Add pivoting to LU decomposition.

[andreasnoack]

To avoid absurdity and craziness.

[jiahao]

Would you like to come postdoc with me? ;)

[andreasnoack]

Definately

[jiahao]

I'll talk to @alanedelman. I think we can make it happen.

[stevengj]

Thanks for taking care of this so quickly, @andreasnoackjensen.

[JeffBezanson]

Is there any reason not to merge this now?

[IainNZ]

This series of commits on this stuff is reminding me of my undergrad computational techniques class, should go back and tell my professors to use Julia and not force non-computer savvy 2nd year engineering students to implement LU with pivots in C!

[andreasnoack]

@jiahao I took a closer look at dgetf2 and it "finishes" the decomposition even when a pivot is detected to be zero. I am not sure why they have chosen to do so, but thought the safe solution here was to mimic LAPACK.

[jiahao]

It makes sense to me now after thinking about it. A singular matrix can have a valid LU decomposition; it is merely not unique.