function [pE,pC] = spm_nmda_priors(A,B,C)
% prior moments for a neural-mass model of ERPs
% FORMAT [pE,pC] = spm_nmm_priors(A,B,C)
%
% A{3},B{m},C  - binary constraints on extrinsic connections
%
% pE - prior expectation - f(x,u,P,M)
%
% population variance
%--------------------------------------------------------------------------
%     E.S    - variance
%
% synaptic parameters
%--------------------------------------------------------------------------
%    pE.T    - synaptic time constants
%    pE.G    - intrinsic connectivity
%
% connectivity parameters
%--------------------------------------------------------------------------
%    pE.A    - extrinsic
%    pE.B    - trial-dependent
%    pE.C    - stimulus input
%
%    pE.SA - switches on extrinsic (excitatory)
%    pE.GE - switches on intrinsic (excitatory)
%    pE.GI - switches on intrinsic (inhibitory)
%
% stimulus and noise parameters
%--------------------------------------------------------------------------
%    pE.R    - onset and dispersion
%    pE.D    - delays
%    pE.U    - exogenous background activity
%
% pC - prior (co)variances
%
% Because priors are specified under log normal assumptions, most
% parameters are simply scaling coefficients with a prior expectation
% and variance of one.  After log transform this renders pE = 0 and
% pC = 1;  The prior expectations of what they scale are specified in
% spm_erp_fx
%__________________________________________________________________________
%
% David O, Friston KJ (2003) A neural mass model for MEG/EEG: coupling and
% neuronal dynamics. NeuroImage 20: 1743-1755
%__________________________________________________________________________
% Copyright (C) 2008 Wellcome Trust Centre for Neuroimaging
 
% Karl Friston
% $Id: spm_nmda_priors.m 5299 2013-03-04 18:19:35Z guillaume $
 
 
% disable log zero warning
%--------------------------------------------------------------------------
warning('off','MATLAB:log:logOfZero');
n     = size(C,1);                                % number of sources
u     = size(C,2);                                % number of inputs
 
% parameters for neural-mass forward model
%==========================================================================
 
% population variance
%--------------------------------------------------------------------------
pE.S   = 0;                 pC.S = 1/16;
 
% set intrinic [excitatory] time constants
%--------------------------------------------------------------------------
pE.T   = log(ones(n,1));    pC.T = ones(n,1)/16;  % excitatory constants
pE.G   = log(ones(n,1));    pC.G = ones(n,1)/16;  % intrinsic connections
 
% set extrinsic connectivity
%--------------------------------------------------------------------------
Q     = sparse(n,n);
for i = 1:length(A)
    A{i}    = ~~A{i};
    pE.A{i} = A{i}*32 - 32;                       % forward
    pC.A{i} = A{i}/8;                             % backward
    Q       = Q | A{i};                           % and lateral connections
end
 
for i = 1:length(B)
    B{i} = ~~B{i};
    pE.B{i} = 0*B{i};                             % input-dependent scaling
    pC.B{i} = B{i}/8;
    Q      = Q | B{i};
end
C     = ~~C;
pE.C  = C*32 - 32;                                % where inputs enter
pC.C  = C/32;
 

% connectivity switches
%==========================================================================

% extrinsic connections
%--------------------------------------------------------------------------
pE.SA   = [1   0   1;  
           0   1   1;
           0   0   0];   pC.SA = sparse(3,3);
 
% intrinsic connections (np x np) - excitatory
%--------------------------------------------------------------------------
pE.GE   = [0   0   1/2;  
           0   0   1;
           1/2 0   0];   pC.GE = sparse(3,3);
 
% intrinsic connections (np x np) - inhibitory
%--------------------------------------------------------------------------
pE.GI   = [0   1/4 0;
           0   0   0;
           0   1   0];   pC.GI = sparse(3,3);


% set stimulus parameters: onset and dispersion
%--------------------------------------------------------------------------
pE.R   = sparse(u,2);    pC.R  = ones(u,1)*[1/16 1/16];

% and delays (intrinsic and extrinsic)
%--------------------------------------------------------------------------
pE.D   = [0 0];          pC.D  = [1 1]/64;

% Exogenous background activity
%--------------------------------------------------------------------------
pE.U   = 0;              pC.U  = 1/16;

% Capacitance
%--------------------------------------------------------------------------
pE.CV  = 0;              pC.CV = 1/16;

warning('on','MATLAB:log:logOfZero');