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function [PredictedStateMean,PredictedStateVarianceSquareRoot,StateVectorMean,StateVectorVarianceSquareRoot] = gaussian_filter_bank(ReducedForm,obs,StateVectorMean,StateVectorVarianceSquareRoot,Q_lower_triangular_cholesky,H_lower_triangular_cholesky,H,DynareOptions)
%
% Computes the proposal with a gaussian approximation for importance
% sampling
% This proposal is a gaussian distribution calculated à la Kalman
%
% INPUTS
% reduced_form_model [structure] Matlab's structure describing the reduced form model.
% reduced_form_model.measurement.H [double] (pp x pp) variance matrix of measurement errors.
% reduced_form_model.state.Q [double] (qq x qq) variance matrix of state errors.
% reduced_form_model.state.dr [structure] output of resol.m.
% Y [double] pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
%
% OUTPUTS
% LIK [double] scalar, likelihood
% lik [double] vector, density of observations in each period.
%
% REFERENCES
%
% NOTES
% The vector "lik" is used to evaluate the jacobian of the likelihood.
% Copyright (C) 2009-2012 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 <http://www.gnu.org/licenses/>.
persistent init_flag2 mf0 mf1
persistent number_of_state_variables number_of_observed_variables
persistent number_of_structural_innovations
% Set local state space model (first-order approximation).
ghx = ReducedForm.ghx;
ghu = ReducedForm.ghu;
% Set local state space model (second-order approximation).
ghxx = ReducedForm.ghxx;
ghuu = ReducedForm.ghuu;
ghxu = ReducedForm.ghxu;
if any(any(isnan(ghx))) || any(any(isnan(ghu))) || any(any(isnan(ghxx))) || any(any(isnan(ghuu))) || any(any(isnan(ghxu))) || ...
any(any(isinf(ghx))) || any(any(isinf(ghu))) || any(any(isinf(ghxx))) || any(any(isinf(ghuu))) || any(any(isinf(ghxu))) ...
any(any(abs(ghx)>1e4)) || any(any(abs(ghu)>1e4)) || any(any(abs(ghxx)>1e4)) || any(any(abs(ghuu)>1e4)) || any(any(abs(ghxu)>1e4))
ghx
ghu
ghxx
ghuu
ghxu
end
constant = ReducedForm.constant;
state_variables_steady_state = ReducedForm.state_variables_steady_state;
% Set persistent variables.
if isempty(init_flag2)
mf0 = ReducedForm.mf0;
mf1 = ReducedForm.mf1;
number_of_state_variables = length(mf0);
number_of_observed_variables = length(mf1);
number_of_structural_innovations = length(ReducedForm.Q);
init_flag2 = 1;
end
if strcmpi(DynareOptions.particle.IS_approximation_method,'cubature') || strcmpi(DynareOptions.particle.IS_approximation_method,'monte-carlo')
[nodes,weights] = spherical_radial_sigma_points(number_of_state_variables+number_of_structural_innovations) ;
weights_c = weights ;
end
if strcmpi(DynareOptions.particle.IS_approximation_method,'quadrature')
[nodes,weights] = nwspgr('GQN',number_of_state_variables+number_of_structural_innovations,DynareOptions.particle.smolyak_accuracy) ;
weights_c = weights ;
end
if strcmpi(DynareOptions.particle.IS_approximation_method,'unscented')
[nodes,weights,weights_c] = unscented_sigma_points(number_of_state_variables+number_of_structural_innovations,DynareOptions) ;
end
xbar = [StateVectorMean ; zeros(number_of_structural_innovations,1) ] ;
sqr_Px = [ [ StateVectorVarianceSquareRoot zeros(number_of_state_variables,number_of_structural_innovations) ] ;
[ zeros(number_of_structural_innovations,number_of_state_variables) Q_lower_triangular_cholesky ] ] ;
sigma_points = bsxfun(@plus,xbar,sqr_Px*(nodes')) ;
StateVectors = sigma_points(1:number_of_state_variables,:) ;
epsilon = sigma_points(number_of_state_variables+1:number_of_state_variables+number_of_structural_innovations,:) ;
yhat = bsxfun(@minus,StateVectors,state_variables_steady_state);
tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,DynareOptions.threads.local_state_space_iteration_2);
PredictedStateMean = tmp(mf0,:)*weights ;
PredictedObservedMean = tmp(mf1,:)*weights;
if strcmpi(DynareOptions.particle.IS_approximation_method,'cubature') || strcmpi(DynareOptions.particle.IS_approximation_method,'monte-carlo')
PredictedStateMean = sum(PredictedStateMean,2) ;
PredictedObservedMean = sum(PredictedObservedMean,2) ;
dState = bsxfun(@minus,tmp(mf0,:),PredictedStateMean)'.*sqrt(weights) ;
dObserved = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean)'.*sqrt(weights);
PredictedStateVarianceSquareRoot = chol(dState'*dState)';
big_mat = [dObserved dState ; [H_lower_triangular_cholesky zeros(number_of_observed_variables,number_of_state_variables)] ] ;
[mat1,mat] = qr2(big_mat,0) ;
mat = mat' ;
clear('mat1');
PredictedObservedVarianceSquareRoot = mat(1:number_of_observed_variables,1:number_of_observed_variables) ;
CovarianceObservedStateSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables),1:number_of_observed_variables) ;
StateVectorVarianceSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables),number_of_observed_variables+(1:number_of_state_variables)) ;
PredictionError = obs - PredictedObservedMean ;
StateVectorMean = PredictedStateMean + (CovarianceObservedStateSquareRoot/PredictedObservedVarianceSquareRoot)*PredictionError ;
end
if strcmpi(DynareOptions.particle.IS_approximation_method,'quadrature') || strcmpi(DynareOptions.particle.IS_approximation_method,'unscented')
dState = bsxfun(@minus,tmp(mf0,:),PredictedStateMean);
dObserved = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean);
PredictedStateVariance = dState*diag(weights_c)*dState';
PredictedObservedVariance = dObserved*diag(weights_c)*dObserved' + H;
PredictedStateAndObservedCovariance = dState*diag(weights_c)*dObserved';
PredictedStateVarianceSquareRoot = chol(PredictedStateVariance)';
PredictionError = obs - PredictedObservedMean;
KalmanFilterGain = PredictedStateAndObservedCovariance/PredictedObservedVariance ;
StateVectorMean = PredictedStateMean + KalmanFilterGain*PredictionError;
StateVectorVariance = PredictedStateVariance - KalmanFilterGain*PredictedObservedVariance*KalmanFilterGain';
StateVectorVariance = .5*(StateVectorVariance+StateVectorVariance');
StateVectorVarianceSquareRoot = reduced_rank_cholesky(StateVectorVariance)';
end
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