# [SciPy-user] determinants

David Goldsmith David.L.Goldsmith@noaa....
Thu Sep 13 16:25:36 CDT 2007

```Anne Archibald wrote:
> On 13/09/2007, David Goldsmith <David.L.Goldsmith@noaa.gov> wrote:
>
>> Anne Archibald wrote:
>>
>>> If you have problems with determinants becoming excessively large, you
>>> may be able to circumvent them by computing the log of the
>>> determinant. The easiest way to do this is to use LU decomposition:
>>>
>>> P,L,U = scipy.linalg.lu(M)
>>> d = sum(log(abs(diag(L))))
>>>
>>> Of course you lose track of the sign doing this (P may be either an
>>> even or odd permutation, though det should be reliable and efficient
>>> on it).
>>>
>> Of course, one can keep track of the sign by cumprod(sgn(diag(L))),
>> yes?  (Sorry, I don't know the numpy functions for these off hand, but I
>> assume they exist, yes?)
>>
>
> In my first draft I suggested this (prod(sign(diag(L)))), but
> unfortunately P may contribute a factor of -1, so you have to extract
> its determinant as well (unless there's some more clever way to get
> the sign of a permutation matrix? some sum involving the positions of
> the ones modulo 2 ought to do it, but it's been a while since I did
> this kind of combinatorics).
>
Right, (clearly) same here. ;-)

However, this suggests something that maybe should be implemented inside
det's "black box"?  (Obviously, if det is being used inside a formula,
the function can't simply return log(det) w/out some manner of user
notification.  Perhaps a custom exception and/or a second function, e.g.
"logdet", to which the user is referred if abs(det) returns inf?  Just a
suggestion.)

DG
> Anne
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```