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BUG: numpy.std returns wrong result with an identity array #27782

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AnonymousPlayer2000 opened this issue Nov 17, 2024 · 3 comments
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BUG: numpy.std returns wrong result with an identity array #27782

AnonymousPlayer2000 opened this issue Nov 17, 2024 · 3 comments
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33 - Question Question about NumPy usage or development

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@AnonymousPlayer2000
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Describe the issue:

I created a (7,)-shape array with the same number. Then I called numpy.std, and it returned 4 (far from the expected 0).

Reproduce the code example:

import numpy as np
np.std(np.prod(np.full((7, 10), 45, dtype="float64"), axis=1),axis=0)

Error message:

No response

Python and NumPy Versions:

I tried this in two versions:

2.1.0
3.10.12 (main, Jul 29 2024, 16:56:48) [GCC 11.4.0]
1.26.3
3.10.12 (main, Nov 20 2023, 15:14:05) [GCC 11.4.0]

Runtime Environment:

[{'numpy_version': '2.1.0',
  'python': '3.10.12 (main, Jul 29 2024, 16:56:48) [GCC 11.4.0]',
  'uname': uname_result(system='Linux', node='1091aa609208', release='6.8.0-48-generic', version='#48~22.04.1-Ubuntu SMP PREEMPT_DYNAMIC Mon Oct  7 11:24:13 UTC 2', machine='x86_64')},
 {'simd_extensions': {'baseline': ['SSE', 'SSE2', 'SSE3'],
                      'found': ['SSSE3',
                                'SSE41',
                                'POPCNT',
                                'SSE42',
                                'AVX',
                                'F16C',
                                'FMA3',
                                'AVX2'],
                      'not_found': ['AVX512F',
                                    'AVX512CD',
                                    'AVX512_KNL',
                                    'AVX512_KNM',
                                    'AVX512_SKX',
                                    'AVX512_CLX',
                                    'AVX512_CNL',
                                    'AVX512_ICL']}},
 {'architecture': 'Haswell',
  'filepath': '/usr/local/lib/python3.10/dist-packages/numpy.libs/libscipy_openblas64_-ff651d7f.so',
  'internal_api': 'openblas',
  'num_threads': 24,
  'prefix': 'libscipy_openblas',
  'threading_layer': 'pthreads',
  'user_api': 'blas',
  'version': '0.3.27'}]
[{'numpy_version': '1.26.3',
  'python': '3.10.12 (main, Nov 20 2023, 15:14:05) [GCC 11.4.0]',
  'uname': uname_result(system='Linux', node='dc5b26f04603', release='6.8.0-48-generic', version='#48~22.04.1-Ubuntu SMP PREEMPT_DYNAMIC Mon Oct  7 11:24:13 UTC 2', machine='x86_64')},
 {'simd_extensions': {'baseline': ['SSE', 'SSE2', 'SSE3'],
                      'found': ['SSSE3',
                                'SSE41',
                                'POPCNT',
                                'SSE42',
                                'AVX',
                                'F16C',
                                'FMA3',
                                'AVX2'],
                      'not_found': ['AVX512F',
                                    'AVX512CD',
                                    'AVX512_KNL',
                                    'AVX512_KNM',
                                    'AVX512_SKX',
                                    'AVX512_CLX',
                                    'AVX512_CNL',
                                    'AVX512_ICL']}},
 {'architecture': 'Prescott',
  'filepath': '/usr/local/lib/python3.10/dist-packages/numpy.libs/libopenblas64_p-r0-0cf96a72.3.23.dev.so',
  'internal_api': 'openblas',
  'num_threads': 24,
  'prefix': 'libopenblas',
  'threading_layer': 'pthreads',
  'user_api': 'blas',
  'version': '0.3.23.dev'}]

Context for the issue:

No response
@rkern
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rkern commented Nov 17, 2024

You're getting floating point errors. Each value in the array that you are passing to std() is very, very large, 3.40506289e+16. Floating point error on the order of 1e-16 times that value (i.e., around 4.0) accumulates within the calculations. Despite the fact that you've set up a situation where the ideal calculation done with infinite precision real numbers would give you exactly 0, with floating point arithmetic, you can only expect to get an answer near that ideal value to roughly 1e-16 times the magnitude of the inputs (very roughly, within an order of magnitude or two; you'd have to work through the numerical analysis to get better error bounds).

If you reduce the size of the inputs, you can see the error more clearly. For example, if instead I have values of 0.1 instead of ~3.4e+16, we get this:

>>> np.std(np.full((7, 10), 0.1))
np.float64(4.163336342344337e-17)

That is, near 0.1 * 1e-16, similar in relative error to what you are seeing with your inputs.

@rkern rkern closed this as not planned Won't fix, can't repro, duplicate, stale Nov 17, 2024
@rkern rkern added 33 - Question Question about NumPy usage or development and removed 00 - Bug labels Nov 17, 2024
@AnonymousPlayer2000
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@rkern Thanks!

@WarrenWeckesser
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FYI: This issue is a duplicate of #9631. The problem arises in the two pass calculation of the variance when the calculated mean of the constant array does not equal the value in the array.

In [65]: x = np.prod(np.full((7, 10), 45, dtype="float64"), axis=1)

In [66]: x
Out[66]: 
array([3.40506289e+16, 3.40506289e+16, 3.40506289e+16, 3.40506289e+16,
       3.40506289e+16, 3.40506289e+16, 3.40506289e+16])

In [67]: x[0]
Out[67]: np.float64(3.4050628916015624e+16)

In [68]: np.mean(x)
Out[68]: np.float64(3.405062891601562e+16)

In [69]: y = np.full((7, 10), 0.1)

In [70]: y[0,0]
Out[70]: np.float64(0.1)

In [71]: np.mean(y)
Out[71]: np.float64(0.09999999999999996)

@mattip mattip mentioned this issue Dec 2, 2024
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@rkern @WarrenWeckesser @AnonymousPlayer2000