Numpy: calculate based on previous element?

Question

Say that I have array x and y:

x = numpy.array([1,2,3,4,5,6,7,8,9,10])  # actual content is the a result of another calculation step
         


        

Answer 1

If you need a recursive computation, if your y[i] should depend on the computed y[i-1] from the same run, then there seems to be no built-in solution in numpy, and you will need to compute it using a simple for loop:

y = np.empty(x.size)
last = 50
for i in range(x.size):
    y[i] = last = last * 2 + x[i]

See this question: Is a "for" loop necessary if elements of the a numpy vector are dependant upon the previous element?

Otherwise, you can implement your formula in one line using numpy:

y = np.concatenate(([50], y[:-1])) * 2 + x

Explanation:

y[:-1]

Creates a N-1-sized array: y_0, y_1, ... y_N-1.

np.concatenate(([50], y[:-1]))

Creates a N-sized array with the first element your starting value 50. So this expression basically is your y[i-1].

Then you can do the math element-wise using numpy array arithmetics.