Fastest way to count array values above a threshold in numpy

Question

I have a numpy array containing 10^8 floats and want to count how many of them are >= a given threshold. Speed is crucial because the operation has to be done on large numbers of such arrays. The contestants so far are

np.sum(myarray >= thresh)

np.size(np.where(np.reshape(myarray,-1) >= thresh))

The answers at Count all values in a matrix greater than a value suggest that np.where() would be faster, but I've found inconsistent timing results. What I mean by this is for some realizations and Boolean conditions np.size(np.where(cond)) is faster than np.sum(cond), but for some it is slower.

Specifically, if a large fraction of entries fulfil the condition then np.sum(cond) is significantly faster but if a small fraction (maybe less than a tenth) do then np.size(np.where(cond)) wins.

The question breaks down into 2 parts:

• Any other suggestions?
• Does it make sense that the time taken by np.size(np.where(cond)) increases with the number of entries for which cond is true?

Answer 1

Using cython might be a decent alternative.

import numpy as np
cimport numpy as np
cimport cython
from cython.parallel import prange


DTYPE_f64 = np.float64
ctypedef np.float64_t DTYPE_f64_t


@cython.boundscheck(False)
@cython.wraparound(False)
@cython.nonecheck(False)
cdef int count_above_cython(DTYPE_f64_t [:] arr_view, DTYPE_f64_t thresh) nogil:

    cdef int length, i, total
    total = 0
    length = arr_view.shape[0]

    for i in prange(length):
        if arr_view[i] >= thresh:
            total += 1

    return total


@cython.boundscheck(False)
@cython.wraparound(False)
@cython.nonecheck(False)
def count_above(np.ndarray arr, DTYPE_f64_t thresh):

    cdef DTYPE_f64_t [:] arr_view = arr.ravel()
    cdef int total

    with nogil:
       total =  count_above_cython(arr_view, thresh)
    return total

Timing of different proposed methods.

myarr = np.random.random((1000,1000))
thresh = 0.33

In [6]: %timeit count_above(myarr, thresh)
1000 loops, best of 3: 693 µs per loop

In [9]: %timeit np.count_nonzero(myarr >= thresh)
100 loops, best of 3: 4.45 ms per loop

In [11]: %timeit np.sum(myarr >= thresh)
100 loops, best of 3: 4.86 ms per loop

In [12]: %timeit np.size(np.where(np.reshape(myarr,-1) >= thresh))
10 loops, best of 3: 61.6 ms per loop

With a larger array:

In [13]: myarr = np.random.random(10**8)

In [14]: %timeit count_above(myarr, thresh)
10 loops, best of 3: 63.4 ms per loop

In [15]: %timeit np.count_nonzero(myarr >= thresh)
1 loops, best of 3: 473 ms per loop

In [16]: %timeit np.sum(myarr >= thresh)
1 loops, best of 3: 511 ms per loop

In [17]: %timeit np.size(np.where(np.reshape(myarr,-1) >= thresh))
1 loops, best of 3: 6.07 s per loop