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: auxiliary_var_selection.m
    path of file: ./repos/Path-Selection-and-Rate-allocation-in-Self-backhauled-mmWave-Networks
    
    the code of the file until where you have to start completion: function [ auxi_var ] = auxiliary_var_selection( vq )

    
function [ auxi_var ] = auxiliary_var_selection( vq )
% This function is to solve the selection of auxiliary variable
% Define the maximum allowed rate and the control parameter V
[nSF, nBS] = size(vq); % number of BSs and subflows
auxi_var = zeros(nSF, nBS);
V = 5;
max_rate = log(1 + 10); % maximum rate of each link
min_rate = 0;
for sub_f = 1:nSF
    for bs = 1:nBS
        if vq(sub_f,bs) ~= 0
            auxi_var(sub_f,bs) = V./vq(sub_f,bs);
        else
            auxi_var(sub_f,bs) =  max_rate;
        end