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
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--
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President and Chief Operating Officer
Structure Inspection and Monitoring, Inc.
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