fsum for numpy.arrays, stable summation

Question

I have a number of multidimensional numpy.array s with small values that I need to add up with little numerical error. For float s, there is math.fsum (with its implementation here ), which has always served me well. numpy.sum isn't stable enough.

How can I get a stable summation for numpy.array s?

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Background

This is for the quadpy package . The arrays of small values are the evaluations of a function at specific points of (many) intervals, times their weights. The sum of these is an approximation of the integral of said function over the intervals.

Answer 1

Alright then, I've implemented accupy which gives a few stable summation algorithms.

Here's a quick and dirty implementation of Kahan summation for numpy arrays. Notice, however, that it is not not very accurate for ill-conditioned sums.

def kahan_sum(a, axis=0):
    '''Kahan summation of the numpy array along an axis.
    '''
    s = numpy.zeros(a.shape[:axis] + a.shape[axis+1:])
    c = numpy.zeros(s.shape)
    for i in range(a.shape[axis]):
        # https://stackoverflow.com/a/42817610/353337
        y = a[(slice(None),) * axis + (i,)] - c
        t = s + y
        c = (t - s) - y
        s = t.copy()
    return s

It does the job, but it's slow because it's Python-looping over the axis -th dimension.