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    filename: DEM_demo_large_fMRI.m
    path of file: ./repos/spm/toolbox/DEM
    
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% Demonstration of DCM for CSD (fMRI) with simulated responses
%__________________________________________________________________________
% This routine demonstrates Bayesian parameter averaging using the
% variational inversion of spectral DCMs for fMRI. A random connectivity
% matrix is generated and inverted. The posterior estimates are then used
% to create new data, that are used to invert a series of DCMs. After each
% inversion, basing parameter averaging is used to illustrate convergence
% to the true values. In principle, this routine can handle large DCMs.
% We illustrate (for time convenience) the inversion of eight nodes and 64
% connections.
%__________________________________________________________________________

    
function DEM_demo_large_fMRI
% Demonstration of DCM for CSD (fMRI) with simulated responses
%__________________________________________________________________________
% This routine demonstrates Bayesian parameter averaging using the
% variational inversion of spectral DCMs for fMRI. A random connectivity
% matrix is generated and inverted. The posterior estimates are then used
% to create new data, that are used to invert a series of DCMs. After each
% inversion, basing parameter averaging is used to illustrate convergence
% to the true values. In principle, this routine can handle large DCMs.
% We illustrate (for time convenience) the inversion of eight nodes and 64
% connections.
%__________________________________________________________________________

% Karl Friston
% Copyright (C) 2008-2022 Wellcome Centre for Human Neuroimaging

% Simulate timeseries
%==========================================================================
rng('default')

% DEM Structure: create random inputs
% -------------------------------------------------------------------------
N  = 4;                               % number of runs
T  = 512;                             % number of observations (scans)
TR = 2;                               % repetition time or timing
n  = 6;                               % number of regions or nodes
t  = (1:T)*TR;                        % observation times

% priors
% -------------------------------------------------------------------------
options.maxnodes   = 4;               % effective number of nodes

options.nonlinear  = 0;
options.two_state  = 0;
options.stochastic = 0;
options.centre     = 1;
options.induced    = 1;

A   = ones(n,n);
B   = zeros(n,n,0);
C   = zeros(n,n);
D   = zeros(n,n,0);
pP  = spm_dcm_fmri_priors(A,B,C,D,options);


% true parameters (reciprocal connectivity)
% -------------------------------------------------------------------------
pP.A = randn(n,n)/12;
pP.A = pP.A - diag(diag(pP.A));
pP.C = eye(n,n);
pP.transit = randn(n,1)/16;

% simulate response to end