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logL_SP_w_grad.m
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logL_SP_w_grad.m
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function varargout = logL_SP_w_grad(varargin)
persistent tau
persistent P_old
persistent logL_old
if isempty(tau)
tau = clock;
end
if isempty(logL_old)
logL_old = -inf;
end
%% Initialization
theta = varargin{1};
Data = varargin{2};
Model = varargin{3};
% Options
options.tau_update = 0;
options.plot = 1;
if nargin >= 4
options = setdefault(varargin{4},options);
end
if nargin >= 5
extract_flag = varargin{5};
end
% Plot options
if (etime(clock,tau) > options.tau_update) && (options.plot == 1)
options.plot = 30;
tau = clock;
else
options.plot = 0;
end
%% Evaluation of likelihood function
% Initialization
logL = 0;
dlogLdtheta = zeros(length(theta),1);
ddlogLdtheta2 = zeros(length(theta));
data_type = {'SCTL','PA','SCSH'};
for s = 1:length(Data)
%% Assignment of global variables
A = Model.exp{s}.A;
B = Model.exp{s}.B;
ind_beta = Model.exp{s}.ind_beta;
ind_D = Model.exp{s}.ind_D;
n_beta = length(ind_beta);
n_D = length(ind_D);
n_b = size(B,2);
type_D = Model.type_D;
%% Construct fixed effects and covariance matrix
beta = theta(ind_beta);
dbeta = eye(length(theta)); dbeta = dbeta(ind_beta,:);
[D,invD,dD,dinvD,~,HinvD] = xi2D(theta(ind_D),type_D);
dD_full = zeros(size(dD,1),size(dD,1),length(theta));
dD_full(:,:,ind_D) = dD;
%% Construction of time vector
t_s = [];
for dtype = 1:length(data_type)
if isfield(Data{s},data_type{dtype})
t_s = union(eval(['Data{s}.' data_type{dtype} '.time']),t_s);
end
end
if isfield(Data{s},'SCTL')
% Evaluation of time index set
[~,ind_t] = ismember(Data{s}.SCTL.time,t_s);
N = size(Data{s}.SCTL.Y,3);
Ym = Data{s}.SCTL.Y(ind_t,:,:);
kappa = [];
[mY,CY,Cxy,mz,Cz,B_SP,Y,dmYdxi,dCYdxi,dCxydxi,dmzdxi,dCzdxi,dB_SPdxi,dYdxi] = getSigmaPointApp(@(phi) nonfun(phi,@(x)Model.exp{s}.model(Data{s}.SCTL.time,x,kappa)),A,B,beta,D,dbeta,dD_full);
beta_f = beta;
beta_f(1) = beta_f(1) + 1e-4;
[mY_f,CY,Cxy,mz,Cz,B_SP,Y,dmYdxi_f,dCYdxi,dCxydxi,dmzdxi,dCzdxi,dB_SPdxi,dYdxi] = getSigmaPointApp(@(phi) nonfun(phi,@(x)Model.exp{s}.model(Data{s}.SCTL.time,x,kappa)),A,B,beta_f,D,dbeta,dD_full);
mYm = mean(Ym,3);
CYm = zeros(size(Ym,1),size(Ym,2),size(Ym,2));
Sigma_mY = zeros(size(Ym,1),size(Ym,2));
Sigma_CY = zeros(size(Ym,1),size(Ym,2));
for s = 1:size(Ym,1)
CYm(s,:) = var(Ym(s,:,:));
Sigma_mY(s,:) = sqrt(CYm(s,:,:)/N);
Sigma_CY(s,:) = sqrt(mean(bsxfun(@minus,Ym(s,:,:),mYm(s,:)).^4,3)...
-(N-3)/(N-1)*CYm(s,:).^2)/sqrt(N);
end
for j = 1:size(Y,2)
res = (mY(ind_t,j)-mYm)./Sigma_mY(:,j) + (CY(ind_t,j)-CYm(:,j))./Sigma_CY(:,j);
dres = squeeze(bsxfun(@times,1./Sigma_mY(:,j),dmYdxi(:,j,:))) + bsxfun(@times,1./Sigma_CY(:,j),squeeze(dCYdxi(:,j,j,:)));
logL = logL - 0.5*res'*res;
dlogLdtheta = dlogLdtheta - dres'*res;
ddlogLdtheta2 = ddlogLdtheta2 - dres'*dres;
end
end
end
if extract_flag
varargout{1} = B_SP;
return
end
%% Output
if nargout <= 1
% One output
varargout{1} = logL;
elseif nargout <= 2
% Two outputs
varargout{1} = logL;
varargout{2} = dlogLdtheta;
else
% Two outputs
varargout{1} = logL;
varargout{2} = dlogLdtheta;
varargout{3} = ddlogLdtheta2;
end
end
function varargout = nonfun(phi,model)
if nargout == 1
[~,~,~,y] = model(exp(phi));
varargout{1} = y;
elseif nargout == 2
[~,~,~,y,~,sy] = model(exp(phi));
varargout{1} = y;
varargout{2} = bsxfun(@times,sy,exp(permute(phi,[3,2,1])));
end
end