MatLUFactor for Complex Matrices - Returns inverse of the diagonal in LU??

[Paul Dostert]

I'm a beginner with PETSc, so please forgive me if this is obvious, but I
couldn't seem to find any help in the archives.

I'm trying to just the hang of the software, so I've been messing around
with routines. I'm going to need complex matrices (Maxwell's with PML) so
everything is configured for this. I'm messing around with some very simple
test cases, and have a symmetric (but not Hermitian) complex matrix with
2-2i on the diagonal and -1+i on the upper and lower diagonals. I am reading
this in from a petsc binary file (again, for testing purposes, eventually
I'm going to be just reading in my matrix and RHS). I view the matrix, and
it has been read in correctly. I perform LU factorization by doing the
following (where ISCreateStride(PETSC_COMM_WORLD,m,0,1,&perm); has been
called earlier):

MatConvert(A,MATSAME,MAT_INITIAL_MATRIX,&LU);
MatFactorInfoInitialize(&luinfo);
MatLUFactor(LU,perm,perm,&luinfo);

I get that LU is:

   (1,1)      0.2500 + 0.2500i
   (2,1)     -0.5000
   (1,2)     -1.0000 + 1.0000i
   (2,2)      0.3333 + 0.3333i
   (3,2)     -0.6667
   (2,3)     -1.0000 + 1.0000i
   (3,3)      0.3750 + 0.3750i
   (4,3)     -0.7500
   (3,4)     -1.0000 + 1.0000i
   (4,4)      0.4000 + 0.4000i
   (5,4)     -0.8000
   (4,5)     -1.0000 + 1.0000i
   (5,5)      0.4167 + 0.4167i
   (6,5)     -0.8333
   (5,6)     -1.0000 + 1.0000i
   (6,6)      0.4286 + 0.4286i

Now, I am interpreting this as L being unit on the diagonal and the
lower diagonal portion of this "LU" matrix, while U being the diagona
+ upper of this "LU" matrix. I can interpret this the other way around
as well, and it doesn't matter.

However, knowing the LU factorization, it is VERY clear the the proper
LU decomposition would have the inverse of the diagonal elements
presented here. So I believe I should have  LU as:

   (1,1)      2.0000 - 2.0000i
   (2,1)     -0.5000
   (1,2)     -1.0000 + 1.0000i
   (2,2)      1.5000 - 1.5000i
   (3,2)     -0.6667
   (2,3)     -1.0000 + 1.0000i
   (3,3)      1.3333 - 1.3333i
   (4,3)     -0.7500
   (3,4)     -1.0000 + 1.0000i
   (4,4)      1.2500 - 1.2500i
   (5,4)     -0.8000
   (4,5)     -1.0000 + 1.0000i
   (5,5)      1.2000 - 1.2000i
   (6,5)     -0.8333
   (5,6)     -1.0000 + 1.0000i
   (6,6)      1.1667 - 1.1667i

Is there some reason this returns the inverse of the diagonal entries,
or am I completely missing something? Is returning the inverse
something standard??

Since I'm new, I'm not quite sure where to look for actual source
code. Is there a location where the LU factorization code is written
and well commented?

Thank you very much!