RFC: Fix behaviour of sqrtm on UpperTriangular matrices

[mfasi]

sqrtm does not automatically promote the work matrix to a complex type if any of the elements on the diagonal is negative. An example of the issue is

A = UpperTriangular([-1 2; 0 3.]); sqrtm(A)

[andreasnoack]

Could you also add a test for this?

[mfasi]

@andreasnoack Thank you, I added a few tests which should achieve complete line coverage (of the sqrtm functions).

[andreasnoack]

Thanks. Just a small detail. We are moving towards using ≈ instead of test_approx_eq so would you change the tests to something like @test sqrtm(Atn) |> t->t*t ≈ Atn.

[mfasi]

I tried to use ≈ but it does not seem to be defined. Should I import something in the test file? The symbol I'm using should be U+2248

[andreasnoack]

which version of Julia are you using?

[mfasi]

My current version was:

Version 0.4.0-dev+6561 (2015-08-09 23:36 UTC)
Commit 5505cf8* (2 days old master)

Now I am rebasing the branch on master, but I doubt things will change -- unless this symbol has been there for less than 2 days. Anyway, it really looks like it's just an issue of mine, the tests apparently work fine on AppVeyor and Travis.

[yuyichao]

unless this symbol has been there for less than 2 days

This is exactly what happend. #12472

[mfasi]

@yuyichao Thank you, it works now.

[andreasnoack]

Great. Thanks for fixing this.