[ http://issues.apache.org/jira/browse/MATH-157?page=comments#action_12446796 ] Tyler Ward commented on MATH-157: ---------------------------------
Not bad. Looks like everything is in the right place, modulo a transpose or two perhaps, but looks good. The eigenvector reduction is really the heart of this algorithm. Your QR iteration will work (I think), but it's really inefficient. The trick is to do two different reductions. The first should reduce to tridiagonal form (this can be done with only 2(N-2) matrix multiplications, rather than the 200 or so you're using), and then use the givens rotations to reduce tridiagonal to diagonal. Should take about 5N rotations, but each is only about 10N operations or so (rather than N-cubed for a regular matrix multiply). Congrats. > 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]
