Matrix multiplication
On Dec 12, 2012, at 08:19 , annek wrote:
Hi,
I have a transition matrix T for which I want to find the steady state matrix for. This could be approximated by taking T^n , for large n.
T= [ 0.8797 0.0382 0.0527 0.0008
0.0212 0.8002 0.0041 0.0143
0.0981 0.0273 0.8802 0.0527
0.0010 0.1343 0.0630 0.9322]
According to a text book I have T^200 should have reached the steady state L
L =[0.17458813 0.17458813 0.17458813 0.17458813
0.05731902 0.05731902 0.05731902 0.05731902
0.35028624 0.35028624 0.35028624 0.35028624
0.44160126 0.44160126 0.44160126 0.44160126]
I am addressing the problem using a for loop doing matrix multiplication (guess there might be better ways, please suggest) and find a steady state matrix after n=30. But if I run the code with n=100 or more I get "Inf" for all entities in L. Does anyone know why is that?
The code I use look like this
#------------------------------------
rep<-20
T <- Ttest
for(i in 1:rep){
print(i)
T<-T%*%Ttest
Ttest<-T
}
L<-T
print(L)
#----------------------------------
Your code is not reproducible, but I notice that at the end of your loop, T==Ttest, so you are squaring a matrix on every iteration. I.e., you are generating T^2, T^4, T^8, so at i=20 you are computing T^1048576 or so. If you go beyond that, I suppose that even a tiny roundoff will cause an eigenvalue slightly bigger than 1 to blow things up.
Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com