Add API functions for standard matrix decompositions

[mikera]

We should have API functions for most standard matrix decompositions.

In particular we should have:

• LU (lower upper trinagular decomposition)
• SVD (singular value decomposition)
• QR
• Cholesky distribution
• probably a few others.....

Naming is TDB, we have various proposals:

• lu
• decompose-lu
• lu-decompose
• decomposition-lu
• lu-decomposition

Need to decide on a consistent and logical naming scheme before we commit to a public API.

Also need to define return values. Current thinking is a map (or defrecord?) that contains clearly labeller values e.g.

(decompose-lu matrix)
=> {lower: [matrix1]
      :upper: [matrix 2]
      :determinant [double value]

See:

• https://groups.google.com/forum/?fromgroups=#!topic/numerical-clojure/DN8aD__q5BU

[ejackson]

I vote for short names: ld, svd, qr etc.

[mikera]

I'm more in favour of being a bit more explicit:

lu-decomposition

It's a close call I admit. But see my reasoning in the newsgroup:

• https://groups.google.com/d/msg/numerical-clojure/DN8aD__q5BU/0_vc3uwRtdIJ

[mikera]

Closing this as now complete.

Opted for the longer names so we can do stuff like:

(let [qr (qr-decomposition m)]
  .... do stuff with qr)