Re: [R] Cholesky Decomposition in R
You got an A+ on the homework, Doug! I got a C- for suggesting svd(), which clearly doesn't yield a lower (or upper) triangular factorization. Ravi. --- Ravi Varadhan, Ph.D. Assistant Professor, The Center on Aging and Health Division of Geriatric Medicine and Gerontology Johns Hopkins University Ph: (410) 502-2619 Fax: (410) 614-9625 Email: rvarad...@jhmi.edu Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html -Original Message- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of Douglas Bates Sent: Tuesday, March 10, 2009 10:14 PM To: Manli Yan Cc: r-help@r-project.org Subject: Re: [R] Cholesky Decomposition in R On Tue, Mar 10, 2009 at 4:33 PM, Manli Yan manliyanrh...@gmail.com wrote: Hi everyone: I try to use r to do the Cholesky Decomposition,which is A=LDL',so far I only found how to decomposite A in to LL' by using chol(A),the function Cholesky(A) doesnt work,any one know other command to decomposte A in to LDL' My r code is: library(Matrix) A=matrix(c(1,1,1,1,5,5,1,5,14),nrow=3) chol(A) [,1] [,2] [,3] [1,] 1 1 1 [2,] 0 2 2 [3,] 0 0 3 Cholesky(A) Error in function (classes, fdef, mtable) : unable to find an inherited method for function Cholesky, for signature matrix whatz wrong??? The answer, surprisingly, is in the documentation, accessible as ?Cholesky which says that the first argument has to be a sparse, symmetric matrix. Because the Cholesky function is intended for sparse matrices it is not the best approach. The object returned is rather obscure Cholesky(as(A, dsCMatrix), LDL = TRUE) 'MatrixFactorization' of Formal class 'dCHMsimpl' [package Matrix] with 10 slots ..@ x : num [1:6] 1 1 1 4 1 9 ..@ p : int [1:4] 0 3 5 6 ..@ i : int [1:6] 0 1 2 1 2 2 ..@ nz : int [1:3] 3 2 1 ..@ nxt : int [1:5] 1 2 3 -1 0 ..@ prv : int [1:5] 4 0 1 2 -1 ..@ colcount: int [1:3] 3 2 1 ..@ perm: int [1:3] 0 1 2 ..@ type: int [1:4] 2 0 0 1 ..@ Dim : int [1:2] 3 3 It turns out that the factorization you want is encoded in the 'x' slot but not in an obvious way. Even if you ask for an expansion expand(Cholesky(as(A, dsCMatrix), LDL = TRUE)) $P [1,] | . . [2,] . | . [3,] . . | $L [1,] 1 . . [2,] 1 2 . [3,] 1 2 3 the result is converted from the LDL' factor to the LL' factor. A better approach is to consider how the LDL' factorization is related to the R'R form of the factorization returned by chol() ch - chol(A) dd - diag(ch) L - t(ch/dd) DD - dd^2 L [,1] [,2] [,3] [1,]100 [2,]110 [3,]111 DD [1] 1 4 9 This is all rather backwards in that the whole purpose of the LDL' form of the factorization is to avoid taking square roots to get the diagonal elements and to contend with positive semidefinite matrices. In other words, the LDL' form avoids some of the possible problems of the LL' form but not if you go through the LL' form to get to it. I think the underlying reason that an LDL' form is not directly available in R is because there is no Lapack subroutine for it. Let me know what our grade on the homework is. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Cholesky Decomposition in R
A - matrix(runif(25),5,5); A - A%*%t(A) ## Example +ve def matrix U - chol(A) ## start from factor given by chol D - diag(U) ## extract sqrt(D) L - t(U/D) ## get unit lower triangular factor D - diag(D^2) ## and diagonal ## So now A = LDL' range(A-L%*%D%*%t(L)) #best, #Simon On Tuesday 10 March 2009 21:33, Manli Yan wrote: Hi everyone: I try to use r to do the Cholesky Decomposition,which is A=LDL',so far I only found how to decomposite A in to LL' by using chol(A),the function Cholesky(A) doesnt work,any one know other command to decomposte A in to LDL' My r code is: library(Matrix) A=matrix(c(1,1,1,1,5,5,1,5,14),nrow=3) chol(A) [,1] [,2] [,3] [1,]111 [2,]022 [3,]003 Cholesky(A) Error in function (classes, fdef, mtable) : unable to find an inherited method for function Cholesky, for signature matrix whatz wrong??? thanks~ [[alternative HTML version deleted]] __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. -- Simon Wood, Mathematical Sciences, University of Bath, Bath, BA2 7AY UK +44 1225 386603 www.maths.bath.ac.uk/~sw283 __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
[R] Cholesky Decomposition in R
Hi everyone: I try to use r to do the Cholesky Decomposition,which is A=LDL',so far I only found how to decomposite A in to LL' by using chol(A),the function Cholesky(A) doesnt work,any one know other command to decomposte A in to LDL' My r code is: library(Matrix) A=matrix(c(1,1,1,1,5,5,1,5,14),nrow=3) chol(A) [,1] [,2] [,3] [1,]111 [2,]022 [3,]003 Cholesky(A) Error in function (classes, fdef, mtable) : unable to find an inherited method for function Cholesky, for signature matrix whatz wrong??? thanks~ [[alternative HTML version deleted]] __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Cholesky Decomposition in R
You can use singular value decomposition: ?svd svd(A) $d [1] 16.3405917 2.8996176 0.7597907 # This is your diagonal matrix D $u [,1] [,2][,3] [1,] 0.08585595 -0.2420411 0.96645997 [2,] 0.40826313 -0.8763116 -0.25573252 [3,] 0.90881790 0.4165261 0.02357989 $v [,1] [,2][,3] [1,] 0.08585595 -0.2420411 0.96645997 [2,] 0.40826313 -0.8763116 -0.25573252 [3,] 0.90881790 0.4165261 0.02357989 Ravi. --- Ravi Varadhan, Ph.D. Assistant Professor, The Center on Aging and Health Division of Geriatric Medicine and Gerontology Johns Hopkins University Ph: (410) 502-2619 Fax: (410) 614-9625 Email: rvarad...@jhmi.edu Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html -Original Message- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of Manli Yan Sent: Tuesday, March 10, 2009 5:33 PM To: r-help@r-project.org Subject: [R] Cholesky Decomposition in R Hi everyone: I try to use r to do the Cholesky Decomposition,which is A=LDL',so far I only found how to decomposite A in to LL' by using chol(A),the function Cholesky(A) doesnt work,any one know other command to decomposte A in to LDL' My r code is: library(Matrix) A=matrix(c(1,1,1,1,5,5,1,5,14),nrow=3) chol(A) [,1] [,2] [,3] [1,]111 [2,]022 [3,]003 Cholesky(A) Error in function (classes, fdef, mtable) : unable to find an inherited method for function Cholesky, for signature matrix whatz wrong??? thanks~ [[alternative HTML version deleted]] __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Cholesky Decomposition in R
try Cholesky() in package Matrix. albyn On Tue, Mar 10, 2009 at 02:33:01PM -0700, Manli Yan wrote: Hi everyone: I try to use r to do the Cholesky Decomposition,which is A=LDL',so far I only found how to decomposite A in to LL' by using chol(A),the function Cholesky(A) doesnt work,any one know other command to decomposte A in to LDL' My r code is: library(Matrix) A=matrix(c(1,1,1,1,5,5,1,5,14),nrow=3) chol(A) [,1] [,2] [,3] [1,]111 [2,]022 [3,]003 Cholesky(A) Error in function (classes, fdef, mtable) : unable to find an inherited method for function Cholesky, for signature matrix whatz wrong??? thanks~ [[alternative HTML version deleted]] __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Cholesky Decomposition in R
On Tue, Mar 10, 2009 at 4:33 PM, Manli Yan manliyanrh...@gmail.com wrote: Hi everyone: I try to use r to do the Cholesky Decomposition,which is A=LDL',so far I only found how to decomposite A in to LL' by using chol(A),the function Cholesky(A) doesnt work,any one know other command to decomposte A in to LDL' My r code is: library(Matrix) A=matrix(c(1,1,1,1,5,5,1,5,14),nrow=3) chol(A) [,1] [,2] [,3] [1,] 1 1 1 [2,] 0 2 2 [3,] 0 0 3 Cholesky(A) Error in function (classes, fdef, mtable) : unable to find an inherited method for function Cholesky, for signature matrix whatz wrong??? The answer, surprisingly, is in the documentation, accessible as ?Cholesky which says that the first argument has to be a sparse, symmetric matrix. Because the Cholesky function is intended for sparse matrices it is not the best approach. The object returned is rather obscure Cholesky(as(A, dsCMatrix), LDL = TRUE) 'MatrixFactorization' of Formal class 'dCHMsimpl' [package Matrix] with 10 slots ..@ x : num [1:6] 1 1 1 4 1 9 ..@ p : int [1:4] 0 3 5 6 ..@ i : int [1:6] 0 1 2 1 2 2 ..@ nz : int [1:3] 3 2 1 ..@ nxt : int [1:5] 1 2 3 -1 0 ..@ prv : int [1:5] 4 0 1 2 -1 ..@ colcount: int [1:3] 3 2 1 ..@ perm: int [1:3] 0 1 2 ..@ type: int [1:4] 2 0 0 1 ..@ Dim : int [1:2] 3 3 It turns out that the factorization you want is encoded in the 'x' slot but not in an obvious way. Even if you ask for an expansion expand(Cholesky(as(A, dsCMatrix), LDL = TRUE)) $P [1,] | . . [2,] . | . [3,] . . | $L [1,] 1 . . [2,] 1 2 . [3,] 1 2 3 the result is converted from the LDL' factor to the LL' factor. A better approach is to consider how the LDL' factorization is related to the R'R form of the factorization returned by chol() ch - chol(A) dd - diag(ch) L - t(ch/dd) DD - dd^2 L [,1] [,2] [,3] [1,]100 [2,]110 [3,]111 DD [1] 1 4 9 This is all rather backwards in that the whole purpose of the LDL' form of the factorization is to avoid taking square roots to get the diagonal elements and to contend with positive semidefinite matrices. In other words, the LDL' form avoids some of the possible problems of the LL' form but not if you go through the LL' form to get to it. I think the underlying reason that an LDL' form is not directly available in R is because there is no Lapack subroutine for it. Let me know what our grade on the homework is. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Cholesky Decomposition in R
A=matrix(c(1,1,1,1,5,5,1,5,14),nrow=3) t(eigen(A)$vector) %*% A %*% eigen(A)$vector mat1 = t(eigen(A)$vector) mat2 = diag(eigen(A)$values)# this is your diagonal matrix Manli Yan wrote: Hi everyone: I try to use r to do the Cholesky Decomposition,which is A=LDL',so far I only found how to decomposite A in to LL' by using chol(A),the function Cholesky(A) doesnt work,any one know other command to decomposte A in to LDL' My r code is: library(Matrix) A=matrix(c(1,1,1,1,5,5,1,5,14),nrow=3) chol(A) [,1] [,2] [,3] [1,]111 [2,]022 [3,]003 Cholesky(A) Error in function (classes, fdef, mtable) : unable to find an inherited method for function Cholesky, for signature matrix whatz wrong??? thanks~ [[alternative HTML version deleted]] __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. -- View this message in context: http://www.nabble.com/Cholesky-Decomposition-in-R-tp22444083p22448498.html Sent from the R help mailing list archive at Nabble.com. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
