linalg.det throws LinAlgError for 0-by-0 matrices

Since LAPACK functions cannot handle 0-by-0 matrices, numpy must explicitly handle those cases. However, while in newer versions of numpy, the inverse is computed correctly, the determinant raises LinAlgError:

>>> A = numpy.empty((0, 0))
>>> numpy.linalg.inv(A)
array([], shape=(0, 0), dtype=float64)
>>> numpy.linalg.det(A)
LinAlgError: Arrays cannot be empty

Since the determinant of a zero-by-zero matrix is well-defined, a LinAlgError is IMHO wrong, since it indicates a numerics problem rather than the purely technical fact that the backend cannot handle this.

Thus, expected result:

>>> numpy.linalg.det(A)
1.0

Numpy version: 1.11.0 (also present in git master) Python version: 2.7.12

[pv]

All “stacked” arrays are always of the same shape, which can be determined from the overall shape so no loops needed.

[eric-wieser]

@ashwinpathak20: This is already well in process (#8368), but has opened a can of worms:

• #8369 - the tests weren’t testing this type of array properly
• #8376 - the current version of lapack bundled with numpy is very out of date, and buggy
• #8381 - the tools for rebundling lapack were also broken

Update: mostly fixed!