Allow k order approximation in nonlinear Kalman Filter (nlkf).
Ref. dynare#1673remove-submodule^2
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function [LIK,lik] = nonlinear_kalman_filter(ReducedForm, Y, start, ParticleOptions, ThreadsOptions)
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function [LIK,lik] = nonlinear_kalman_filter(ReducedForm, Y, start, ParticleOptions, ThreadsOptions, DynareOptions, Model)
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% Evaluates the likelihood of a non-linear model approximating the
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% Evaluates the likelihood of a non-linear model approximating the
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% predictive (prior) and filtered (posterior) densities for state variables
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% predictive (prior) and filtered (posterior) densities for state variables
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% by a Kalman filter.
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% by a Kalman filter.
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@ -30,7 +31,8 @@ function [LIK,lik] = nonlinear_kalman_filter(ReducedForm, Y, start, ParticleOpti
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%
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%
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% NOTES
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% NOTES
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% The vector "lik" is used to evaluate the jacobian of the likelihood.
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% The vector "lik" is used to evaluate the jacobian of the likelihood.
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% Copyright (C) 2009-2017 Dynare Team
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% Copyright (C) 2009-2019 Dynare Team
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%
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%
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% This file is part of Dynare.
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% This file is part of Dynare.
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%
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%
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@ -47,55 +49,41 @@ function [LIK,lik] = nonlinear_kalman_filter(ReducedForm, Y, start, ParticleOpti
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% You should have received a copy of the GNU General Public License
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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persistent init_flag mf0 mf1 nodes weights weights_c
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persistent sample_size number_of_state_variables number_of_observed_variables number_of_structural_innovations
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% Set default
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% Set default
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if isempty(start)
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if isempty(start)
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start = 1;
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start = 1;
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end
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end
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% Set local state space model (first-order approximation).
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if ReducedForm.use_k_order_solver
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ghx = ReducedForm.ghx;
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dr = ReducedForm.dr;
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ghu = ReducedForm.ghu;
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else
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% Set local state space model (second-order approximation).
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% Set local state space model (first-order approximation).
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ghxx = ReducedForm.ghxx;
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ghx = ReducedForm.ghx;
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ghuu = ReducedForm.ghuu;
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ghu = ReducedForm.ghu;
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ghxu = ReducedForm.ghxu;
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% Set local state space model (second-order approximation).
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ghxx = ReducedForm.ghxx;
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if any(any(isnan(ghx))) || any(any(isnan(ghu))) || any(any(isnan(ghxx))) || any(any(isnan(ghuu))) || any(any(isnan(ghxu))) || ...
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ghuu = ReducedForm.ghuu;
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any(any(isinf(ghx))) || any(any(isinf(ghu))) || any(any(isinf(ghxx))) || any(any(isinf(ghuu))) || any(any(isinf(ghxu))) ...
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ghxu = ReducedForm.ghxu;
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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))
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ghx
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ghu
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ghxx
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ghuu
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ghxu
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end
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end
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constant = ReducedForm.constant;
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constant = ReducedForm.constant;
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state_variables_steady_state = ReducedForm.state_variables_steady_state;
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state_variables_steady_state = ReducedForm.state_variables_steady_state;
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% Set persistent variables.
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mf0 = ReducedForm.mf0;
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if isempty(init_flag)
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mf1 = ReducedForm.mf1;
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mf0 = ReducedForm.mf0;
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sample_size = size(Y,2);
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mf1 = ReducedForm.mf1;
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number_of_state_variables = length(mf0);
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sample_size = size(Y,2);
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number_of_observed_variables = length(mf1);
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number_of_state_variables = length(mf0);
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number_of_structural_innovations = length(ReducedForm.Q);
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number_of_observed_variables = length(mf1);
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number_of_structural_innovations = length(ReducedForm.Q);
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init_flag = 1;
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end
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% compute gaussian quadrature nodes and weights on states and shocks
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% compute gaussian quadrature nodes and weights on states and shocks
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if ParticleOptions.proposal_approximation.montecarlo
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if ParticleOptions.proposal_approximation.montecarlo
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nodes = randn(ParticleOptions.number_of_particles,number_of_state_variables+number_of_structural_innovations) ;
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nodes = randn(ParticleOptions.number_of_particles,number_of_state_variables+number_of_structural_innovations);
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weights = 1/ParticleOptions.number_of_particles ;
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weights = 1/ParticleOptions.number_of_particles;
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weights_c = weights ;
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weights_c = weights;
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elseif ParticleOptions.proposal_approximation.cubature
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elseif ParticleOptions.proposal_approximation.cubature
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[nodes,weights] = spherical_radial_sigma_points(number_of_state_variables+number_of_structural_innovations) ;
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[nodes,weights] = spherical_radial_sigma_points(number_of_state_variables+number_of_structural_innovations);
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weights_c = weights ;
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weights_c = weights;
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elseif ParticleOptions.proposal_approximation.unscented
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elseif ParticleOptions.proposal_approximation.unscented
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[nodes,weights,weights_c] = unscented_sigma_points(number_of_state_variables+number_of_structural_innovations,ParticleOptions);
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[nodes,weights,weights_c] = unscented_sigma_points(number_of_state_variables+number_of_structural_innovations,ParticleOptions);
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else
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else
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@ -120,27 +108,28 @@ lik = NaN(sample_size,1);
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LIK = NaN;
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LIK = NaN;
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for t=1:sample_size
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for t=1:sample_size
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xbar = [StateVectorMean ; zeros(number_of_structural_innovations,1) ] ;
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xbar = [StateVectorMean ; zeros(number_of_structural_innovations,1) ] ;
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sqr_Px = [ [ StateVectorVarianceSquareRoot zeros(number_of_state_variables,number_of_structural_innovations) ] ;
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sqr_Px = [StateVectorVarianceSquareRoot zeros(number_of_state_variables,number_of_structural_innovations);
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[ zeros(number_of_structural_innovations,number_of_state_variables) Q_lower_triangular_cholesky ] ];
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zeros(number_of_structural_innovations,number_of_state_variables) Q_lower_triangular_cholesky];
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sigma_points = bsxfun(@plus,xbar,sqr_Px*(nodes'));
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sigma_points = bsxfun(@plus,xbar,sqr_Px*(nodes'));
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StateVectors = sigma_points(1:number_of_state_variables,:);
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StateVectors = sigma_points(1:number_of_state_variables,:);
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epsilon = sigma_points(number_of_state_variables+1:number_of_state_variables+number_of_structural_innovations,:);
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epsilon = sigma_points(number_of_state_variables+1:number_of_state_variables+number_of_structural_innovations,:);
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yhat = bsxfun(@minus,StateVectors,state_variables_steady_state);
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yhat = bsxfun(@minus,StateVectors,state_variables_steady_state);
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tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,ThreadsOptions.local_state_space_iteration_2);
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if ReducedForm.use_k_order_solver
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tmp = local_state_space_iteration_k(yhat, epsilon, dr, Model, DynareOptions);
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else
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tmp = local_state_space_iteration_2(yhat, epsilon, ghx, ghu, constant, ghxx, ghuu, ghxu, ThreadsOptions.local_state_space_iteration_2);
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end
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PredictedStateMean = tmp(mf0,:)*weights ;
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PredictedStateMean = tmp(mf0,:)*weights ;
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PredictedObservedMean = tmp(mf1,:)*weights;
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PredictedObservedMean = tmp(mf1,:)*weights;
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if ParticleOptions.proposal_approximation.cubature || ParticleOptions.proposal_approximation.montecarlo
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if ParticleOptions.proposal_approximation.cubature || ParticleOptions.proposal_approximation.montecarlo
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PredictedStateMean = sum(PredictedStateMean,2);
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PredictedStateMean = sum(PredictedStateMean,2);
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PredictedObservedMean = sum(PredictedObservedMean,2);
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PredictedObservedMean = sum(PredictedObservedMean,2);
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dState = bsxfun(@minus,tmp(mf0,:),PredictedStateMean)'.*sqrt(weights);
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dState = bsxfun(@minus,tmp(mf0,:),PredictedStateMean)'.*sqrt(weights);
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dObserved = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean)'.*sqrt(weights);
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dObserved = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean)'.*sqrt(weights);
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big_mat = [dObserved dState ; [H_lower_triangular_cholesky zeros(number_of_observed_variables,number_of_state_variables)] ];
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big_mat = [dObserved dState ; [H_lower_triangular_cholesky zeros(number_of_observed_variables,number_of_state_variables)] ];
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[mat1,mat] = qr2(big_mat,0);
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[~, mat] = qr2(big_mat,0);
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mat = mat';
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mat = mat';
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clear('mat1');
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PredictedObservedVarianceSquareRoot = mat(1:number_of_observed_variables,1:number_of_observed_variables);
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PredictedObservedVarianceSquareRoot = mat(1:number_of_observed_variables,1:number_of_observed_variables);
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CovarianceObservedStateSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables),1:number_of_observed_variables);
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CovarianceObservedStateSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables),1:number_of_observed_variables);
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StateVectorVarianceSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables),number_of_observed_variables+(1:number_of_state_variables));
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StateVectorVarianceSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables),number_of_observed_variables+(1:number_of_state_variables));
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@ -162,16 +151,14 @@ for t=1:sample_size
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lik(t)=-Inf;
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lik(t)=-Inf;
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return
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return
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end
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end
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[PredictedObservedVarianceSquareRoot, p]= chol(PredictedObservedVariance,'lower');
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[~, p]= chol(PredictedObservedVariance,'lower');
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if p
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if p
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LIK=-Inf;
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LIK=-Inf;
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lik(t)=-Inf;
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lik(t)=-Inf;
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return
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return
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end
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end
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end
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end
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% lik(t) = log( probability2(0,PredictedObservedVarianceSquareRoot,PredictionError) ) ;
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lik(t) = log( sum(probability2(Y(:,t),H_lower_triangular_cholesky,tmp(mf1,:)).*weights,1) ) ;
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lik(t) = log( sum(probability2(Y(:,t),H_lower_triangular_cholesky,tmp(mf1,:)).*weights,1) ) ;
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% lik(t) = log(sum(probability2(Y(:,t),PredictedObservedVarianceSquareRoot,tmp(mf1,:)).*weights,1) ) ;
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end
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end
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LIK = -sum(lik(start:end));
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LIK = -sum(lik(start:end));
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