Fix mistakes and increase clarity of norm documentation

[kurtamohler]

• Removes incorrect statement that "the vector norm will be applied to the last dimension".
• More clearly describe each different combination of p, ord, and input size.
• Moves norm tests from test/test_torch.py to test/test_linalg.py
• Adds test ensuring that p='fro' and p=2 give same results for mutually valid inputs

Fixes #41388

[dr-ci]

💊 CI failures summary and remediations

As of commit 210dd6d (more details on the Dr. CI page):

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💚 💚 Looks good so far! There are no failures yet. 💚 💚

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1 failure confirmed as flaky and can be ignored:

• pytorch_macos_10_13_py3_test

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This comment has been revised 27 times.

[ezyang]

@WANGZhaowei-Wesley could you help take a look at this fix? Thanks!

[kurtamohler]

This might be nice to have merged before the next release. Although, we now have a warning on torch.norm that deprecates it in favor of torch.linalg.norm, so perhaps it's moot now.

[facebook-github-bot]

@ezyang has imported this pull request. If you are a Facebook employee, you can view this diff on Phabricator.

[codecov]

Codecov Report

Merging #42696 into master will decrease coverage by 0.00%.
The diff coverage is n/a.

@@            Coverage Diff             @@
##           master   #42696      +/-   ##
==========================================
- Coverage   68.19%   68.19%   -0.01%     
==========================================
  Files         410      410              
  Lines       53403    53403              
==========================================
- Hits        36418    36417       -1     
- Misses      16985    16986       +1     

Impacted Files	Coverage Δ
torch/functional.py	88.21% <ø> (ø)
torch/testing/_internal/expecttest.py	77.55% <0.00%> (-1.03%)	⬇️

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[mruberry]

@kurtamohler It looks like this was never merged and #41388 never closed. Is this still relevant? Should I take a look for you?

[kurtamohler]

@mruberry, thanks for asking, yes I think this is still relevant since torch.norm is still available.

[kurtamohler]

@mruberry, maybe hold off on reviewing for a bit. I want to see if I can fix some of the confusing points brought up here: #44796 (comment)

[mruberry]

@mruberry, maybe hold off on reviewing for a bit. I want to see if I can fix some of the confusing points brought up here: #44796 (comment)

Sounds great. We'll wait for your update.

[kurtamohler]

@mruberry, OK I think this is a bit better, ready for review.

[mruberry]

I think I finally understand what torch.norm does. Thanks @kurtamohler. Just ping me when the test(s) are move to test_linalg.py.

[kurtamohler]

I think I finally understand what torch.norm does.

Haha yes, me too, even though I've been working with it for a couple months now.

[kurtamohler]

@mruberry , I've moved the tests, should be good to go now.
EDIT: actually, getting some errors, just a minute
Fixed

[facebook-github-bot]

@mruberry has imported this pull request. If you are a Facebook employee, you can view this diff on Phabricator.

[facebook-github-bot]

@mruberry merged this pull request in a0a8bc8.