[ http://issues.apache.org/jira/browse/MATH-157?page=comments#action_12446426 ] Tyler Ward commented on MATH-157: ---------------------------------
One more thing. I don't think you can just use the Q from the QR reduction (slipped my mind earlier). Try it, you'll see that it doesn't come out tridiagonal. The trick is that you need to do both sides, front and back on each iteration of the householder reduction. The household reduction reduces each column of the matrix my multiplying by a Q matrix that has a single column of values, and the rest is the identity matrix. Like this A2 = Q1A1. You need to do this ... A2 = Q1A1Q1`, on each iteration, so A3 = Q3Q2Q1A1Q1`Q2`Q3`, etc... Make sure it doesn't come out right before doing this, but I think the QR decomposition will compute the matrix wrong, because it's assuming a one sided (forward only) transformation, but check first. > 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 > > > 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]
