_inizio14step_LOG(17);

%nominal_parameters=[be b0 b1 b2 b3 a0 a1 f g0 g1 p1 g2 p2 g3 u]; 
nominal_parameters_name={'be', 'b0', 'b1', 'b2','b3', 'FracSevere', 'FracCritical', 'FracAsym', 'IncubPeriod', 'DurMildInf', 'DurAsym', 'DurHosp', 'TimeICUDeath', 'ProbDeath', 'PresymPeriod'};

derived_parameters=1;
derived_parameters_name={'R0'};

Tlock1=23;

num_observables=9;
observables_name={'S','E0','E1','I0','I1','I2','I3','R','D'};

model=struct('name',model_name,'odesolver',ode_solver,'time',time_axis,'stop',stop_time,'step',step_size,'nominal_parameters',nominal_parameters,'nominal_parameters_name',{nominal_parameters_name},'derived_parameters',derived_parameters,'derived_parameters_name',{derived_parameters_name},'num_observables',num_observables,'observables_name',{observables_name},'initial_conditions',x0,'Tlock1',Tlock1,'s01',s01,'s11',s11);

Nr=10;

%define specific boundaries for each parameter
LBpi=[0.5 0.25 0.25 0.25 0.25 0.125 0.125 0.25 1 0.4311 0.6988 0.1504 0.9213 0.5 0.2995];
UBpi=[2 4 4 4 4 32 16 10 2.81 2.8741 6.9881 1.5042 9.2128 2 1.1980];
Ns=10000;

variable_name='I3';
current_func=TimeOfMaximum(); %current evaluation function
tail_size=1000;  %number of samples for the lower and upper tail
step_size=0.001;  %this parameter needs to be defined only when current_tm=tmp_sum(step_size)
current_tm=sorted();

folder='covid19_TimeMax_results';

%model simulation for each sample of the Latin Hypercube
disp('Starting model simulation with perturbed parameters');
[AllResults,AllPerturbations,AllDerivedParam]=start_simulation_v2_apr2020(model,Nr,LBpi,UBpi,Ns);
disp('All done! Model simulation completed!');

%computation of the MIRI for the chosen evaluation function and model
%variable
disp('Starting computation of the MIRI for each parameter...');
try
  compute_MIRI(model,variable_name,current_func,tail_size,current_tm,Nr,Ns,AllResults,AllPerturbations,AllDerivedParam,folder)
catch ME
    %break  
    return
end
%plot and save probability density function of the evaluation function
disp('Plot of the probability density function of the chosen evaluation function');
plotpdf_evalfunc(folder,variable_name);

%plot and save conditional probability density functions of the parameters 
disp('Plot of the parameter probability density functions');
plotpdf_param(folder,variable_name,model,Nr);

toc;