[ http://issues.apache.org/jira/browse/MATH-157?page=all ]
Remi Arntzen updated MATH-157:
------------------------------
Attachment: svd2.tar.gz
Now it works perfectly (At least according to how I think it should work).
However it is not to your specifications, e.g. I do the eigenvector calculation
on the larger of U and V and then use the property M*v_i=q_i*u_i and
M^T*u_i=q_i*v_i. While I continue to learn more about the properties of the
SVD I will refine it as I go along, but right now I have to get ready for
school.
> Add support for SVD.
> --------------------
>
> Key: MATH-157
> URL: http://issues.apache.org/jira/browse/MATH-157
> Project: Commons Math
> Issue Type: New Feature
> Reporter: Tyler Ward
> Attachments: svd.tar.gz, svd2.tar.gz
>
>
> 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.
--
This message is automatically generated by JIRA.
-
If you think it was sent incorrectly contact one of the administrators:
http://issues.apache.org/jira/secure/Administrators.jspa
-
For more information on JIRA, see: http://www.atlassian.com/software/jira
---------------------------------------------------------------------
To unsubscribe, e-mail: [EMAIL PROTECTED]
For additional commands, e-mail: [EMAIL PROTECTED]
