If you want fast and accurate eigenvalue or SVD routines please consider LAPACK.
http://www.jsoftware.com/jwiki/Addons/math/lapack ----- Original Message ----- From: "Leigh J. Halliwell" <[email protected]> Date: Wednesday, March 25, 2009 9:13 Subject: Re: [Jprogramming] QR Decomposition To: 'Programming forum' <[email protected]> > Dear Roger: > > Thanks for you two replies. Yes, I understand now the > Vocabulary comment > that the domain of 128!:0 and that of %. are the same. I > knew that %. (and > APL before it) could perform left-inverses of matrices of full- > column rank. > But I think more as a statistician than as a J programmer. > According to J > standards, the Vocabulary offers a sufficient explanation. > > My interest in the QR decompositon is to code an efficient eigen > decomposition. I have programmed the Jacobi method; but > I'd like a faster > and more accurate routine. Are you aware of good J code > for the eigen (or > singular value decomposition) problem? > > Sincerely, > > Leigh > > Leigh Joseph Halliwell, FCAS, MAAA > Chief Manager > L. J. Halliwell, LLC > P. O. Box 21385 > Chattanooga, TN 37424 > 423-296-2739 > 423-605-5789 cell > 423-954-2772 fax > [email protected] > www.lhalliwell.com > > This communication is intended solely for the use of the > individual to whom > or the entity to which it is addressed. It may contain > information that is > privileged, confidential, and exempt from disclosure under > applicable law. > If you are neither the intended recipient, nor the employee, nor > the agent > responsible for delivering the communication to the intended > recipient, you > are hereby notified that any dissemination, distribution, or > copying of this > communication is strictly prohibited. If you have received this > communication in error, please notify us immediately by > telephone or email, > delete the communication from any computer or other electronic storage > media, and destroy all other copies in your possession. > > > -----Original Message----- > From: [email protected] > [mailto:[email protected]] On Behalf Of Roger Hui > Sent: Wednesday, March 25, 2009 11:25 AM > To: Programming forum > Subject: Re: [Jprogramming] QR Decomposition > > I should have said that matrix inverse accepts most > "tall" matrices and most square matrices, and rejects > "wide" matrices. > > The reason is that the argument matrix must be > non-singular, i.e. having linearly independent columns. > A matrix can have at most {:$y independent columns, > so no wide matrix can qualify. "Most" because most tall > and most square matrices are non-singular. > > > > ----- Original Message ----- > From: Roger Hui <[email protected]> > Date: Tuesday, March 24, 2009 23:04 > Subject: Re: [Jprogramming] QR Decomposition > To: Programming forum <[email protected]> > > > The documentation does say that the argument y must be > > in the domain of matrix inverse (%.). Matrix inverse > > accepts "tall" matrices and rejects "wide" matrices. > > (And of course accepts most square matrices.) > > > > > > > > ----- Original Message ----- > > From: "Leigh J. Halliwell" <[email protected]> > > Date: Monday, March 23, 2009 16:05 > > Subject: [Jprogramming] QR Decomposition > > To: 'Programming forum' <[email protected]> > > > > > Dear J Forum: > > > > > > I've been experimenting with 128!:0 (QR matrix > decomposition) > > as > > > follows: > > > B =. |: A =. ? 4 7 $10 > > > $ each B;A > > > ----T---+ > > > |7 4|4 7| > > > L---+---- > > > $ each 128!:0 A > > > |length error > > > | $each 128!:0 A > > > $ each 128!:0 B > > > ----T---+ > > > |7 4|4 4| > > > L---+---- > > > > > > This suggests that the row dimension of the argument must be > > > greater than or > > > equal to the column dimension, and hence that T(Q) mmult Q > is > > > the identity > > > matrix (orthogonal/Hermetian). If so, then noting this > in > > > the Vocabulary > > > would be helpful. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
