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    filename: spm_MDP.m
    path of file: ./repos/malini/Codes/deconvolution - model/spm8/toolbox/DEM
    
    the code of the file until where you have to start completion: function spm_MDP(X,V,T)
% Demo for Discrete Markov Decision process (planning)
% FORMAT spm_MDP(X,V,T)
% X    - initial and goal position
% V    - initial and goal velocity
% T    - number of time-steps
%
% P.a  - 0th order coefficients of force
% P.b  - 1st order coefficients of force
% P.c  – 2nd order coefficients of force
% P.d  - action coefficient
%
% M    - model structure
%
% f    - flow dx/dt
%
% This routine uses a Markov decisions process formulation of the mountain
% car problem to illustrate prospective free energy minimization under a
% variational Bayesian learning scheme. The key notion here is that the
% agent represents future states and action (in a pullback sense), where it

    
function spm_MDP(X,V,T)
% Demo for Discrete Markov Decision process (planning)
% FORMAT spm_MDP(X,V,T)
% X    - initial and goal position
% V    - initial and goal velocity
% T    - number of time-steps
%
% P.a  - 0th order coefficients of force
% P.b  - 1st order coefficients of force
% P.c  – 2nd order coefficients of force
% P.d  - action coefficient
%
% M    - model structure
%
% f    - flow dx/dt
%
% This routine uses a Markov decisions process formulation of the mountain
% car problem to illustrate prospective free energy minimization under a
% variational Bayesian learning scheme. The key notion here is that the
% agent represents future states and action (in a pullback sense), where it
% has strong prior beliefs about future states. The intervening states and
% actions are optimized with respect to current sensory data to provide
% predictions about the next sensory state, which action fulfills. The
% result is a planned trajectory through state space that realizes prior
% beliefs in a prospective sense.
%__________________________________________________________________________
% Copyright (C) 2005 Wellcome Trust Centre for Neuroimaging
 
% Karl Friston
% $Id: spm_MDP.m 4339 2011-06-02 13:04:49Z karl $
 
% set up and preliminaries
%==========================================================================
TOL  = 64;                                  % tolerance for log
u    = [-2 -1 0 1 2];                       % levels of control
Nu   = length(u);                           % number of control/actions
Nx   = 32;                                  % number of cells per dimension
Ns   = Nx*Nx;                               % number of states
dt   = 2;
 
% fisrt and final states
%--------------------------------------------------------------------------
try, T;  catch, T = 16;    end