Hi, In its present form (CM2.0), SingularValueDecomposition suffers some problems when the matrix is (numerically) singular. Luc proposed a way to improve the situation by limiting the singular values to non zero ones. Whereas the result is OK if someone is interested in getting the singular values, it is not from a purely mathematical point of view. Indeed, the resulting U matrix does no longer hold the right dimension. Instead of a number of columns equal to the number of columns of the original matrix, U now has as many columns as non-zero singular values. The product U*S*V^T yields the original matrix but the wrong size might put some users into trouble (that is true for the size of S as well).
I propose to compute U ... without taking advantage of V. That means calling EigenDecomposition a second time but should work even in case of singular matrices. That is the solution I am working on. However, doing so, I notice that EigenDecomposition also suffers major problems in case of singular matrices. A 3x3 singular matrix where 0 is an eigen value with multiplicity 2 ... yields only 2 distinct eigen vectors. The vectors associated to the null eigen value are equal!! So, before I can improve SVD, I have to improve EigenDecomposition! By the way, going through SVD, EigenDecomposition, I noticed that BidiagonalTransformer and TridiagonalTransformer both use the Householder vector computation deeply imbedded in their code. In order to make both classes easier to read (and to debug), I wonder if it might be useful to introduce a class Householder which would take care of the computation of the vector in a unique place. Regards, Dim. ---------------------------------------------------------------------------- Dimitri Pourbaix * Institut d'Astronomie et d'Astrophysique * Don't worry, be happy CP 226, office 2.N4.211, building NO * and CARPE DIEM. Universite Libre de Bruxelles * Boulevard du Triomphe * Tel : +32-2-650.35.71 B-1050 Bruxelles * Fax : +32-2-650.42.26 http://sb9.astro.ulb.ac.be/~pourbaix * mailto:pourb...@astro.ulb.ac.be --------------------------------------------------------------------- To unsubscribe, e-mail: dev-unsubscr...@commons.apache.org For additional commands, e-mail: dev-h...@commons.apache.org
