ENH: linalg: Add an axis argument to linalg.norm

[WarrenWeckesser]

Example:

In [8]: a = array([[0,1,2],[3,4,0]])

In [9]: a
Out[9]: 
array([[0, 1, 2],
       [3, 4, 0]])

In [10]: norm(a, axis=0)
Out[10]: array([ 3.        ,  4.12310563,  2.        ])

In [11]: norm(a, axis=1)
Out[11]: array([ 2.23606798,  5.        ])

In [12]: norm(a, ord=np.Inf, axis=1)
Out[12]: array([2, 4])

axis can be a 2-tuple:

In [52]: a = np.arange(8).reshape(2,2,2)

In [53]: a
Out[53]: 
array([[[0, 1],
        [2, 3]],

       [[4, 5],
        [6, 7]]])

In [54]: norm(a, axis=(1,2))
Out[54]: array([  3.74165739,  11.22497216])

This PR also fixes a bug that occurs when computing the norm of an integer array with a negative ord. Before this change, norm([1,3], ord=-1) returned the incorrect value 1.0. Now,

In [13]: norm([1,3], ord=-1)
Out[13]: 0.75

[njsmith]

The vector/matrix dual-nature of this function mean that it has a pretty weird and overloaded calling convention. This is too bad, but, given that it is what it is -- shouldn't this API also support the ability to compute matrix norms over some subset of the axes?

[WarrenWeckesser]

I agree about the "weirdness"--initially I created a new function, norm1d(a, ord, axis), that was solely for computing vector norms. But I figured the first question I'd get was "Why don't you just add an axis argument to the existing function?".

I think of the axis argument as saying "I want the vector norms of a collection of vectors". I guess it could be generalized so that if axis is a 2-tuple, it means "I want the matrix norms of a collection of matrices." So if a has shape (2,3,4), then norm(a, axis=(1,2)) would return an array with shape (2,). That sounds fine to me. Is that what you are suggesting?

[njsmith]

Yes.
On 3 Jun 2013 17:51, "Warren Weckesser" notifications@github.com wrote:

I agrees about the "weirdness"--initially I created a new function, norm1d(a,
ord, axis), that was solely for computing vector norms. But I figured the
first question I'd get was "Why don't you just add an axis argument to
the existing function?".

I think of the axis argument as saying "I want the vector norms of a
collection of vectors". I guess it could be generalized so that if axisis a 2-tuple, it means "I want the matrix norm of a collection of
matrices." So if a has shape (2,3,4), then norm(a, axis=(1,2)) would
return an array with shape (2,). That sounds fine to me. Is that what you
are suggesting?

—
Reply to this email directly or view it on GitHubhttps://github.com//pull/3387#issuecomment-18854585
.

[WarrenWeckesser]

The PR has been updated to allow axis to be a 2-tuple, as described above.

[njsmith]

IMO it's better style (esp. pedagogical style) to replace m[0] with m[0, :, :] or m[0, ...].

[WarrenWeckesser]

👍

[WarrenWeckesser]

The latest commit makes the changes suggest by @njsmith

[njsmith]

+1 from me pending travis results.