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_fx_hdm.m
    path of file: ./repos/bspm/thirdparty/spm12
    
    the code of the file until where you have to start completion: function [f] = spm_fx_hdm(x,u,P,M)
% state equation for the hemodynamic model
% FORMAT [f] = spm_fx_hdm(x,u,P,M)
% x      - state vector
%   x(1) - vascular signal                                    s
%   x(2) - rCBF                                           log(f)
%   x(3) - venous volume                                  log(v)
%   x(4) - dHb                                            log(q)
% u      - input (neuronal activity)                      (u)
% P      - free parameter vector
%   P(1) - signal decay                                   d(ds/dt)/ds)
%   P(2) - autoregulation                                 d(ds/dt)/df)
%   P(3) - transit time                                   (t0)
%   P(4) - exponent for Fout(v)                           (alpha)
%   P(5) - resting oxygen extraction                      (E0)
%   P(6) - ratio of intra- to extra-vascular components   (epsilon)
%          of the gradient echo signal   
%
%   P(6 + 1:m)   - input efficacies                       d(ds/dt)/du)
%
% y      - dx/dt
%__________________________________________________________________________
%
% Ref Buxton RB, Wong EC & Frank LR. Dynamics of blood flow and oxygenation
% changes during brain activation: The Balloon model. MRM 39:855-864 (1998)
%__________________________________________________________________________
% Copyright (C) 2008 Wellcome Trust Centre for Neuroimaging

% Karl Friston
% $Id: spm_fx_hdm.m 6856 2016-08-10 17:55:05Z karl $


% hemodynamic parameters
%--------------------------------------------------------------------------
%   H(1) - signal decay                                   d(ds/dt)/ds)
%   H(2) - autoregulation                                 d(ds/dt)/df)
%   H(3) - transit time                                   (t0)
%   H(4) - exponent for Fout(v)                           (alpha)
%   H(5) - resting oxygen extraction                      (E0)
%   H(6) - ratio of intra- to extra-vascular components   (epsilon)
%--------------------------------------------------------------------------

    
function [f] = spm_fx_hdm(x,u,P,M)
% state equation for the hemodynamic model
% FORMAT [f] = spm_fx_hdm(x,u,P,M)
% x      - state vector
%   x(1) - vascular signal                                    s
%   x(2) - rCBF                                           log(f)
%   x(3) - venous volume                                  log(v)
%   x(4) - dHb                                            log(q)
% u      - input (neuronal activity)                      (u)
% P      - free parameter vector
%   P(1) - signal decay                                   d(ds/dt)/ds)
%   P(2) - autoregulation                                 d(ds/dt)/df)
%   P(3) - transit time                                   (t0)
%   P(4) - exponent for Fout(v)                           (alpha)
%   P(5) - resting oxygen extraction                      (E0)
%   P(6) - ratio of intra- to extra-vascular components   (epsilon)
%          of the gradient echo signal   
%
%   P(6 + 1:m)   - input efficacies                       d(ds/dt)/du)
%
% y      - dx/dt
%__________________________________________________________________________
%
% Ref Buxton RB, Wong EC & Frank LR. Dynamics of blood flow and oxygenation
% changes during brain activation: The Balloon model. MRM 39:855-864 (1998)
%__________________________________________________________________________
% Copyright (C) 2008 Wellcome Trust Centre for Neuroimaging

% Karl Friston
% $Id: spm_fx_hdm.m 6856 2016-08-10 17:55:05Z karl $


% hemodynamic parameters
%--------------------------------------------------------------------------
%   H(1) - signal decay                                   d(ds/dt)/ds)
%   H(2) - autoregulation                                 d(ds/dt)/df)
%   H(3) - transit time                                   (t0)
%   H(4) - exponent for Fout(v)                           (alpha)
%   H(5) - resting oxygen extraction                      (E0)
%   H(6) - ratio of intra- to extra-vascular components   (epsilon)
%--------------------------------------------------------------------------
if isstruct(P)
    H     = [0.64 0.32 2.00 0.32 0.4 1 1];
    for i = 1:numel(P.decay)
        H(1)   = H(1)*exp(P.decay(i));
        H(3)   = H(3)*exp(P.transit(i));
        f(i,:) = spm_fx_hdm(x(i,:),u(i),H);
    end