R help - Apr 2007 - how to convert the lower triangle of a matrix to a symmetric matrix

Hi,

I have a vector of p*(p+1)/2 elements, essentially the lower triangle of a
symmetric matrix. I was wondering if there is an easy way to make it fill a
symmetric matrix. I have to do it several times, hence some efficient approach
would be very useful.

Many thanks and best wishes,
Ranjan

On Thu, 19 Apr 2007, Ranjan Maitra wrote:
> Hi,
>
> I have a vector of p*(p+1)/2 elements, essentially the lower triangle of 
> a symmetric matrix. I was wondering if there is an easy way to make it 
> fill a symmetric matrix. I have to do it several times, hence some 
> efficient approach would be very useful.
It depends on what the ordering of elements in your vector is.

Many programs will order those elements (1,1), (2,1), (2,2), (3,1) , ...

In which case this shows how:

> k.given.i.j <- function(x , y ) ifelse( y<x, x*(x-1)/2 + y, y*(y-1)/2
+ x )
> k.mat <- function(p) outer( 1:p, 1:p, k.given.i.j )
> k.mat( 3 )
      [,1] [,2] [,3]
[1,]    1    2    4
[2,]    2    3    5
[3,]    4    5    6
> matrix( rnorm( choose(4,2) )[ k.mat( 3 ) ] , nr = 3 )
            [,1]        [,2]        [,3]
[1,] -1.2165313  0.28262740  0.62448849
[2,]  0.2826274 -1.19842868  0.05676263
[3,]  0.6244885  0.05676263 -1.80957190
>
For efficiency, you might save and reuse the result of k.mat().

If the elements are ordered (1,1), (2,1), (3,1), ..., you will need to 
write your own version of k.given.i.j()


>
> Many thanks and best wishes,
> Ranjan
>
> ______________________________________________
> 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
> and provide commented, minimal, self-contained, reproducible code.
>
Charles C. Berry                        (858) 534-2098
                                          Dept of Family/Preventive Medicine
E mailto:cberry at tajo.ucsd.edu	         UC San Diego
http://biostat.ucsd.edu/~cberry/         La Jolla, San Diego 92093-0901

Dear Ranjan,

If the elements are ordered by rows, then the following should do the trick:

    X <- diag(p)
    X[upper.tri(X, diag=TRUE)] <- elements
    X <- X + t(X) - diag(diag(X))

If they are ordered by columns, substitute lower.tri() for upper.tri().

I hope this helps,
 John

--------------------------------
John Fox, Professor
Department of Sociology
McMaster University
Hamilton, Ontario
Canada L8S 4M4
905-525-9140x23604
http://socserv.mcmaster.ca/jfox 
-------------------------------- 
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Ranjan Maitra
> Sent: Thursday, April 19, 2007 9:28 PM
> To: r-help at stat.math.ethz.ch
> Subject: [R] how to convert the lower triangle of a matrix to 
> a symmetricmatrix
> 
> Hi,
> 
> I have a vector of p*(p+1)/2 elements, essentially the lower 
> triangle of a symmetric matrix. I was wondering if there is 
> an easy way to make it fill a symmetric matrix. I have to do 
> it several times, hence some efficient approach would be very useful.
> 
> Many thanks and best wishes,
> Ranjan
> 
> ______________________________________________
> 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
> and provide commented, minimal, self-contained, reproducible code.
>

Ranjan and Prof. Fox,

Similar approach can be found in stats:::as.matrix.dist().

Andy 

From: John Fox
> 
> Dear Ranjan,
> 
> If the elements are ordered by rows, then the following 
> should do the trick:
> 
>     X <- diag(p)
>     X[upper.tri(X, diag=TRUE)] <- elements
>     X <- X + t(X) - diag(diag(X))
> 
> If they are ordered by columns, substitute lower.tri() for 
> upper.tri().
> 
> I hope this helps,
>  John
> 
> --------------------------------
> John Fox, Professor
> Department of Sociology
> McMaster University
> Hamilton, Ontario
> Canada L8S 4M4
> 905-525-9140x23604
> http://socserv.mcmaster.ca/jfox 
> -------------------------------- 
> 
> > -----Original Message-----
> > From: r-help-bounces at stat.math.ethz.ch 
> > [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Ranjan
Maitra
> > Sent: Thursday, April 19, 2007 9:28 PM
> > To: r-help at stat.math.ethz.ch
> > Subject: [R] how to convert the lower triangle of a matrix to 
> > a symmetricmatrix
> > 
> > Hi,
> > 
> > I have a vector of p*(p+1)/2 elements, essentially the lower 
> > triangle of a symmetric matrix. I was wondering if there is 
> > an easy way to make it fill a symmetric matrix. I have to do 
> > it several times, hence some efficient approach would be 
> very useful.
> > 
> > Many thanks and best wishes,
> > Ranjan
> > 
> > ______________________________________________
> > 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
> > and provide commented, minimal, self-contained, reproducible code.
> >
> 
> ______________________________________________
> 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
> and provide commented, minimal, self-contained, reproducible code.
> 
> 
> 

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