return SVD from pinv(::SVD)

[stevengj]

As suggested by @andreasnoack in #1387 (comment), this changes the pinv(::SVD) function to instead return the SVD of the pseudo-inverse, rather than an explicit matrix, so that it can be applied stably.

(No backwards-compatibility issue since the pinv(::SVD) method was introduced in #1387.)

[stevengj]

Whoops, failing because *(::SVD, ::AbstractVector) is not defined. This should be fixed — otherwise returning an SVD object from pinv is useless.

Update: fixed.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 93.85%. Comparing base (9e2ed1c) to head (b3921af).
Report is 1 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1398      +/-   ##
==========================================
- Coverage   93.85%   93.85%   -0.01%     
==========================================
  Files          34       34              
  Lines       15827    15830       +3     
==========================================
+ Hits        14855    14857       +2     
- Misses        972      973       +1     

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[stevengj]

CI failure on Windows is an unrelated server glitch.

[stevengj]

Yay, green again.

[MasonProtter]

Maybe a dumb question, but why not also have inv(::SVD) return an SVD?

[dkarrasch]

We have an open issue (#635) regarding whether inv of factorizations should return a Factorization. The issue is that not every factorization has an inverse that can be represented by a type that we already have. SVD is tempting, of course, but I guess consistency is a potential issue here.

[stevengj]

@MasonProtter, the other issue is that changing inv(::SVD) would be a breaking change, whereas pinv(::SVD) was a new method (added a few days ago).