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: arNLSstep.m
    path of file: ./repos/d2d/arFramework3/MatlabTools
    
    the code of the file until where you have to start completion: % generate trial steps within box bounds
%
% [dp, solver_calls, qred, dpmem, grad_dir_frac, llh_expect, normdpmu_type] = ...
%     arNLSstep(llh, g, H, sres, mu, p, lb, ub, solver_calls, dpmem, useInertia, method)
%
% llh:  likelihood
% g:    gradient
% H:    Hessian matrix
% mu:   trust region size (for LM: lambda = 10/mu)
% p:    current parameters
% lb:   lower bounds
% ub:   upper bounds
%
% method:   
%  0 = trust region (based on modified trust.m)
%  1 = Levenberg-Marquardt
%  2 = Newton (with maximal step length mu)
%  3 = gradient descent (with steplength mu)
%  4 = gradient descent (to cauchy point with steplength mu)
%  5 = dogleg
%  6 = generalized trust region (based on modified trust.m)
%  7 = MATLABs trdog
%  8 = Newton pcgr (with maximal step length mu)
%  9 = trdog pcgr (with maximal step length mu)
% 10 = dogleg Newton pcgr
% 11 = dogleg trdog pcgr
% 12 = trdog pcgr (no DM)
% 13 = trdog pcgr (no DG)
% 14 = trdog pcgr Levenberg-Marquardt
% 15 = trdog pcgr 2D subspace 
% 16 = trdog pcgr (no DM) 2D subspace 
% 17 = trdog pcgr (no DM) 3D subspace 
% 18 = trust region (with DG, based on modified trust.m)
% 19 = trust region solution (with EV)

function [dp, solver_calls, qred, grad_dir_frac, llh_expect, normdpmu_type] = ...
    arNLSstep(llh, g, H, sres, mu, p, lb, ub, s
    
function [v,dv]= definev(g,x,l,u)
n = length(x); 
v = zeros(n,1); 
dv=zeros(n,1);
arg1 = (g < 0)  & (u <  inf ); 
arg2 = (g >= 0) & (l > -inf);
arg3 = (g < 0)  & (u == inf); 
arg4 = (g >= 0) & (l == -inf);
v(arg1)  = (x(arg1) - u(arg1)); 
dv(arg1) = 1;
v(arg2)  = (x(arg2) - l(arg2)); 
dv(arg2) = 1;
v(arg3)  = -1;
dv(arg3) = 0;
v(arg4)  = 1;
dv(arg4) = 0;



function A = mgrscho(A)
%MGRSHO Modified Gram-Schmidt orthogonalization procedure. 
% -For a basis of fundamentals on classical Gram-Schmidt process, procedure
% and its origin. Please see the text of the m-file cgrsho you can download
% from www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=12465
% The classical Gram-Scmidt algorithm is numerically unstable, mainly 
% because of all the successive subtractions in the order they appear. When
% this process is implemented on a computer, then the vectors s_n are not
% quite orthogonal because of rounding errors. This loss of orthogonality
% is particularly bad; therefore, it is said that the (naive) classical 
% Gram–Schmidt process is numerically unstable. If we write an algorithm
% based on the way we developed the Gram-Schmidt iteration (in terms of 
% projections), we get a better algorithm.
% The Gram–Schmidt process can be stabilized by a small modification. 
% Instead of computing the vector u_n as,
%
%     u_n = v_k - proj_u_1 v_n - proj_u_2 v_n -...- proj_u_n-1 v_n
%
% it is computed as,
%
%     u_n = u_n ^n-2 - proj_u_n-1 u_n ^n-2
%
% This series of computations gives the same result as the original formula
% in exact arithmetic, but it introduces smaller errors in finite-precision
% arithmetic. A stable algorithm is one which does not suffer drastically 
% from perturbations due to roundoff errors. This is called as the modified
% Gram-Schmidt orthogonalization process. 
% There are several different variations of the Gram-Schmidt process 
% including classical Gram-Schmidt (CGS), modified Gram-Schmidt (MGS) and 
% modified Gram-Schmidt with pivoting (MGSP). MGS economizes storage and is
% generally more stable than CGS.
% The Gram-Schmidt process can be used in calculating Legend