You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: spm_DEM.m
    path of file: ./repos/malini/Codes/deconvolution - model/spm8
    
    the code of the file until where you have to start completion: function [DEM] = spm_DEM(DEM)
% Dynamic expectation maxmisation
% FORMAT DEM   = spm_DEM(DEM)
%
% DEM.M  - hierarchical model
% DEM.Y  - response variable, output or data
% DEM.U  - explanatory variables, inputs or prior expectation of causes
% DEM.X  - confounds
%__________________________________________________________________________
%
% generative model
%--------------------------------------------------------------------------
%   M(i).g  = y(t)  = g(x,v,P)    {inline function, string or m-file}
%   M(i).f  = dx/dt = f(x,v,P)    {inline function, string or m-file}
%
%   M(i).pE = prior expectation of p model-parameters
%   M(i).pC = prior covariances of p model-parameters
%   M(i).hE = prior expectation of h log-precision (cause noise)
%   M(i).hC = prior covariances of h log-precision (cause noise)
%   M(i).gE = prior expectation of g log-precision (state noise)
%   M(i).gC = prior covariances of g log-precision (state noise)
%   M(i).Q  = precision components (input noise)
%   M(i).R  = precision components (state noise)
%   M(i).V  = fixed precision (input noise)
%   M(i).W  = fixed precision (state noise)
%   M(i).xP = precision (states)
%
%   M(i).m  = number of inputs v(i + 1);
%   M(i).n  = number of states x(i);
%   M(i).l  = number of output v(i);
%
% conditional moments of model-states - q(u)
%--------------------------------------------------------------------------
%   qU.x    = Conditional expectation of hidden states
%   qU.v    = Conditional expectation of causal states
%   qU.w    = Conditional prediction error (states)
%   qU.z    = Conditional prediction error (causes)
%   qU.C    = Conditional covariance: cov(v)
%   qU.S    = Conditional covariance: cov(x)
%
% conditional moments of model-parameters - q(p)
%--------------------------------------------------------------------------
%   qP.P    = Conditional expectation
%   qP.C    = Conditional covariance
%
% conditional moments of hyper-parameters (log-transformed) - q(h)
%--------------------------------------------------------------------------
%   qH.h    = Conditional expectation (cause noise)
%   qH.g    = Conditional expectation (state noise)
%   qH.C    = Conditional covariance

    
function [DEM] = spm_DEM(DEM)
% Dynamic expectation maxmisation
% FORMAT DEM   = spm_DEM(DEM)
%
% DEM.M  - hierarchical model
% DEM.Y  - response variable, output or data
% DEM.U  - explanatory variables, inputs or prior expectation of causes
% DEM.X  - confounds
%__________________________________________________________________________
%
% generative model
%--------------------------------------------------------------------------
%   M(i).g  = y(t)  = g(x,v,P)    {inline function, string or m-file}
%   M(i).f  = dx/dt = f(x,v,P)    {inline function, string or m-file}
%
%   M(i).pE = prior expectation of p model-parameters
%   M(i).pC = prior covariances of p model-parameters
%   M(i).hE = prior expectation of h log-precision (cause noise)
%   M(i).hC = prior covariances of h log-precision (cause noise)
%   M(i).gE = prior expectation of g log-precision (state noise)
%   M(i).gC = prior covariances of g log-precision (state noise)
%   M(i).Q  = precision components (input noise)
%   M(i).R  = precision components (state noise)
%   M(i).V  = fixed precision (input noise)
%   M(i).W  = fixed precision (state noise)
%   M(i).xP = precision (states)
%
%   M(i).m  = number of inputs v(i + 1);
%   M(i).n  = number of states x(i);
%   M(i).l  = number of output v(i);
%
% conditional moments of model-states - q(u)
%--------------------------------------------------------------------------
%   qU.x    = Conditional expectation of hidden states
%   qU.v    = Conditional expectation of causal states
%   qU.w    = Conditional prediction error (states)
%   qU.z    = Conditional prediction error (causes)
%   qU.C    = Conditional covariance: cov(v)
%   qU.S    = Conditional covariance: cov(x)
%
% conditional moments of model-parameters - q(p)
%--------------------------------------------------------------------------
%   qP.P    = Conditional expectation
%   qP.C    = Conditional covariance
%
% conditional moments of hyper-parameters (log-transformed) - q(h)
%--------------------------------------------------------------------------
%   qH.h    = Conditional expectation (cause noise)
%   qH.g    = Conditional expectation (state noise)
%   qH.C    = Conditional covariance
%
% F         = log evidence = log marginal likelihood = negative free energy
%__________________________________________________________________________
%
% spm_DEM implements a variational Bayes (VB) scheme under the Laplace
% approximation to the conditional densities of states (u), parameters (p)
% and hyperparameters (h) of any analytic nonlinear hierarchical dynamic
% model, with additive Gaussian innovations.  It comprises three
% variational steps (D,E and M) that update the conditional moments of u, p
% and h respectively
%
%                D: qu.u = max <L>q(p,h)
%                E: qp.p = max <L>q(u,h)
%                M: qh.h = max <L>q(u,p)
%
% where qu.u corresponds to the conditional expectation of hidden states x
% and causal states v and so on.  L is the ln p(y,u,p,h|M) under the model
% M. The conditional covariances obtain analytically from the curvature of
% L with respect to u, p and h.
%
% The D-step is embedded in the E-step because q(u) changes with each
% sequential observation.  The dynamical model is transformed into a static
% model using temporal derivatives at each time point.  Continuity of the
% conditional trajectories q(u,t) is assured by a continuous ascent of F(t)
% in generalised co-ordinates.  This means DEM can deconvolve online and can
% represents an alternative to Kalman filtering or alternative Bayesian
% update procedures.
%
%
% To accelerate computations one can specify the nature of the model using
% the field:
%
% M(1).E.linear = 0: full        - evaluates 1st and 2nd derivatives
% M(1).E.linear = 1: linear      - equations are linear in x and v
% M(1).E.linear = 2: bilinear    - equations are linear in x, v and x.v
% M(1).E.linear = 3: nonlinear   - equations are linear in x, v, x.v, and x.x
% M(1).E.linear = 4: full linear - evaluates 1st derivatives (for generalised 
%                                  filtering, where parameters change)
%__________________________________________________________________________
% Copyright (C) 2008 Wellcome Trust Centre for Neuroimaging
 
% Karl Friston
% $Id: spm_DEM.m 4310 2011-04-18 16:07:35Z guillaume $



% check model, data, priors and confounds and unpack
%--------------------------------------------------------------------------
[M Y U X] = spm_DEM_set(DEM);
 
% find or create a DEM figure
%--------------------------------------------------------------------------
Fdem = spm_figure('GetWin','DEM');
 
% tolerance for changes in norm
%--------------------------------------------------------------------------
TOL  = exp(-4);
 
% order parameters (d = n = 1 for static models) and checks
%==========================================================================
d    = M(1).E.d + 1;                   % embedding order of q(v)
n    = M(1).E.n + 1;                   % embedding order of q(x) (n >= d)
 
% number of states and parameters
%--------------------------------------------------------------------------
nY   = size(Y,2);                      % number of samples
nl   = size(M,2);                      % number of levels
nv   = sum(spm_vec(M.m));              % number of v (casual states)
nx   = sum(spm_vec(M.n));              % number of x (hidden states)
ny   = M(1).l;                         % number of y (inputs)
nc   = M(end