Preallocating a Vector:
There are necessarily two programming techniques that can be used to simulate the cumsum function. One technique is to begin with an empty vector and concatenate each running sum value to the vector. Extending a vector, though, is very ineffective. A better technique is to preallocate the vector to the right size and then change the value of each element to be succeeding running sums. Both techniques will be shown here.
In the function below, the output argument is initialized to the empty vector []. Then, every time the later element in the vector is added to the running sum, this latest sum is appended to the vector.