MATLAB: Using a function instead of inlining increases the time it takes to run

functionMATLABmemorytime

I use 64-bit Matlab R2014b.
I have a large matrix in which I iteratively change one element and I have another operation in which I sort a smaller matrix. I have two minimal working examples and I would like to know why one approach takes longer than the other. The first example uses a direct approach, whereas the second approach uses a function to perform the task.
Minimal working example 1
   n_iter = 1e7;
   A = zeros(n_iter,1);
   B = sort(rand(1e3,1));
   for i = 1:n_iter
       A(i) = 1;
       B = sort([ B(2:end); B(1) ]);
   end
Minimal working example 2
   function deallocating_large_matrices_function
   n_iter = 1e7;
   A = zeros(n_iter,1);
   B = sort(rand(1e3,1));
   for i = 1:n_iter
       A(i) = 1;
       B = sortB(B(2:end),B(1));
   end
   end
   function B = sortB(B,new_entry)
       B = sort([ B ; new_entry ]);
   end
Results
Below a table showing the time it took to run both examples as a function of n_iter, using the profiler.
   n_iter | time MWE 1 (sec) | time MWE 2 (sec)
   --------------------------------------------
   1e4    | 0.13             | 0.21
   1e5    | 1.38             | 1.98
   1e6    | 13.5             | 19.7
   1e7    | 137              | 196
The time it takes to run both MWE 1 and MWE2 increases linearly. Running MWE 2 takes approximately 46% more time. What is the cause of this increase?

Best Answer

The issue is in subfunction
     function B = sortB(B,new_entry)
         B = sort([ B ; new_entry ]);
     end
You are passing a vector of size 'n-1' as B and the returning the same variable B but with size 'n'. This requires rewriting and reallocating memory, in other words more time!
Try this: function deallocating_large_matrices_function
   n_iter = 1e7;
   A = zeros(n_iter,1);
   B = sort(rand(1e3,1));
   for i = 1:n_iter
       A(i) = 1;
       B = sortB([B(2:end);B(1)]);
   end
   end
     function B = sortB(B)
         B = sort(B);
     end
This will result in more comparable time.
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