是什么导致numpy中的C和F有序数组沿轴的数组总和不同 [英] what causes different in array sum along axis for C versus F ordered arrays in numpy

问题描述

我很好奇，是否有人可以解释到底是什么导致了numpy中C与Fortran有序数组的这种特殊处理方式的差异.请参见下面的代码:

I am curious if anyone can explain what exactly leads to the discrepancy in this particular handling of C versus Fortran ordered arrays in numpy. See the code below:

system:
Ubuntu 18.10
Miniconda python 3.7.1
numpy 1.15.4

def test_array_sum_function(arr):
    idx=0
    val1 = arr[idx, :].sum()
    val2 = arr.sum(axis=(1))[idx]
    print('axis sums:', val1)
    print('          ', val2)
    print('    equal:', val1 == val2)
    print('total sum:', arr.sum())

n = 2_000_000
np.random.seed(42)
rnd = np.random.random(n)

print('Fortran order:')
arrF = np.zeros((2, n), order='F')
arrF[0, :] = rnd
test_array_sum_function(arrF)

print('\nC order:')
arrC = np.zeros((2, n), order='C')
arrC[0, :] = rnd
test_array_sum_function(arrC)

打印:

Fortran order:
axis sums: 999813.1414744433
           999813.1414744079
    equal: False
total sum: 999813.1414744424

C order:
axis sums: 999813.1414744433
           999813.1414744433
    equal: True
total sum: 999813.1414744433

推荐答案

几乎可以肯定这是numpy的结果，有时会使用有时不是.

This is almost certainly a consequence of numpy sometimes using pairwise summation and sometimes not.

让我们建立一个诊断阵列:

Let's build a diagnostic array:

eps = (np.nextafter(1.0, 2)-1.0) / 2
1+eps+eps+eps
# 1.0
(1+eps)+(eps+eps)
# 1.0000000000000002

X = np.full((32, 32), eps)
X[0, 0] = 1
X.sum(0)[0]
# 1.0
X.sum(1)[0]
# 1.000000000000003
X[:, 0].sum()
# 1.000000000000003

这强烈表明一维数组和连续轴使用成对求和，而多维数组中的跨轴不使用.

This strongly suggests that 1D arrays and contiguous axes use pairwise summation while strided axes in a multidimensional array don't.

请注意，要看到这种效果，数组必须足够大，否则numpy会退回到普通求和.

Note that to see that effect the array has to be large enough, otherwise numpy falls back to ordinary summation.

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