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Slepi/Code/Utilities/spm12/spm_dcm_fmri_graph_gen.m
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spm_dcm_fmri_graph_gen.m
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function [P] = spm_dcm_fmri_graph_gen(x,v,P)
% Generates adjacency graph for spectral DCM for fMRI
% FORMAT [g] = spm_dcm_fmri_graph_gen(x,v,P)
%
% This routine computes the adjacency matrix (A) for spm_fx_fmri
%
% see also: spm_fx_fmri
%__________________________________________________________________________
% Copyright (C) 2008 Wellcome Trust Centre for Neuroimaging
% Karl Friston
% $Id: spm_dcm_fmri_graph_gen.m 5821 2013-12-31 14:26:41Z karl $
% compute bias for log connectivity using functional space
%==========================================================================
% spectral deomposition
%--------------------------------------------------------------------------
P.A = full(P.A);
if isfield(P,'modes')
% outer product
%======================================================================
n = length(P.A); % number of nodes
m = length(v); % number of modes
s = [-exp(-v); (zeros(n - m,1) - 1)];
P.A = P.modes*diag(s)*P.modes';
P.A = full(P.A + diag(log(-2*diag(P.A)) - diag(P.A)));
P = rmfield(P,'modes');
return
end
if isnumeric(v)
% static modes (explicit negativity constraints on self excitation)
%======================================================================
% P.A = v'*v;
% dynamical modes (implicit negative definite constraints)
%======================================================================
P.A = logm(v'*v + eye(size(v,2),size(v,2))*exp(-16))/16;
P.A = P.A + diag(log(-2*diag(P.A)) - diag(P.A));
return
end
% Distance-based bias on (empirical) prior mean of log connectivity
%--------------------------------------------------------------------------
[n m] = size(v.x);
if size(P.A,3) == 1 && numel(v.a) == 1
% one-state model of (MoG) connectivity
%======================================================================
for i = 1:m
for j = (i + 1):m
% Euclidean distance
%--------------------------------------------------------------
P.A(i,j) = ...
exp(v.a - sum((v.x(:,i) - v.x(:,j)).^2)/2)/4 - ... % excitatory
exp(v.a - sum((v.x(:,i) - v.x(:,j)).^2)/8)/8; % inhibitory
P.A(j,i) = P.A(i,j);
end
end
elseif size(P.A,3) == 1 && numel(v.a) == 2
% one-state model of centre-surround connectivity
%======================================================================
for i = 1:m
for j = (i + 1):m
% Euclidean distance
%--------------------------------------------------------------
D = exp(-sum((v.x(:,i) - v.x(:,j)).^2)/2);
P.A(i,j) = exp(v.a(1))*D/16 + v.a(2);
P.A(j,i) = P.A(i,j);
end
end
elseif size(P.A,3) == 2
% assume two-state model of log connectivity
%======================================================================
for i = 1:m
for j = (i + 1):m
% Euclidean distance
%--------------------------------------------------------------
P.A(i,j,1) = v.a - sum((v.x(:,i) - v.x(:,j)).^2)/2;
P.A(j,i,1) = P.A(i,j,1);
% hierarchical distance
%--------------------------------------------------------------
P.A(i,j,2) = (sqrt(sum(v.x(:,i).^2)) - sqrt(sum(v.x(:,j)).^2))/2;
P.A(j,i,2) = -P.A(i,j,2);
end
end
end
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