Vectorizing a recursive for-loop

Hey, I need help vectorizing this for-loop. In general, I need help vectorizing a for-loop with a term that references it's previous value.

In my case, DT is already a vector, and I want to fill out the Time vector as such

Time = zeros(1,N)
  Time(1) = DT(1)/2
  for i=2:N
       Time(i)=Time(i-1)+0.5*(DT(i)+DT(i-1));
  end

Is there a simple vectorization to this for loop?

Thank you.

Answer 1

[Sean de Wolski]

Usually cumsum and diff will be the two functions that help referencing adjacency.

    Time2 = cumsum([DT(1)/2 0.5*(DT(2:end)+DT(1:end-1))]);

And to check

isequal(Time,Time2)

ans = 1

[Noah Chrein]

Very nice, thank you.