[ 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]