There are a couple of things about the decomposition API that are starting to bug me. Apologies for not having raised them until now, since they apply to LU as well as the new Eigen decomp.

1) I don't like the state dependencies bleeding into the decomposition interfaces - i.e., having the interface contract include the requirement that decompose() be called before the getters. Logically, the decomposition interfaces should just *be* the getters, which is now the case for EigenDecomposition, but not LU (where the interface includes the decompose method). The state dependency is an implementation artifact that should not be included in the decomposition interface.

2) It would seem natural for decompose return a decomposition, rather than void. I am not sure if there is an efficient way to address both of these, since the caching and incremental computation in the current impls is sort of essential. At a minimum, we should probably remove the advertised exceptions and decompose methods from the interfaces.

Here is one idea that may or may not work. It would make the API a little more complicated, but if we split the implementation classes into decomposers and decompositions, with decompose producing a decomposition, the decompositions would be able to handle state transparently to users.

Phil

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