which one is faster np.vstack, np.append, np.concatenate or a manual function made in cython?

Question

I coded some program which updates a numpy list in each iteration and does some operations on it. the number of iterations depends on time. for example in 1 second, there might be 1000 to 2500 iterations. It means that the items in the numpy list wouldn't be more than 2500 for running program for 1 second.

I had implemented a basic algorithm which I am not sure if it's the fastest way to calculate bonus:

import numpy as np

cdef int[:, :] pl_list
cdef list pl_length
cdef list bonus
pl_list = np.array([[8, 7]], dtype=np.int32)

def modify(pl_list, pl_length):
    cdef int k_const = 10
    mean = np.mean(pl_list, axis=0)
    mean = np.subtract(mean, pl_length)
    dev = np.std(pl_list, axis=0)
    mean[0] / dev[0] if dev[0] != 0 else 0
    mean[1] / dev[1] if dev[1] != 0 else 0

    bonus = -1 + (2 / (1 + np.exp(-k_const * mean)))
    return list(bonus)


for i in range(2499): # I just simplified the loop. the main loop works like startTime - time.clock() < seconds
    rand = np.random.randint(8, 64)
    pl_length = [rand, rand-1]

    pl_list = np.append(pl_list, [pl_length], axis=0)
    bonus = modify(pl_list, pl_length)

I was thinking of speed up this program using these ideas:

1. using np.vstack, np.stack or maybe np.concatenate instead of np.append(pl_list, [pl_length]).(which one might be faster?)

2. Using self-made functions to calculate the np.std, np.mean like this (because iterating in memoryviews are so fast in cython):

   cdef int i,sm = 0
for i in range(pl_list.shape[0]):
    sm += pl_list[i]
mean = sm/pl_list.shape[0]
   

3. I was also thinking of defining a static length(like 2500) for memoryviews, so I wouldn't need to use np.append and I can build a queue structure on that numpy list. (How about Queue library? Is that faster than numpy lists in such operations?)

Sorry if my questions are too many and complicated. I'm just trying to get the best possible performance in speed.

Answer 1

Ignoring for the modify function, the core of your loop is:

pl_list = np.array([[8, 7]], dtype=np.int32)
....

for i in range(2499):
    ....
    pl_list = np.append(pl_list, [pl_length], axis=0)
    ...

As a general rule we discourage the use of np.concatenate, and its derivatives, in a loop. It is faster to append to a list, and do the concatenate once at the end. (more on that later)

Is pl_list a list or an array? By name it is a list, but as created it is an array. I haven't studied modify to see whether it requires an array or list.

Look at the source code for functions like np.append. The base function is np.concatenate, which takes a list, and joins them into a new array along the specified axis. In other words, it works well with a long list of arrays.

np.append replaces that list input with 2 arguments. So it has to be applied iteatively. And that is slow. Each append creates a new array.

np.hstack just makes sure the list elements are atleast 1d, np.vstack makes them 2d, stack adds a dimension, etc. So basically they all do the same thing, with minor tweaks to the inputs.

The other model is to allocate a large enough array to start with, e.g. res = np.zeros((n,2)), and insert values at res[i,:] = new_value. Speeds are about the same as the list append approach. This model can be moved to cython and typed memoryviews for a (potentially) big speed improvement.