Charles C. Berry wrote:
On Sat, 21 Nov 2009, simona.racio...@libero.it wrote:
Hi Everyone,
I need to take the square root of the following matrix:
[,1] [,2] [,3]
[1,] 0.5401984 -0.3998675 -1.3785897
[2,] -0.3998675 1.0561872 0.8158639
[3,] -1.3785897 0.8158639 1.6073119
I tried Choleski which fails. I then tried Choleski with pivoting, but
unfortunately the square root I get is not valid. I also tried eigen
decomposition but i did no get far.
Any clue on how to do it?!
If you want to take the square root of a negative definite matrix, you
could use
sqrtm( neg.def.mat )
from the expm package on rforge:
http://r-forge.r-project.org/projects/expm/
But that matrix is not negative definite! It has 2 positive and one
negative eigenvalue. It is non-positive definite.
It is fairly easy in any case to get a matrix square root from the eigen
decomposition:
> v%*%diag(sqrt(d+0i))%*%t(v)
[,1] [,2] [,3]
[1,] 0.5164499+0.4152591i -0.1247682-0.0562317i -0.7257079+0.3051868i
[2,] -0.1247682-0.0562317i 0.9618445+0.0076145i 0.3469916-0.0413264i
[3,] -0.7257079+0.3051868i 0.3469916-0.0413264i 1.0513849+0.2242912i
> ch <- v%*%diag(sqrt(d+0i))%*%t(v)
> t(ch)%*% ch
[,1] [,2] [,3]
[1,] 0.5401984+0i -0.3998675-0i -1.3785897-0i
[2,] -0.3998675-0i 1.0561872+0i 0.8158639-0i
[3,] -1.3785897-0i 0.8158639-0i 1.6073119-0i
A triangular square root is, er, more difficult, but hardly impossible.
--
O__ ---- Peter Dalgaard Øster Farimagsgade 5, Entr.B
c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K
(*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalga...@biostat.ku.dk) FAX: (+45) 35327907
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