Add logdet and logabsdet methods for Symmetric/Hermitian matrices

[ElOceanografo]

There was a method for det already, but not for log[abs]det.

[dkarrasch]

This needs tests. In particular, logabsdet returns a tuple, on which real is not defined. Another question is whether these methods are needed at all. Don't they fall back on the det implementation? It seems that all of these three methods are working, e.g., for some real Symmetric matrix.

[ElOceanografo]

The logdet methods do not in general fall back on det, rather they do a lu decomposition of the matrix and call logabsdet on that. These methods are needed in particular for the case where Symmetric or Hermitian is wrapping a sparse matrix. Currently in this situation, logabsdet ends up calling a generic version of lu which is orders of magnitude slower than the specialized sparse one in UMFPACK:

using LinearAlgebra, SparseArrays
Q = sprandn(1000, 1000, 0.0002)
Q = Q'Q + I
@time logdet(Q) # 0.000180 seconds (108 allocations: 559.406 KiB)
@time logdet(Symmetric(Q)) # 5.488019 seconds (7 allocations: 82.953 KiB)

This PR seemed like the minimal change to allow the factorization method to specialize on the underlying matrix structure, though I'm open to being corrected on that!

[dkarrasch]

Ok, the failing tests indicate that these methods are exercised. It remains to fix the logabsdet definition, perhaps using broadcasting hoist it out of the loop? Perhaps these few methods can be just spelled out directly.

[dkarrasch]

I think we should have specific tests for these cases, both real and complex, both positive and negative sign, and nail down the desired behaviour.