On Wed, 13 Jul 2005, Makram Talih wrote: > Dear R-users, > > Is there a preferred method for testing whether a real symmetric matrix is > positive definite? [modulo machine rounding errors.] > > The obvious way of computing eigenvalues via "E <- eigen(A, symmetric=T, > only.values=T)$values" and returning the result of "!any(E <= 0)" seems > less efficient than going through the LU decomposition invoked in > "determinant.matrix(A)" and checking the sign and (log) modulus of the > determinant. > > I suppose this has to do with the underlying C routines. Any thoughts or > anecdotes?
It has to do with what exactly you want to test. Knowing the determinant does not tell you if the matrix is close to non-positive definite or not. For numerical work, a comparison of the smallest eigenvalue to the largest is usually the most useful indication of possible problems in computations. An alternative is to try a Choleski decomposition, which may be faster but is less informative. Given how fast eigenvalues can be computed by current algorithms (and note the comments in ?eigen) I would suggest not worrying about speed until you need to (probably never). -- Brian D. Ripley, [EMAIL PROTECTED] Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595 ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
