use in-place inv, since lufact already made a copy

[fredrikekre]

Basically cuts allocated memory in half for generic inv calls.

Matrix size	master	PR
10	1.750 μs (9 allocations: 7.28 KiB)	1.688 μs (7 allocations: 6.25 KiB)
100	165.047 μs (11 allocations: 208.38 KiB)	156.498 μs (8 allocations: 129.30 KiB)
500	4.250 ms (11 allocations: 4.07 MiB)	3.976 ms (8 allocations: 2.16 MiB)
1000	27.447 ms (11 allocations: 15.76 MiB)	26.299 ms (8 allocations: 8.13 MiB)
2000	210.670 ms (11 allocations: 62.04 MiB)	204.308 ms (8 allocations: 31.51 MiB)
4000	1.539 s (13 allocations: 246.16 MiB)	1.482 s (9 allocations: 124.05 MiB)

[Sacha0]

Nice catch! :)

[fredrikekre]

Failure because LU{T} where T <: Union{BigFloat, Rational} does not support inv!, so I added a fallback for such cases.

[tkelman]

I don't think that fallback is right, since

inv!(F);
F

won't have the desired effect for some types

[fredrikekre]

You mean because you expected the matrix wrapped in the factorization to be the inverse? That's true...
For this PR it is only needed to have an in-place for LU, so I can add that instead? One that updates the correct matrix.

[fredrikekre]

Pushed an updated version.

[fredrikekre]

Timeout on Travis i686

[tkelman]

so does this copy twice?

[fredrikekre]

Yea, for the non BlasFloat case..

[tkelman]

there's a copy(A) on this line, then another copy(A) in the inv!(A::LU{T,<:StridedMatrix}) that it calls, right?

[fredrikekre]

I guess we can not use the inv(A) = inv!(copy(A)) pattern for the non BlasFloat case then. Instead

inv(A::LU) = A_ldiv_B!(A, eye(size(A)))

then. But we do still need to make the copy in the fallback inv! such that we can overwrite the stored matrix and use it as the left hand side in the solve at the same time.

[fredrikekre]

Rebased, good to go?

[ararslan]

Yes indeed. I'll let you do the honors. 😄

[fredrikekre]

Thanks! It was scary, but I managed :)