[SciPy-Dev] PR to add get_array_bandwidth, issymmetric, ishermitian functions

[Eric Larson]

>
> I am not sure about the business case for it but I'd like to fish for some
> feedback here too.
>

I hit this sort of thing often working with floating point data, for
example with a simple left-and-right multiplies of some matrix (and its
transpose, respectively) that should preserve symmetry:

>>> import numpy as np
>>> rng = np.random.RandomState(0)
>>> x = rng.randn(10, 10)
>>> y = x @ x.T  # symmetric
>>> np.array_equal(y, y.T)
True
>>> p = rng.randn(10, 10)
>>> z = p @ y @ p.T  # this should still be symmetric
>>> np.array_equal(z, z.T)
False
>>> np.allclose(z, z.T)  # it is symmetric to numerical precision
True
>>> z[0, 1]
7.912658519091485
>>> z[1, 0]
7.9126585190914875

The main issues I can see is that int types have no room for noise and also
> the tolerance adjustment would be quite difficult to pull off since it
> would depend on the magnitudes of the nonzero entries to decide what
> constitutes as noise.
>

I would vote for / expect `atol=0, rtol=1e-7` keyword arguments (maybe with
different defaults) to have an API similar to `np.allclose`. Here I chose
the defaults for `assert_allclose` because I have found in practice the
`atol=1e-8` to be a bit dangerous / lead to silent bugs in people's code.

Finally, though I started this in SciPy, I still have some doubts whether
> this should go into NumPy or not. But we can do that anytime later.
>

To me NumPy would be a more natural fit for this sort of thing, and I would
enjoy having `np.testing.*` variants of these things, too, for code
development in other downstream libraries.

My 2c,
Eric
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