1. Martin Maechler's comments should be taken as replacements for anything I wrote where appropriate. Any apparent conflict is a result of his superior knowledge.

2. 'eigen' returns the eigenvalue decomposition assuming the matrix is symmetric, ignoring anything in m[upper.tri(m)].


3. The basic idea behind both posdefify and nearPD is to compute the eigenenvalues and vectors, then replace any eigenvalues that are small or negative with some suitable small positive number and reconstruct the matrix from this modified eigenvalue decomposition. posdefify and nearPD implement modifications of this basic idea.


4. I recommend in the summary you mention nearPD but not posdefify, because nearPD was written more recently using the results of research not available to the authors when posdefify was written.


MARTIN: There is a typo in the first line of the documentation for "symmpart". It currently reads, "symmpart(x) computes the symmetric part (x + t(x))/2 and the skew symmetric part (x - t(x))/2 of a square matrix x.". It should read, "symmpart(x) computes the symmetric part (x + t(x))/2 and skewpart the skew symmetric part (x - t(x))/2 of a square matrix x."


      Hope this helps.
      Spencer


On 2/4/2011 6:26 AM, Stefano Sofia wrote:
Dear R-users,
I followed with high interest the thread about positive definite matrix.
I tracked all the messages of the discussion and I am trying to make a summary 
of all the correlated problems that arose from the discussion and the best 
solutions to overcome them.
As far as I understood, the main problems are two: assessing the symmetry of 
the given matrix and dealing with eigenvalues very close to zero.
Do I miss some important points?

The functions that have been mentioned are eigen (I think in particualr the 
isSymmetric.matrix function), the function posdefify of the sfmisc package and 
the function nearPD of the Matrix package. I believe that some conversations 
have not been shared with the mailing list and therefore I find difficult to 
trace everything.

I understood very well the summary in four points given by Dr.Spencer Graves 
(message 53 of ISSUE 30, VOL 95), and parts of the comments added by Dr.Martin 
Maechler (message 71 of the same issue).
I am not able to understand the improvement given by posdefify with respect to 
eigen and why nearPD is even better.

Any final help?
thank you for your attention

Stefano Sofia PhD
Weather Department of Civil Protection Marche Region

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. Se si è ricevuto questo messaggio per errore, inoltrarlo al 
mittente ed eliminarlo completamente dal sistema del proprio computer. Ai sensi 
dell’art. 6 della  DGR n. 1394/2008 si segnala che, in caso di necessità ed 
urgenza, la risposta al presente messaggio di posta elettronica può essere 
visionata da persone estranee al destinatario.
IMPORTANT NOTICE: This e-mail message is intended to be received only by 
persons entitled to receive the confidential information it may contain. E-mail 
messages to clients of Regione Marche may contain information that is 
confidential and legally privileged. Please do not read, copy, forward, or 
store this message unless you are an intended recipient of it. If you have 
received this message in error, please forward it to the sender and delete it 
completely from your computer system.


--
Spencer Graves, PE, PhD
President and Chief Operating Officer
Structure Inspection and Monitoring, Inc.
751 Emerson Ct.
San José, CA 95126
ph:  408-655-4567

______________________________________________
R-help@r-project.org mailing list
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.

Reply via email to