Dear John, thank you for your considerations. This matrix (which is a variance matrix) is part of an algorithm for forward-filtering and backward-sampling of Dynamic Linear Models (West and Harrison, 1997), applied to DLM representation of ARIMA processes (Petris, Petrone, Campagnoli). It is therefore very difficult to explain why this variance matrix becomes so ill conditioned. This already happens at the first iteration of the algorithm. I will try to work on initial conditions and some fixed parameters.
Thank you again Stefano ________________________________________ Da: Fox, John [j...@mcmaster.ca] Inviato: giovedì 10 dicembre 2015 14.41 A: Stefano Sofia; r-help@r-project.org Oggetto: RE: matrix which results singular but at the same time positive definite Dear Stefano, You've already had a couple of informative responses directly addressing your question, but are you aware how ill-conditioned the matrix is (one of the responses alluded to this)? > kappa(X, exact=TRUE) [1] 7.313338e+12 > eigen(X)$values [1] 4.964711e+00 9.356881e-01 4.863392e-12 6.788344e-13 Two of the variables have variances around 10^0 and the other two around 10^-12. Of course, you haven't said anything about the context, but does it really make sense to analyze the data on these scales? Best, John ----------------------------- John Fox, Professor McMaster University Hamilton, Ontario Canada L8S 4M4 Web: socserv.mcmaster.ca/jfox > -----Original Message----- > From: R-help [mailto:r-help-boun...@r-project.org] On Behalf Of Stefano Sofia > Sent: December 10, 2015 5:08 AM > To: r-help@r-project.org > Subject: [R] matrix which results singular but at the same time positive > definite > > Dear list users, > through the "matrixcalc" package I am performing some checks of variance > matrices (which must be positive definite). > In this example, it happens that the matrix A here reported is singular but > positive definite. Is it possible? > > [,1] [,2] [,3] [,4] > [1,] 1.904255e-12 -1.904255e-12 -8.238960e-13 -1.240294e-12 [2,] - > 1.904255e-12 3.637979e-12 1.364242e-12 1.818989e-12 [3,] -8.238960e-13 > 1.364242e-12 4.809988e+00 7.742369e-01 [4,] -1.240294e-12 1.818989e-12 > 7.742369e-01 1.090411e+00 > > print(is.non.singular.matrix(A, tol = 1e-18)) FALSE > print(is.positive.definite(A, > tol=1e-18)) TRUE > > Is there something wrong with this matrix? > Any comment will be appreciated. > Stefano > > > ________________________________ > > AVVISO IMPORTANTE: Questo messaggio di posta elettronica può contenere > informazioni confidenziali, pertanto è destinato solo a persone autorizzate > alla > ricezione. I messaggi di posta elettronica per i client di Regione Marche > possono contenere informazioni confidenziali e con privilegi legali. Se non > si è il > destinatario specificato, non leggere, copiare, inoltrare o archiviare questo > messaggio. 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If you have received this message in error, please forward it to the sender and delete it completely from your computer system. ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
