The output of numpy.dot appears to be impacted by the total array shape (possibly only with MKL.)

Example

import numpy as np
np.random.seed(42)

a = np.random.rand(4, 10000).astype('float32')
m1 = np.dot(a, a.T)
m2 = np.dot(a[:2], a[:2].T)

print(m1[:2, :2])
print(m2)

Expected output

Identical arrays printed in both cases,

[[3269.1648 2488.9185]
 [2488.9185 3382.3335]]
[[3269.1648 2488.9185]
 [2488.9185 3382.3335]]

Actual output

[[3269.1653 2488.9177]
 [2488.9177 3382.334 ]]
[[3269.1648 2488.918 ]
 [2488.918  3382.3337]]

i.e. only a 1e-4 absolute precision.

Environment information

Using the following conda environment,

conda create -n numpy-env numpy==1.15.0 python=3.7

the above output with bad precision is produced on the following 4 CPU core Linux system,

$ uname -ap
Linux [..] 4.4.30-mod-std-ipv6-64 #9 SMP Tue Nov 1 17:58:26 CET 2016 x86_64 GNU/Linux
$ cat /proc/cpuinfo  | grep "model name" | head -n 1
model name      : Intel(R) Xeon(R) CPU E3-1225 V2 @ 3.20GHz

while the same environment produces the correct result exactly on the following (2 CPU core) Linux system,

$ uname -a
Linux 4.11.6-gentoo #9 SMP Fri Sep 29 14:28:20 CEST 2017 x86_64 Intel(R) Core(TM) i5-6200U CPU @ 2.30GHz GenuineIntel GNU/Linux

This issue was originally indirectly detected in scikit-learn/scikit-learn#11711 where it was reported for Linux, Mac OS, and Windows. Thanks to @TomDLT for a reproducible minimal numpy code snippet.

Additional information

• Creating the python 3.7 env with conda then installing numpy OpenBLAS wheel with pip doesn't have this issue
• in conda installing numpy together with openblas nomkl also doesn't have this issue, so it seem that it's due to MKL.
• 64 bit floats don't appear to be impacted: the obtained absolute precision is 1e-12, for number of a few 1e3, which appears consistent with ~16 digits precision.
• setting MKL_NUM_THREADS=1, MKL_DOMAIN_NUM_THREADS=1 doesn't help.