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From Luc Maisonobe <Luc.Maison...@free.fr>
Subject [math] linear algebra decomposition algorithms (SVD, Cholesky, QR, LU, eigen values ...)
Date Sun, 08 Jun 2008 20:18:23 GMT
One of the task scheduled for 2.0 is the implementation of the Singular
Value Decomposition.

I think this addition should be done together with several other
decompositions in a consistent scheme. What we have currently is:

 - LU decomposition embedded directly into [Real/Big]MatrixImpl
   without any reference to it in the [Real/Big]Matrix interfaces

 - one QR decomposition as
    1) an interface which is really only a way to retrieve results
    2) an implementation which performs the decomposition on RealMatrix

 - another QR decomposition hidden in the Levenberg-Marquardt estimator

An API for these tasks was proposed by MathWorks and NIST with the JAMA
package (http://math.nist.gov/javanumerics/jama/). This package provides
specific classes for the decomposition (LUDecomposition, QRDecomposition
...). These classes provide accessors for the elements of the
decomposition (say L and U) but more importantly they provide methods to
use the decomposition: a solve method for LU, QR and Cholesky for
example. Jama has been widely used but is dead now (see for example
http://cio.nist.gov/esd/emaildir/lists/jama/msg01384.html). The code is
in the public domain.

I would propose to roughly follow Jama API, probably adding interfaces
on top of the decomposition classes to be consistent with our other
algorithms, and using the public domain Jama code as a basis. We could
also address simply the issue about SVD in the original message.

The changes in our code would be to extract LU from the XxxMatrixImpl
classes, to add new methods to the QR interface and to see how the
Levenberg-Marquardt algorithm can use this (I think this last step is
the most difficult, as the QR decomposition used there is slightly
distorted).

What do you think about it ?

Luc


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