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_vpca_f.m
    path of file: ./repos/bspm/thirdparty/spm12/toolbox/mlm
    
    the code of the file until where you have to start completion: function [Fm] = spm_vpca_f (pca,c) 
% Compute free energy of VPCA model
% FORMAT [Fm] = spm_vpca_f (pca,c)
%
% pca   data structure (see eg. spm_vpca.m)
% c     information about single component

    
function [Fm] = spm_vpca_f (pca,c) 
% Compute free energy of VPCA model
% FORMAT [Fm] = spm_vpca_f (pca,c)
%
% pca   data structure (see eg. spm_vpca.m)
% c     information about single component
%
% Fm    negative free energy of model
%__________________________________________________________________________
% Copyright (C) 2012-2014 Wellcome Trust Centre for Neuroimaging

% Will Penny 
% $Id: spm_vpca_f.m 5962 2014-04-17 12:47:43Z spm $


d=pca.d;
q=c(1).q;
pca.q=q;

N=pca.N;
pca.sum_quad_exp=c(1).sum_quad_exp;
pca.T1b=c(1).T1b;
pca.Sigma_x=c(1).Sigma_x;
pca.qb_alpha=c(1).qb_alpha;
pca.mean_alpha=c(1).mean_alpha;
pca.M_w=c(1).M_w;
pca.Sigma_w=c(1).Sigma_w;
pca.mean_mu=c(1).mean_mu;
pca.Sigma_mu=c(1).Sigma_mu;

l_av1 = psi(pca.qa_tau) - log(pca.qb_tau); % Term 1
l_av1 = 0.5*pca.N*pca.d*l_av1 - 0.5*pca.N*pca.d*log(2*pi);
l_av1 = l_av1 - 0.5 * pca.mean_tau * pca.sum_quad_exp;

I_T=l_av1;

l_av2 = - 0.5*pca.N*pca.q * log (2*pi) + sum(pca.T1b);

l_av3=0.5*pca.N*pca.q*(1+log(2*pi))+0.5*pca.N*spm_logdet(pca.Sigma_x);

I_X=l_av2+l_av3;

l_av=l_av1+l_av2+l_av3;

W_term=0;
W_term=-0.5*q*d*log(2*pi);
dig_qa=psi(pca.qa_alpha);
for i=1:q,
    exp_log_alpha_i= dig_qa - log(pca.qb_alpha(i));
    W_term=W_term+0.5*d*exp_log_alpha_i;
end