I have the following problem: I try to make the spectral decomposition for the following matrix by utilising the function eigen. 0.4015427 0.08903581 -0.2304132 0.08903581 1.60844812 0.9061157 -0.23041322 0.9061157 2.9692562 When checking the result I was not able to produce the original matrix by using the decomposition. It also appears that the product T'T, where T is a matrix of eigenvectors, is not an identity matrix. Tapio Nummi University of Tampere -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
spectral-decomposition
6 messages · Tapio Nummi, Brian Ripley, Jonathan Rougier +3 more
On Mon, 22 Jan 2001, Tapio Nummi wrote:
I have the following problem: I try to make the spectral decomposition for the following matrix by utilising the function eigen. 0.4015427 0.08903581 -0.2304132 0.08903581 1.60844812 0.9061157 -0.23041322 0.9061157 2.9692562 When checking the result I was not able to produce the original matrix by using the decomposition. It also appears that the product T'T, where T is a matrix of eigenvectors, is not an identity matrix.
Did your version of R pass make check? Some compilers have trouble with eigen, so try example(eigen). And *PLEASE* give your R version and platform. On mine (1.2.1, Solaris)
sm <- eigen(m, sym=TRUE) sm
$values
[1] 3.4311626 1.1970027 0.3510817
$vectors
[,1] [,2] [,3]
[1,] -0.05508142 -0.2204659 0.9738382
[2,] 0.44231784 -0.8797867 -0.1741557
[3,] 0.89516533 0.4211533 0.1459759
V <- sm$vectors t(V) %*% V
[,1] [,2] [,3] [1,] 1.000000e+00 -1.665335e-16 -5.551115e-17 [2,] -1.665335e-16 1.000000e+00 2.428613e-16 [3,] -5.551115e-17 2.428613e-16 1.000000e+00
V %*% diag(sm$values) %*% t(V)
[,1] [,2] [,3] [1,] 0.40154270 0.08903581 -0.2304132 [2,] 0.08903581 1.60844812 0.9061157 [3,] -0.23041320 0.90611570 2.9692562 I reckon you have a broken installation.
Brian D. Ripley, ripley at stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272860 (secr) Oxford OX1 3TG, UK Fax: +44 1865 272595 -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
On Mon, 22 Jan 2001, Tapio Nummi wrote:
I try to make the spectral decomposition for the following matrix by utilising the function eigen. 0.4015427 0.08903581 -0.2304132 0.08903581 1.60844812 0.9061157 -0.23041322 0.9061157 2.9692562 When checking the result I was not able to produce the original matrix by using the decomposition. It also appears that the product T'T, where T is a matrix of eigenvectors, is not an identity matrix.
Hi Tapio, I'm not having your problems:
A
[,1] [,2] [,3] [1,] 0.40154270 0.08903581 -0.2304132 [2,] 0.08903581 1.60844812 0.9061157 [3,] -0.23041320 0.90611570 2.9692562
sdec <- eigen(A, symm=TRUE)
t(sdec$vectors) %*% sdec$vectors
[,1] [,2] [,3] [1,] 1.000000e+00 -1.665335e-16 -5.551115e-17 [2,] -1.665335e-16 1.000000e+00 2.428613e-16 [3,] -5.551115e-17 2.428613e-16 1.000000e+00
sdec$vectors %*% diag(sdec$values) %*% t(sdec$vectors) - A
[,1] [,2] [,3] [1,] -5.551115e-17 -2.775558e-17 2.000000e-08 [2,] -5.551115e-17 1.998401e-15 8.881784e-16 [3,] -1.387779e-16 7.771561e-16 2.220446e-15 Cheers, Jonathan. Jonathan Rougier Science Laboratories Department of Mathematical Sciences South Road University of Durham Durham DH1 3LE tel: +44 (0)191 374 2361, fax: +44 (0)191 374 7388 http://www.maths.dur.ac.uk/stats/people/jcr/jcr.html -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
I try to make the spectral decomposition for the following matrix by utilising the function eigen. 0.4015427 0.08903581 -0.2304132 0.08903581 1.60844812 0.9061157 -0.23041322 0.9061157 2.9692562 When checking the result I was not able to produce the original matrix by using the decomposition. It also appears that the product T'T, where T is a matrix of eigenvectors, is not an identity matrix.
- I think that a couple of people have reported problems with eigen, that were actually traceable to their BLAS, but I can't now find the messages in the archive, so I may be mis-remembering. Simon ______________________________________________________________________
Simon Wood snw at st-and.ac.uk http://www.ruwpa.st-and.ac.uk/simon.html The Mathematical Institute, North Haugh, St. Andrews, Fife KY16 9SS UK Direct telephone: (0)1334 463799 Indirect fax: (0)1334 463748
-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
Need to set the symmetry argument. Say x = the matrix eigen(x,sym=T)
At 06:33 PM 1/22/01 +0300, Tapio Nummi wrote:
I have the following problem: I try to make the spectral decomposition for the following matrix by utilising the function eigen. 0.4015427 0.08903581 -0.2304132 0.08903581 1.60844812 0.9061157 -0.23041322 0.9061157 2.9692562 When checking the result I was not able to produce the original matrix by using the decomposition. It also appears that the product T'T, where T is a matrix of eigenvectors, is not an identity matrix. Tapio Nummi University of Tampere -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-
.-.-
r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
._._
Yudi Pawitan yudi at stat.ucc.ie Department of Statistics UCC Cork, Ireland Ph 353-21-490 2906 Fax 353-21-427 1040 -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
On Mon, 22 Jan 2001, Simon Wood wrote:
I try to make the spectral decomposition for the following matrix by utilising the function eigen. 0.4015427 0.08903581 -0.2304132 0.08903581 1.60844812 0.9061157 -0.23041322 0.9061157 2.9692562 When checking the result I was not able to produce the original matrix by using the decomposition. It also appears that the product T'T, where T is a matrix of eigenvectors, is not an identity matrix.
- I think that a couple of people have reported problems with eigen, that were actually traceable to their BLAS, but I can't now find the messages in the archive, so I may be mis-remembering.
There was a problem at one time with AIX systems, apparently due to C/Fortran compatibility issues. I think it has been resolved, though we have only tested a few C/Fortran compiler combinations. -thomas Thomas Lumley Asst. Professor, Biostatistics tlumley at u.washington.edu University of Washington, Seattle -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._