function [initialconditions, samplesize, innovations, options_, M_, oo_, endonames, exonames, dynamic_resid, dynamic_g1, y] = ...
    initialize(initialconditions, samplesize, options_, M_, oo_, innovations)
% [initialconditions, samplesize, innovations, options_, M_, oo_, endonames, exonames, dynamic_resid, dynamic_g1, y] = ...
%     initialize(initialconditions, samplesize, options_, M_, oo_, innovations)
% Initialization of the routines simulating backward models.

% Copyright © 2017-2025 Dynare Team
%
% This file is part of Dynare.
%
% Dynare is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% Dynare is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with Dynare.  If not, see <https://www.gnu.org/licenses/>.

% Test if the model is backward.
if M_.maximum_lead
    error('simul_backward_nonlinear_model:: The specified model is not backward looking!')
end

% Test if the first argument is a dseries object.
if ~(isdseries(initialconditions) || isempty(initialconditions))
    error('First input argument must be a dseries object or an empty array!')
end

% If initialconditions is empty instantiates a dseries object with the information available in M_.endo_histval.
if isempty(initialconditions)
    yinitdata = zeros(M_.orig_endo_nbr, M_.orig_maximum_lag);
    yinitdata(:,1) = M_.endo_histval(1:M_.orig_endo_nbr);
    xinitdata = zeros(M_.exo_nbr, M_.orig_maximum_lag);
    if M_.orig_maximum_endo_lag>1
        for i = 1:length(M_.aux_vars)
            if M_.aux_vars(i).type==1
                yinitdata(M_.aux_vars(i).orig_index, abs(M_.aux_vars(i).orig_lead_lag)+1) = ...
                    M_.endo_histval(M_.orig_endo_nbr+i);
            end
        end
        yinitdata = flip(yinitdata, 2);
    end
    if M_.orig_maximum_exo_lag>0
        for i = 1:length(M_.aux_vars)
            if M_.aux_vars(i).type==3
                xinitdata(M_.aux_vars(i).orig_index, abs(M_.aux_vars(i).orig_lead_lag)+1) = ...
                    M_.endo_histval(M_.orig_endo_nbr+i);
            end
        end
        xinitdata = flip(xinitdata, 2);
    end
    initialconditions = dseries([transpose(yinitdata) transpose(xinitdata)], '1Y', ...
                                vertcat(M_.endo_names(1:M_.orig_endo_nbr), M_.exo_names));
end

initialconditions = checkdatabase(initialconditions, M_, false, true);

% Test if the first argument contains all the lagged endogenous variables
endonames = M_.endo_names;
missingendogenousvariables = setdiff(endonames, initialconditions.name);
endolags = get_lags_on_endogenous_variables(M_);
endolags_ = endolags(find(endolags));
endowithlagnames = endonames(find(endolags));
if ~isempty(missingendogenousvariables)
    missingendogenousvariables = setdiff(endowithlagnames, initialconditions.name);
    missingendogenouslaggedvariables = intersect(endowithlagnames, missingendogenousvariables);
    if ~isempty(missingendogenouslaggedvariables)
        disp('You have to initialize the following endogenous variables:')
        msg = sprintf('%s\n', missingendogenouslaggedvariables{1:end-1});
        msg = sprintf('%s%s', msg, missingendogenouslaggedvariables{end});
        disp(msg)
        skipline()
        error('Please fix the dseries object used for setting the initial conditions!')
    end
end

% Test if we have enough periods in the database.
maxlag = abs(min(endolags));
if maxlag>initialconditions.nobs
    error('The dseries object provided as first input argument should at least have %s periods!', num2str(maxlag))
end
missinginitialcondition = false;
for i = 1:length(endowithlagnames)
    lags = abs(endolags_(i));
    variable = initialconditions{endowithlagnames{i}};
    nanvalues = isnan(variable.data);
    if any(nanvalues(end-(lags-1):end))
        missinginitialcondition = true;
        for j=variable.nobs:-1:variable.nobs-(lags-1)
            if isnan(variable.data(j))
                dprintf('Variable %s should not have a NaN value in period %s.', endowithlagnames{i}, date2string(variable.dates(j)))
            end
        end
    end
end
if missinginitialcondition
    skipline()
    error('Please fix the dseries object used for setting the initial conditions!')
end

% If the model has lags on the exogenous variables, test if we have corresponding initial conditions.
exonames = M_.exo_names;
missingexogenousvariables = setdiff(exonames, initialconditions.name);
exolags = get_lags_on_exogenous_variables(M_);
exolags_ = exolags(find(exolags));
exowithlagnames = exonames(find(exolags));
if ~isempty(missingexogenousvariables)
    missingexogenousvariables = setdiff(exowithlagnames, initialconditions.name);
    missingexogenouslaggedvariables = intersect(exowithlagnames, missingexogenousvariables);
    if ~isempty(missingexogenouslaggedvariables)
        disp('You have to initialize the following exogenous variables:')
        msg = sprintf('%s\n', missingexogenouslaggedvariables{1:end-1});
        msg = sprintf('%s%s', msg, missingexogenouslaggedvariables{end});
        disp(msg)
        skipline()
        error('Please fix the dseries object used for setting the initial conditions!')
    end
end

% Test if we have enough periods in the database.
maxlag = abs(min(exolags));
if maxlag>initialconditions.nobs
    error('The dseries object provided as first input argument should at least have %s periods!', num2str(maxlag))
end
missinginitialcondition = false;
for i = 1:length(exowithlagnames)
    lags = abs(exolags_(i));
    variable = initialconditions{exowithlagnames{i}};
    nanvalues = isnan(variable.data);
    if any(nanvalues(end-(lags-1):end))
        missinginitialcondition = true;
        for j=variable.nobs:-1:variable.nobs-(lags-1)
            if isnan(variable.data(j))
                dprintf('Variable %s should not have a NaN value in period %s.', exowithlagnames{i}, date2string(variable.dates(j)))
            end
        end
    end
end
if missinginitialcondition
    skipline()
    error('Please fix the dseries object used for setting the initial conditions!')
end

if nargin<6 || isempty(innovations)
    % Set the covariance matrix of the structural innovations.
    variances = diag(M_.Sigma_e);
    number_of_shocks = length(M_.Sigma_e);
    positive_var_indx = find(variances>0);
    effective_number_of_shocks = length(positive_var_indx);
    covariance_matrix = M_.Sigma_e(positive_var_indx,positive_var_indx);
    covariance_matrix_upper_cholesky = chol(covariance_matrix);
    % Set seed to its default state.
    if options_.bnlms.set_dynare_seed_to_default
        set_dynare_seed_local_options([],false,'default');
    end
    % Simulate structural innovations.
    switch options_.bnlms.innovation_distribution
      case 'gaussian'
        oo_.bnlms.shocks = randn(samplesize,effective_number_of_shocks)*covariance_matrix_upper_cholesky;
      otherwise
        error(['simul_backward_nonlinear_model:: ' options_.bnlms.innovation_distribution ' distribution for the structural innovations is not (yet) implemented!'])
    end
    % Put the simulated innovations in oo_.exo_simul.
    oo_.exo_simul = zeros(samplesize,number_of_shocks);
    oo_.exo_simul(:,positive_var_indx) = oo_.bnlms.shocks;
    innovations = oo_.exo_simul;
else
    oo_.exo_simul = innovations; % innovations
end

% Initialization of the returned simulations.
oo_.endo_simul = NaN(M_.endo_nbr, samplesize+initialconditions.nobs);
for i=1:length(endonames)
    if ismember(endonames{i}, initialconditions.name)
        oo_.endo_simul(i,1:initialconditions.nobs) = transpose(initialconditions{endonames{i}}.data);
    end
end

% Initialization of the array for the exogenous variables.
oo_.exo_simul = [NaN(initialconditions.nobs, M_.exo_nbr); oo_.exo_simul ];
for i=1:length(exonames)
    if ismember(exonames{i}, initialconditions.name)
        oo_.exo_simul(1:initialconditions.nobs, i) = initialconditions{exonames{i}}.data;
    end
end


if nargout>8
    % Get function handles to the dynamic model routines.
    dynamic_resid = str2func([M_.fname,'.dynamic_resid']);
    dynamic_g1 = str2func([M_.fname,'.dynamic_g1']);
    % initialization of vector y.
    y = NaN(3*M_.endo_nbr,1);
end


function l = get_lags_on_exogenous_variables(M_)
% l = get_lags_on_exogenous_variables(M_)
% Returns a vector with the max lag for each exogenous variable.

l = zeros(M_.exo_nbr, 1);

if ~isempty(M_.aux_vars)
    aux_var_for_lagged_exogenous = find([M_.aux_vars(:).type]==3);
    for i=1:length(aux_var_for_lagged_exogenous)
        l(M_.aux_vars(aux_var_for_lagged_exogenous(i)).orig_index) = ...
            M_.aux_vars(aux_var_for_lagged_exogenous(i)).orig_lead_lag-1;
    end
end

function l = get_lags_on_endogenous_variables(M_)
% l = get_lags_on_endogenous_variables(M_)
% Returns a vector with the max lag for each endogenous variable.

l = zeros(M_.orig_endo_nbr, 1);
l(find(M_.lead_lag_incidence(1,1:M_.orig_endo_nbr))) = -1;

if ~isempty(M_.aux_vars)
    aux_var_for_lagged_endogenous = find([M_.aux_vars(:).type]==1);
    for i=1:length(aux_var_for_lagged_endogenous)
        l(M_.aux_vars(aux_var_for_lagged_endogenous(i)).orig_index) = ...
            M_.aux_vars(aux_var_for_lagged_endogenous(i)).orig_lead_lag;
    end
end