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_int_E.m
    path of file: ./repos/ExploreASL/External/SPMmodified
    
    the code of the file until where you have to start completion: function [y] = spm_int_E(P,M,U)
% integrates a MIMO nonlinear system using a bilinear eigenreduced Jacobian
% FORMAT [y] = spm_int_E(P,M,U)
% P   - model parameters
% M   - model structure
% U   - input structure or matrix
%
% y   - (v x l)  response y = g(x,u,P)
%__________________________________________________________________________
%
% Integrates the MIMO system described by
%
%    dx/dt = f(x,u,P,M)
%    y     = g(x,u,P,M)
%
% using the update scheme:
%
%    x(t + dt) = x(t) + U*dx(t)/dt
%
%            U = (expm(dt*J) - I)*inv(J)
%            J = df/dx
%
% at input times.  This integration scheme evaluates the update matrix (Q)
% at each time point
%
%--------------------------------------------------------------------------
%
% SPM solvers or integrators
%
% spm_int_ode:  uses ode45 (or ode113) which are one and multi-step solvers
% respectively.  They can be used for any ODEs, where the Jacobian is

    
function [y] = spm_int_E(P,M,U)
% integrates a MIMO nonlinear system using a bilinear eigenreduced Jacobian
% FORMAT [y] = spm_int_E(P,M,U)
% P   - model parameters
% M   - model structure
% U   - input structure or matrix
%
% y   - (v x l)  response y = g(x,u,P)
%__________________________________________________________________________
%
% Integrates the MIMO system described by
%
%    dx/dt = f(x,u,P,M)
%    y     = g(x,u,P,M)
%
% using the update scheme:
%
%    x(t + dt) = x(t) + U*dx(t)/dt
%
%            U = (expm(dt*J) - I)*inv(J)
%            J = df/dx
%
% at input times.  This integration scheme evaluates the update matrix (Q)
% at each time point
%
%--------------------------------------------------------------------------
%
% SPM solvers or integrators
%
% spm_int_ode:  uses ode45 (or ode113) which are one and multi-step solvers
% respectively.  They can be used for any ODEs, where the Jacobian is
% unknown or difficult to compute; however, they may be slow.
%
% spm_int_J: uses an explicit Jacobian-based update scheme that preserves
% nonlinearities in the ODE: dx = (expm(dt*J) - I)*inv(J)*f.  If the
% equations of motion return J = df/dx, it will be used; otherwise it is
% evaluated numerically, using spm_diff at each time point.  This scheme is
% infallible but potentially slow, if the Jacobian is not available (calls
% spm_dx).
%
% spm_int_E: As for spm_int_J but uses the eigensystem of J(x(0)) to eschew
% matrix exponentials and inversion during the integration. It is probably
% the best compromise, if the Jacobian is not available explicitly.
%
% spm_int_B: As for spm_int_J but uses a first-order approximation to J
% based on J(x(t)) = J(x(0)) + dJdx*x(t).
%
% spm_int_L: As for spm_int_B but uses J(x(0)).
%
% spm_int_U: like spm_int_J but only evaluates J when the input changes.
% This can be useful if input changes are sparse (e.g., boxcar functions).
%
% spm_int:   Fast integrator that uses a bilinear approximation to the
% Jacobian evaluated using spm_bireduce. This routine will also allow for
% sparse sampling of the solution and delays in observing outputs. It is
% used primarily for integrating fMRI models
%___________________________________________________________________________
% Copyright (C) 2008 Wellcome Trust Centre for Neuroimaging
 
% Karl Friston
% $Id: spm_int_E.m 5219 2013-01-29 17:07:07Z spm $

% convert U to U.u if necessary
%--------------------------------------------------------------------------
if ~isstruct(U)
    u.u = U;
    U   = u;
end