Camarda, Carlo Giovanni
2013-Apr-19 14:13 UTC
[R] extracting the diagonal of an inverse matrix
Dear R-users, I would like to know whether there is a way to extract a diagonal of an inverse matrix without computing the inverse of the matrix itself. The size of my matrices are really huge and, also using sparse matrix, computing the inverse leads to storage problems and low speed. In other words, given a square matrix A, I aim to know diag(B), where B=solve(A), without computing solve(A). Accidentally (I do not know whether it helps), I could write the matrix A as follows: A <- D + P where D is a diagonal matrix. I read there are methods around, but, before implementing one of them by myself, could you please inform whether there is already an R-routine for this issue? Thanks in advance for the help you could provide, Carlo Giovanni Camarda ---------- This mail has been sent through the MPI for Demographic Research. Should you receive a mail that is apparently from a MPI user without this text displayed, then the address has most likely been faked. If you are uncertain about the validity of this message, please check the mail header or ask your system administrator for assistance.
This link http://math.stackexchange.com/questions/18488/diagonal-of-an-inverse-of-a-sparse-matrix might help. It is about sparse matrices, but the general idea should be able to be extended to non-sparse matrices as well. On Fri, Apr 19, 2013 at 8:13 AM, Camarda, Carlo Giovanni < Camarda@demogr.mpg.de> wrote:> Dear R-users, > > I would like to know whether there is a way to extract a diagonal of an > inverse matrix without computing the inverse of the matrix itself. The size > of my matrices are really huge and, also using sparse matrix, computing the > inverse leads to storage problems and low speed. > > In other words, given a square matrix A, I aim to know diag(B), where > B=solve(A), without computing solve(A). > > Accidentally (I do not know whether it helps), I could write the matrix A > as follows: > A <- D + P > where D is a diagonal matrix. > > I read there are methods around, but, before implementing one of them by > myself, could you please inform whether there is already an R-routine for > this issue? > > Thanks in advance for the help you could provide, > Carlo Giovanni Camarda > ---------- > This mail has been sent through the MPI for Demographic Research. Should > you receive a mail that is apparently from a MPI user without this text > displayed, then the address has most likely been faked. If you are > uncertain about the validity of this message, please check the mail header > or ask your system administrator for assistance. > > ______________________________________________ > 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. >-- Gregory (Greg) L. Snow Ph.D. 538280@gmail.com [[alternative HTML version deleted]]
Camarda, Carlo Giovanni
2013-Apr-22 08:51 UTC
[R] extracting the diagonal of an inverse matrix
Dear Greg,
thanks a lot for your prompt reply. I was aware of the link and the associated
papers.
In my previous mail I was wondering whether there was already an R-routine for
coping with this issue.
I add below a testable example which reproduces my problem.
Thanks again,
Giancarlo
## dimensions (my actual dimensions are much larger and I use sparse matrices)
m <- 3
n <- 3
## building A
## diagonal part
d <- 1:(m*n)
D <- diag(d)
## additional ~dense part (:penalty term)
P1 <- diff(diag(m), diff=2)
P2 <- diff(diag(n), diff=2)
P1a <- kronecker(diag(n), t(P1)%*%P1)
P2a <- kronecker(t(P2)%*%P2, diag(m))
P <- 1000 * P1a + 1000 * P2a
## final matrix A
A <- D + P
## solving A
B <- solve(A)
## what I just actually need
diag(B)
________________________________________
From: Greg Snow [538280 at gmail.com]
Sent: Saturday, April 20, 2013 12:16 AM
To: Camarda, Carlo Giovanni
Cc: r-help at stat.math.ethz.ch
Subject: Re: [R] extracting the diagonal of an inverse matrix
This link
http://math.stackexchange.com/questions/18488/diagonal-of-an-inverse-of-a-sparse-matrix
might help. It is about sparse matrices, but the general idea should be able to
be extended to non-sparse matrices as well.
On Fri, Apr 19, 2013 at 8:13 AM, Camarda, Carlo Giovanni <Camarda at
demogr.mpg.de<mailto:Camarda at demogr.mpg.de>> wrote:
Dear R-users,
I would like to know whether there is a way to extract a diagonal of an inverse
matrix without computing the inverse of the matrix itself. The size of my
matrices are really huge and, also using sparse matrix, computing the inverse
leads to storage problems and low speed.
In other words, given a square matrix A, I aim to know diag(B), where
B=solve(A), without computing solve(A).
Accidentally (I do not know whether it helps), I could write the matrix A as
follows:
A <- D + P
where D is a diagonal matrix.
I read there are methods around, but, before implementing one of them by myself,
could you please inform whether there is already an R-routine for this issue?
Thanks in advance for the help you could provide,
Carlo Giovanni Camarda
----------
This mail has been sent through the MPI for Demographic ...{{dropped:19}}
You could save the space required to store the inverse of A by repeating solve(A,column) for each column of an identity matrix the size of A, and store just the relevant element of the result. E.g.,> diag(solve(A))[1] 0.39576620 0.12064108 0.20705171 0.10067892 0.03191425 0.05857497 0.10749426 0.03868911 0.08550176> sapply(seq_len(nrow(A)), function(i)solve(A, seq_len(nrow(A))==i)[i])[1] 0.39576620 0.12064108 0.20705171 0.10067892 0.03191425 0.05857497 0.10749426 0.03868911 0.08550176 It may take more time that you would like. Bill Dunlap Spotfire, TIBCO Software wdunlap tibco.com> -----Original Message----- > From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf > Of Camarda, Carlo Giovanni > Sent: Monday, April 22, 2013 1:51 AM > To: Greg Snow > Cc: r-help at stat.math.ethz.ch > Subject: Re: [R] extracting the diagonal of an inverse matrix > > Dear Greg, > > thanks a lot for your prompt reply. I was aware of the link and the associated papers. > In my previous mail I was wondering whether there was already an R-routine for coping > with this issue. > > I add below a testable example which reproduces my problem. > > Thanks again, > Giancarlo > > ## dimensions (my actual dimensions are much larger and I use sparse matrices) > m <- 3 > n <- 3 > ## building A > ## diagonal part > d <- 1:(m*n) > D <- diag(d) > ## additional ~dense part (:penalty term) > P1 <- diff(diag(m), diff=2) > P2 <- diff(diag(n), diff=2) > P1a <- kronecker(diag(n), t(P1)%*%P1) > P2a <- kronecker(t(P2)%*%P2, diag(m)) > P <- 1000 * P1a + 1000 * P2a > ## final matrix A > A <- D + P > ## solving A > B <- solve(A) > ## what I just actually need > diag(B) > > > ________________________________________ > From: Greg Snow [538280 at gmail.com] > Sent: Saturday, April 20, 2013 12:16 AM > To: Camarda, Carlo Giovanni > Cc: r-help at stat.math.ethz.ch > Subject: Re: [R] extracting the diagonal of an inverse matrix > > This link http://math.stackexchange.com/questions/18488/diagonal-of-an-inverse-of-a- > sparse-matrix might help. It is about sparse matrices, but the general idea should be able > to be extended to non-sparse matrices as well. > > > On Fri, Apr 19, 2013 at 8:13 AM, Camarda, Carlo Giovanni > <Camarda at demogr.mpg.de<mailto:Camarda at demogr.mpg.de>> wrote: > Dear R-users, > > I would like to know whether there is a way to extract a diagonal of an inverse matrix > without computing the inverse of the matrix itself. The size of my matrices are really > huge and, also using sparse matrix, computing the inverse leads to storage problems and > low speed. > > In other words, given a square matrix A, I aim to know diag(B), where B=solve(A), > without computing solve(A). > > Accidentally (I do not know whether it helps), I could write the matrix A as follows: > A <- D + P > where D is a diagonal matrix. > > I read there are methods around, but, before implementing one of them by myself, could > you please inform whether there is already an R-routine for this issue? > > Thanks in advance for the help you could provide, > Carlo Giovanni Camarda > ---------- > This mail has been sent through the MPI for Demographic ...{{dropped:19}} > > ______________________________________________ > R-help at 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.