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From "Luc Maisonobe (JIRA)" <j...@apache.org>
Subject [jira] Commented: (MATH-157) Add support for SVD.
Date Sun, 23 Mar 2008 14:09:25 GMT

    [ https://issues.apache.org/jira/browse/MATH-157?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12581387#action_12581387
] 

Luc Maisonobe commented on MATH-157:
------------------------------------

Looking again at this issue, as we are now looking for 2.0 which should include SVD.
We now have two very different proposals, a simple one from Remi and a more rich from Andrew.
The simple one fits in the existing structure while the rich one introduces a new org.apache.commons.math.linear.decomposition
package with several utilities, among which SVD.
Both are more than a few lines and hence can be included in [math] only after some IP clearance
has been done.
Some work is also needed to match our existing code conventions, this is a detail and can
be handled later.

For now, we have to decide which proposal is chosen and to clear IP stuff.
My personal choice would be to choose the rich version from Andrew, because it introduces
many interesting things. What do other people think ?

> Add support for SVD.
> --------------------
>
>                 Key: MATH-157
>                 URL: https://issues.apache.org/jira/browse/MATH-157
>             Project: Commons Math
>          Issue Type: New Feature
>    Affects Versions: 1.1
>            Reporter: Tyler Ward
>            Assignee: Luc Maisonobe
>             Fix For: 2.0
>
>         Attachments: svd.tar.gz, svd2.tar.gz, svd_src.zip
>
>
> SVD is probably the most important feature in any linear algebra package, though also
one of the more difficult. 
> In general, SVD is needed because very often real systems end up being singular (which
can be handled by QR), or nearly singular (which can't). A good example is a nonlinear root
finder. Often the jacobian will be nearly singular, but it is VERY rare for it to be exactly
singular. Consequently, LU or QR produces really bad results, because they are dominated by
rounding error. What is needed is a way to throw out the insignificant parts of the solution,
and take what improvements we can get. That is what SVD provides. The colt SVD algorithm has
a serious infinite loop bug, caused primarily by Double.NaN in the inputs, but also by underflow
and overflow, which really can't be prevented. 
> If worried about patents and such, SVD can be derrived from first principals very easily
with the acceptance of two postulates.
> 1) That an SVD always exists.
> 2) That Jacobi reduction works. 
> Both are very basic results from linear algebra, available in nearly any text book. Once
that's accepted, then the rest of the algorithm falls into place in a very simple manner.


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