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    Metadata details:
    filename: DEMO_VL.m
    path of file: ./repos/spm/toolbox/DEM
    
    the code of the file until where you have to start completion: % function DEMO_VL
% evaluates the free energy landscape around the posterior
% FORMAT: spm_dcm_local_minima(DCM)
% DCM - (invert) model structure
%
%__________________________________________________________________________
 
% Karl Friston
% Copyright (C) 2008-2022 Wellcome Centre for Human Neuroimaging

% Model specification
%==========================================================================
clear; rng('default');

% specify network (connections)
%--------------------------------------------------------------------------
A{1}  = 0;
A{2}  = 0;
A{3}  = 0;
B     = {};
C     = 1;

M.dipfit.model = 'CMC';
M.dipfit.type  = 'LFP';
M.dipfit.Nc    = 1
    
function DEMO_VL
% evaluates the free energy landscape around the posterior
% FORMAT: spm_dcm_local_minima(DCM)
% DCM - (invert) model structure
%
%__________________________________________________________________________
 
% Karl Friston
% Copyright (C) 2008-2022 Wellcome Centre for Human Neuroimaging

% Model specification
%==========================================================================
clear; rng('default');

% specify network (connections)
%--------------------------------------------------------------------------
A{1}  = 0;
A{2}  = 0;
A{3}  = 0;
B     = {};
C     = 1;

M.dipfit.model = 'CMC';
M.dipfit.type  = 'LFP';
M.dipfit.Nc    = 1;
M.dipfit.Ns    = 1;

% get priors
%--------------------------------------------------------------------------
[pE pC] = spm_dcm_neural_priors(A,B,C,M.dipfit.model);  % neuronal priors
[pE pC] = spm_L_priors(M.dipfit,pE,pC);                 % spatial  priors
[pE pC] = spm_ssr_priors(pE,pC);                        % spectral priors

[x,f]   = spm_dcm_x_neural(pE,M.dipfit.model);

rC      = spm_zeros(pC);
rC.G(1) = 1/4;
rC.G(2) = pC.G(2);

% create LFP model
%--------------------------------------------------------------------------
M.IS  = @spm_gen_erp;
M.f   = f;
M.g   = @spm_gx_erp;
M.x   = x;
M.pE  = pE;
M.pC  = rC;
M.hE  = 6;
M.hC  = 1/4;
M.m   = 1;
M.n   = numel(x);
M.l   = 1;



% Integrate system to see response (time-frequency and hemodynamic)
%==========================================================================
spm_figure('GetWin','Figure 1');clf

PP      = pE;
PP.G(1) = 2;
PP.G(2) = 0.5;


M.ons  = 64;
M.dur  = 16;
N      = 64;
U.dt   = 4/1000;
t      = (1:N)*U.dt;
pst    = t*1000;
U.u    = spm_erp_u(t,PP,M);
Yy     = spm_gen_erp(PP,M,U);
Y.y{1} = Yy{1} + mean(std(Yy{1}))*randn(size(Yy{1}))/4;
Y.dt   = U.dt;

% input
%--------------------------------------------------------------------------
subplot(2,2,1)
plot(pst,U.u)
axis square
xlabel('time (ms)')
title('Exogenous input')

% LFP
%--------------------------------------------------------------------------
subplot(2,2,2)
plot(pst,Y.y{1},':',pst,Yy{1})
axis square
xlabel('time (ms)')
title('LFP response')
drawnow

% return

% Stability analysis (over excitatory and inhibitory time constants)
%==========================================================================
fprintf('Stability analysis - please wait\n')
n     = 32;
P1    = linspace(0,3,n);
P2    = linspace(0,3,n);
for i = 1:length(P1)
    for j = 1:length(P2)
        P        = M.pE;
        P.G(:,1) = P1(i);
        P.G(:,2) = P2(j);
        S        = spm_ssm2s(P,M,0);
        S        = S(abs(imag(S)) > 2*pi & abs(imag(S)) < 128*2*pi);
        try
            [s k]   = max(real(S));
            HZ(i,j) = abs(imag(S(k)))/(2*pi);
            LE(i,j) = s;
        end