Thanks for looking into this! Sure, I will try and provide more info, but sorry I seem to be doing really badly with posting....
> > Having cut&pasted from the data placed in the body of the > message (omitted here) I get 216 numbers. Having put these > in a vector x (in my own way): > > length(x) > ##[1] 216 > > Question 1: > =========== > Is this correct? Or has there been a problem with your > posting of the data? Yes, this is correct: it is supposed to be such that the circulant matrix is symmetric and so Toeplitz. I am just ignoring the rest (which are pretty close to x[107:1]. > > If it is correct, given that you seem to only use x[1:109], > was there some point in giving the rest? No, I should have deleted it -- sorry. > Question 2: > =========== > Next, using your command: > > y<-x[c(109:1,0:108)] > > I now get > > length(y) > ##[1] 217 My mistake: that should be 1 instead of 0. I sincerely apologize! > > (as expected). The "0" in "0:108" seems to have been ignored > (again as expected), so this is equivalent to > > y<-x[c(109:1,1:108)] > > Is this as intended? If so, why use "0:108" instead of "1:108"? > Check: > > y[1] ##[1] 19.4495 > x[109] ##[1] 19.4495 > > y[109] ##[1] -0.00116801 > x[1] ##[1] -0.00116801 > > y[110] ##[1] -0.00116801 > x[1] ##[1] -0.00116801 > > y[217] ##[1] -6.28085 > x[108] ##[1] -6.28085 > > Can you confirm that this is as intended? > > Comment 3: > ========== > You next command X=toeplitz(y): No apparent problems, > it gives a symmetric result: > > which(X != t(X)) ## numeric(0) > > with 217 rows and columns: > > dim(X) ##[1] 217 217 > > and looks circulant: > > X[(1:5),(1:5)] > [,1] [,2] [,3] [,4] [,5] > [1,] 19.449500 -6.280850 -0.486405 -0.826079 -0.167792 > [2,] -6.280850 19.449500 -6.280850 -0.486405 -0.826079 > [3,] -0.486405 -6.280850 19.449500 -6.280850 -0.486405 > [4,] -0.826079 -0.486405 -6.280850 19.449500 -6.280850 > [5,] -0.167792 -0.826079 -0.486405 -6.280850 19.449500 > > Question 4: > =========== > Your next command, "eigen(X)", would simply output the results > to screen and does not assign to anything. true. But in my case, eigen(X)$vectors indicates the four columns to be NaN. > Your next command "write(X,ncol=216,file="test.dat")" as it > stands will write the toeplitz matrix X, constructed by > your command "X<-toeplitz(y)" to file, but with 216 > columns instead of 217. However, the result consists > simply of numbers, and there is nothing like "NA" or "NaN" > in the file which I get. I made a mistake in typing -- it is 1:108, instead of 0. The file test.dat contains the symmetric circulant matrix on which I run the eigendecomposition using LAPACK. > Nor are there any NAs or NaNs in X itself, of course. No, there are none. > > But, when you yourself did "write(X,ncol=216,file="test.dat")", > perhaps the "X" in this command was different from the "X" > which is the toeplitz matrix. So, was it the result of an > assignment from "eigen(X)" and, if so, which component or > components? No, no, X was the Toeplitz matrix and all the confusion stems from my typo (extremely sorry again!) > Question/Comment 5: > =================== > So I have tried Z<-eigen(X). First of all, I get no problems > with NAs or NaNs: > > which(is.na(Z$values)) ##numeric(0) > which(is.nan(Z$values)) ##numeric(0) > which(is.na(Z$vectors)) ##numeric(0) > which(is.nan(Z$vectors)) ##numeric(0) > > Next, trying various options for wirting to file: > > write(Z,ncol=216,file="test.dat") > > simply does not work (not a writable structure), while > > write(Z$values,ncol=216,file="test.dat") > > produces simply a set of numbers, no NAs of NaNs, and likewise > > write(Z$vectors,ncol=216,file="test.dat") > > (the only occurrences of non-numeric characters are "e", as > in "e-05"). > > >> reports the following columns full of NaN's: 18, 58, 194, 200. > >> (Note that eigen(X,symmetric=T) makes no difference and I get > >> the same as above). > > Question 6: > =========== > Was the file "test.dat" the result of your "write" command? > Or was it left over from a previous activity, the "write" > from this session having failed to execute for some reason? > (In which case the NaNs would have nothing to do with the > results of "eigen(X)"). > > > >> The second attachment contains only the eigenvectors > >> obtained on calling a LAPACK routine directly (from C). > >> The eigenvalues are essentially the same as that obtained > >> using R. Here, I use the LAPACK-recommended double > >> precision routine dspevd() routine for symmetric matrices > >> in packed storage format. > >> Note the absence of the NaN's....I would be happy to send > >> my C programs to whoever is interested. > > Well, I didn't get any NaNs in R either -- quite consistent > with your C program! > > Please clarify according to the questions above. > > Best wishes, > Ted. > I am very sorry for all the errors and extra extra work that my typo caused you.I should have been more careful. I apologize again! Many thanks and best wishes! ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
