einsum broadcast regression (with optimize=True)

[d70-t]

In numpy 1.13.3, it was possible to execute the following snippet without errors, while in 1.14.0 this happens:

In [1]: import numpy as np
In [2]: a = np.ones((10,2))
In [3]: b = np.ones((1,2))
In [4]: np.einsum('t...i,ti->t...', a, b)
Traceback (most recent call last):
  File "<ipython-input-4-fa62d1d882f9>", line 1, in <module>
    np.einsum('t...i,ti->t...', a, b)
  File "/usr/local/lib/python2.7/dist-packages/numpy/core/einsumfunc.py", line 1087, in einsum
    einsum_call=True)
  File "/usr/local/lib/python2.7/dist-packages/numpy/core/einsumfunc.py", line 710, in einsum_path
    "not match previous terms.", char, tnum)
ValueError: ("Size of label '%s' for operand %d does not match previous terms.", 't', 1)

However optimize=False solves the problem:

In [5]: np.einsum('t...i,ti->t...', a, b, optimize=False)
Out[5]: array([2., 2., 2., 2., 2., 2., 2., 2., 2., 2.])

Is this intended behavior and the user is now responsible to explicitly disable optimization or is this a bug?

[charris]

Both? optimize=True was made the default, but it shouldn't be causing errors.

@dgasmith Another one ;)

[eric-wieser]

Seems we failed to format the error message correctly either

[mhvk]

This hit at least one user of astropy (though not our tests, annoyingly!). The following breaks (but works with optimize=False):

np.einsum('...ij,j...->i...', np.eye(3)[np.newaxis], np.array([[1., 1.], [2., 2.], [3., 3.]]))

[mhvk]

The fix in #10352 seems correct. Note also that the current optimization choice makes no sense: for 2 argument, optimization should not be attempted; see #10357.

[mhvk]

A very simple fix for the slowdown is in #10359 - I think we should consider reverting the change in default of optimize, though. In the end, einsum is very likely used mostly with small numbers of arrays, for which the additional cost is not worth it. It seems more likely that users with long expressions will read the docstring and realize there is an optimize keyword than that users with short ones will realize the default is bad for their case.