Replace inner1d bei einsum

[fs446]

We use
from numpy.core.umath_tests import inner1d as _inner1d
which is suboptimal, since its deprecated and requires non-standard library import.
See also #77

We could use numpy's einsum do to this job instead, thus I've changed (hopefully) all occurrences of inner1d to einsum.

Besides that in the files, some PEP8 modifications were done, these suggestions came from PyCharm.

Maybe numpy's tensordot is even more performant/suitable. I don't know currently how/if these functions support parallel computation, which inner1d seemed to do and was chosen for. I will check this.

In the meantime, using einsum in this PR is definitely an improvement for the code.

[mgeier]

I like the PEP8 changes, except for the spaces around **.

In the meantime, using einsum in this PR is definitely an improvement for the code.

"definitely" is quite a strong word. "improvement", too.

What if it's much slower?

[mgeier]

I guess some instances can be replaced with the @ operator (a.k.a. __matmul__). Have you checked the performance of that?

[hagenw]

The test for Python 3.5 fails as the installed sphinxcontrib-bibtex package no longer supports Python 3.5:

Exception occurred:
899  File "/home/travis/virtualenv/python3.5.7/lib/python3.5/site-packages/sphinxcontrib/bibtex/roles.py", line 12, in <module>
900    import pybtex.database
901  File "/home/travis/virtualenv/python3.5.7/lib/python3.5/site-packages/pybtex/database/__init__.py", line 124
902    f"  entries={repr_entry},\n\n"
903    ^
904SyntaxError: invalid syntax

I also very much dislike Python 3.5 and would simply remove support for it.

[hagenw]

The other test fails as homebrew seems not to be installing pandoc

[hagenw]

I created a pull request where I run the tests directly on Github (and skip Python 3.5): #166
There the MacOS tests work as well. So it just seems to be a bug in how travis is configured.

[hagenw]

I rebased the master, now the tests are passing.

[fs446]

I rebased and made code work for recent 0.6.1 / 0.6.2. We will need a handling once inner1d() is discontinued, so it might be a good idea to keep this einsum() handling up to date. I would vote using this some time.

[gerazov]

Could this be merged? inner1d has been removed from new versions of NumPy. If not merged maybe set explicitly the NumPy version in the setup.py?

Here's the issue on numpy/numpy#10815 they suggest using np.dot(arr2, arr1):

If that's all the broadcasting you need, I think np.dot(arr2, arr1) would be the better alternative, as you may get parallelization from the BLAS library. np.einsum may use SIMD if possible, so it is likely also faster than inner1d, and may come up on top of np.dot if it can avoid making copies of the arrays.

numpy/numpy#10815 (comment)

[fs446]

we can close this, because #180 handled this in another way