Fwd: Re: [R] eigenvalues of a circulant matrix
Janusz Kawczak
jkawczak at uncc.edu
Tue May 3 06:33:19 CEST 2005
I am not sure where your problem is, but I get these eigenvalues (no
NaNs):
> eigen(X)$values
[1] 33.6609067 33.6609067 33.3657337 33.3657337 33.1688489 33.1688489
[7] 32.9120603 32.9120603 32.6971529 32.6971529 32.4486757 32.4486757
[13] 32.2266513 32.2266513 31.9811880 31.9811880 31.7549774 31.7549774
[19] 31.5106802 31.5106802 31.2814636 31.2814636 31.0374623 31.0374623
[25] 30.8058168 30.8058168 30.5616180 30.5616180 30.3278637 30.3278637
[31] 30.0831665 30.0831665 29.8474910 29.8474910 29.6020821 29.6020821
[37] 29.3645937 29.3645937 29.1183207 29.1183207 28.8790883 28.8790883
[43] 28.6318199 28.6318199 28.3908814 28.3908814 28.1425171 28.1425171
[49] 27.8998862 27.8998862 27.6503394 27.6503394 27.4060152 27.4060152
[55] 27.1552045 27.1552045 26.9091770 26.9091770 26.6570228 26.6570228
[61] 26.4092748 26.4092748 26.1557083 26.1557083 25.9062128 25.9062128
[67] 25.6511554 25.6511554 25.3998797 25.3998797 25.1432660 25.1432660
[73] 24.8901666 24.8901666 24.6319253 24.6319253 24.3769595 24.3769595
[79] 24.1170167 24.1170167 23.8601266 23.8601266 23.5984086 23.5984086
[85] 23.3395425 23.3395425 23.0759756 23.0759756 22.8150622 22.8150622
[91] 22.5495580 22.5495580 22.2865330 22.2865330 22.0190111 22.0190111
[97] 21.7537982 21.7537982 21.4841613 21.4841613 21.2166787 21.2166787
[103] 20.9448339 20.9448339 20.6749916 20.6749916 20.4008361 20.4008361
[109] 20.1285318 20.1285318 19.8519563 19.8519563 19.5770843 19.5770843
[115] 19.2979657 19.2979657 19.0204113 19.0204113 18.7386197 18.7386197
[121] 18.4582550 18.4582550 18.1736507 18.1736507 17.8903299 17.8903299
[127] 17.6027615 17.6027615 17.3163357 17.3163357 17.0256338 17.0256338
[133] 16.7359239 16.7359239 16.4419046 16.4419046 16.1487284 16.1487284
[139] 15.8511833 15.8511833 15.5543204 15.5543204 15.2530227 15.2530227
[145] 14.9522432 14.9522432 14.6469402 14.6469402 14.3419740 14.3419740
[151] 14.0323742 14.0323742 13.7229182 13.7229182 13.4087011 13.4087011
[157] 13.0944062 13.0944062 12.7751956 12.7751956 12.4556716 12.4556716
[163] 12.1310382 12.1310382 11.8058191 11.8058191 11.4752626 11.4752626
[169] 11.1438118 11.1438118 10.8067417 10.8067417 10.4684198 10.4684198
[175] 10.1241331 10.1241331 9.7781642 9.7781642 9.4258124 9.4258124
[181] 9.0712521 9.0712521 8.7097773 8.7097773 8.3454594 8.3454594
[187] 7.9735359 7.9735359 7.5979459 7.5979459 7.2138560 7.2138560
[193] 6.8250204 6.8250204 6.4264559 6.4264559 6.0216592 6.0216592
[199] 5.6053886 5.6053886 5.1807131 5.1807131 4.7419171 4.7419171
[205] 4.2912801 4.2912801 3.8221094 3.8221094 3.3349406 3.3349406
[211] 2.8206308 2.8206308 2.2746353 2.2746353 1.6787279 1.6787279
[217] 0.9988213
Again, what is the issue here?
Janusz.
On Mon, 2 May 2005, Globe Trotter wrote:
> Looks like the files did not go through again. In any case, here is the kinv:
> please cut and paste and save to a file:
>
>
>
> -1.16801E-03 -2.24310E-03 -1.16864E-03 -2.24634E-03 -1.17143E-03
> -2.25358E-03 -1.17589E-03 -2.26484E-03 -1.18271E-03 -2.27983E-03
> -1.19124E-03 -2.29896E-03 -1.20164E-03 -2.32206E-03 -1.21442E-03
> -2.34911E-03 -1.22939E-03 -2.38073E-03 -1.24626E-03 -2.41702E-03
> -1.26596E-03 -2.45828E-03 -1.28801E-03 -2.50458E-03 -1.31296E-03
> -2.55646E-03 -1.34048E-03 -2.61444E-03 -1.37127E-03 -2.67887E-03
> -1.40531E-03 -2.75026E-03 -1.44311E-03 -2.82930E-03 -1.48481E-03
> -2.91652E-03 -1.53081E-03 -3.01281E-03 -1.58131E-03 -3.11930E-03
> -1.63727E-03 -3.23708E-03 -1.69907E-03 -3.36712E-03 -1.76720E-03
> -3.51113E-03 -1.84251E-03 -3.67073E-03 -1.92580E-03 -3.84787E-03
> -2.01834E-03 -4.04507E-03 -2.12087E-03 -4.26509E-03 -2.23531E-03
> -4.51127E-03 -2.36357E-03 -4.78743E-03 -2.50664E-03 -5.09847E-03
> -2.66813E-03 -5.45027E-03 -2.85019E-03 -5.84987E-03 -3.05664E-03
> -6.30596E-03 -3.29224E-03 -6.82972E-03 -3.56187E-03 -7.43448E-03
> -3.87322E-03 -8.13766E-03 -4.23449E-03 -8.96182E-03 -4.65684E-03
> -9.93567E-03 -5.15519E-03 -1.10980E-02 -5.74887E-03 -1.25006E-02
> -6.46346E-03 -1.42143E-02 -7.33466E-03 -1.63391E-02 -8.41211E-03
> -1.90180E-02 -9.76709E-03 -2.24632E-02 -1.15055E-02 -2.70006E-02
> -1.37894E-02 -3.31497E-02 -1.68780E-02 -4.17865E-02 -2.12092E-02
> -5.44795E-02 -2.75722E-02 -7.42814E-02 -3.75180E-02 -0.107820
> -5.44778E-02
> -0.171908 -8.74660E-02 -0.320830 -0.167792 -0.826079 -0.486405
> -6.28085
> 19.4495 -6.28085 -0.486405 -0.826079 -0.167792 -0.320830
> -8.74660E-02
> -0.171908 -5.44778E-02 -0.107820 -3.75180E-02 -7.42816E-02
> -2.75722E-02
> -5.44795E-02 -2.12092E-02 -4.17865E-02 -1.68780E-02 -3.31495E-02
> -1.37894E-02 -2.70004E-02 -1.15055E-02 -2.24632E-02 -9.76708E-03
> -1.90179E-02 -8.41210E-03 -1.63391E-02 -7.33465E-03 -1.42142E-02
> -6.46346E-03 -1.25005E-02 -5.74887E-03 -1.10979E-02 -5.15519E-03
> -9.93565E-03 -4.65686E-03 -8.96166E-03 -4.23449E-03 -8.13766E-03
> -3.87320E-03 -7.43444E-03 -3.56187E-03 -6.82968E-03 -3.29223E-03
> -6.30590E-03 -3.05665E-03 -5.84988E-03 -2.85020E-03 -5.45026E-03
> -2.66813E-03 -5.09848E-03 -2.50664E-03 -4.78742E-03 -2.36358E-03
> -4.51160E-03 -2.23531E-03 -4.26516E-03 -2.12088E-03 -4.04506E-03
> -2.01834E-03 -3.84791E-03 -1.92580E-03 -3.67066E-03 -1.84251E-03
> -3.51094E-03 -1.76720E-03 -3.36700E-03 -1.69907E-03 -3.23702E-03
> -1.63727E-03 -3.11926E-03 -1.58130E-03 -3.01269E-03 -1.53081E-03
> -2.91633E-03 -1.48480E-03 -2.82912E-03 -1.44311E-03 -2.75018E-03
> -1.40531E-03 -2.67891E-03 -1.37126E-03 -2.61459E-03 -1.34048E-03
> -2.55652E-03 -1.31296E-03 -2.50461E-03 -1.28801E-03 -2.45833E-03
> -1.26595E-03 -2.41717E-03 -1.24626E-03 -2.38063E-03 -1.22938E-03
> -2.34904E-03 -1.21443E-03 -2.32207E-03 -1.20164E-03 -2.29903E-03
> -1.19124E-03 -2.27985E-03 -1.18271E-03 -2.26497E-03 -1.17589E-03
> -2.25364E-03 -1.17145E-03 -2.24634E-03 -1.16863E-03 -2.24284E-03
>
> Thanks!
>
>
>
> --- Globe Trotter <itsme_410 at yahoo.com> wrote:
> > Date: Mon, 2 May 2005 19:51:24 -0700 (PDT)
> > From: Globe Trotter <itsme_410 at yahoo.com>
> > Subject: Re: [R] eigenvalues of a circulant matrix
> > To: r-help at stat.math.ethz.ch
> >
> > OK, here we go:
> >
> > I am submitting two attachments. The first is the datafile called kinv used
> > to
> > create my circulant matrix, using the following commands:
> >
> >
> > x<-scan("kinv")
> > y<-x[c(109:1,0:108)]
> > X=toeplitz(y)
> > eigen(X)
> > write(X,ncol=216,file="test.dat")
> >
> > 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).
> >
> > 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.
> >
> > I am using
> >
> > :~> uname -a
> > Linux 2.6.11-1.14_FC3 #1 Thu Apr 7 19:23:49 EDT 2005 i686 i686 i386 GNU/Linux
> >
> > and R.2.0.1.
> >
> > Many thanks and best wishes!
> >
> > ______________________________________________
> > R-help at 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
> >
>
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