On Wed, Apr 8, 2020 at 1:17 PM Sebastian Berg <sebastian@sipsolutions.net> wrote:
> > > But, backward compatibility aside, could we have ONLY Scalars?
> > Well, it is hard to write functions that work on N-Dimensions
> > (where N
> > can be 0), if the 0-D array does not exist. 
 
So as a (silly) example, the following does not generalize to 0d, even
though it should:

def weird_normalize_by_trace_inplace(stacked_matrices)
    """Devides matrices by their trace but retains sign
    (works in-place, and thus e.g. not for integer arrays)

    Parameters
    ----------
    stacked_matrices : (..., N, M) ndarray
    """
    assert stacked_matrices.shape[-1] == stacked_matrices.shape[-2]

    trace = np.trace(stacked_matrices, axis1=-2, axis2=-1)
    trace[trace < 0] *= -1
    stacked_matrices /= trace

Sure that function does not make sense and you could rewrite it, but
the fact is that in that function you want to conditionally modify
trace in-place, but trace can be 0d and the "conditional" modification
breaks down.

I guess that's what I'm getting at -- there is always an endpoint to reducing the rank. a function that's designed to work on a "stack" of something doesn't have to work on a single something, when it can, instead, work on a "stack" of hight one.

Isn't the trace of a matrix always a scalar? and thus the trace(s) of a stack of matrixes would always  be 1-D?

So that function should do something like:

stacked_matrixes.shape = (-1, M, M)

yes?

and then it would always work.

Again, backwards compatibility, but there is a reason the np.atleast_*() functions exist -- you often need to make sure your inputs have the dimensionality expected.

-CHB

--

Christopher Barker, Ph.D.
Oceanographer

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