bug in cp_fm_invert ?

[flo]

Hi Hanning,

thanks for looking into it. The index problem is solved in a bit a
hidden way. The definition of SMO in cp2k is
C_2^T S C_1 = SMO =S_21
note here as S, the overlap is symmetric it is valid
S_21^T=(C_2^T S C_1)^T=C_1^T S C_2=S_12
furthermore the definition of the matrices
rest_MO(1)=C_2^T V C_1=V_21   and  rest_MO(2)=C_1^T V C_2=V_12
as b is computed as
rest_MO(2) _kj * (S_21)^-1_kj
this is equivalent to
(V_12)_kj*(S_21)^-1_kj= (V_12)_kj * [(S_21)^-1]^T_jk = (V_12)_kj *
(S_12)^-1_jk

Took me as well a little while to understand this again. But yet I
could not see (remember), why tttt (the kind of permutation operator)
is in there. I had the formula out of the Loewdin paper
P.-O. Löwdin, Phys. Rev. 97, 1474 (1955).
The formulas there are not as straightforward as yours and it could
be, that I derived a wrong formula for the determinant of minors in
formula 51 in this paper. Trying to derive it again, I am almost sure
that this permutation operator is wrong. I will change this in the
code and submit the changes as soon as possible.

Thank you very for having a look into this,

Flo