[Rd] unexpected behaviour of isSymmetric() (PR#14000)

[Douglas Bates]

On Mon, Oct 12, 2009 at 6:41 AM, Romain Francois
<romain.francois at dbmail.com> wrote:
> On 10/12/2009 02:05 AM, mike at stat.ubc.ca wrote:
>>
>> Full_Name: Mike Danilov
>> Version: 2.9.0
>> OS: Fedora Core 9
>> Submission from: (NULL) (142.103.121.198)
>>
>>
>> When checking for the symmetry of a matrix, function isSymmetric.matrix()
>> gets
>> confused by the discrepancy of colnames/rownames if its argument. See the
>> code
>> snippet below. Perhaps it's a problem of the matrix product which copies
>> colnames of the first argument but not the rownames of the second to its
>> value.
>> Not sure which one should be fixed but the way it is now it seems
>> illogical that
>> X'X is deemed to be non-symmetric.
>>
>> x<- c(1,2,3)
>> names(x)<- c("v1","v2","v3")
>> isSymmetric(x%*%t(x)) ## returns FALSE instead of TRUE
>
> It seems to be concerned with the names
>
>> y <- x %*% t(x)
>> y
>     v1 v2 v3
> [1,]  1  2  3
> [2,]  2  4  6
> [3,]  3  6  9
>
>> isSymmetric( y )
> [1] FALSE
>
> # dropping the dimnames
>> isSymmetric( structure( y, dimnames = NULL ) )
> [1] TRUE
>
> # pass the ... along this path : isSymmetric > all.equal > all.equal.numeric
>> isSymmetric( y, check.attributes = F )
> [1] TRUE
>
> # set the dimnames equal
>> dimnames( y ) <- rep( list( names(x) ), 2 )
>> isSymmetric( y )
> [1] TRUE
>
> Not sure this is expected behaviour
>
> Romain

I think the problem is more with the propagation of the column names
in the construction x %*% t(x).  If you use the tcrossprod function to
create x %*% t(x) more carefully then the results are sensible


> x<- c(1,2,3); names(x)<- c("v1","v2","v3")
> isSymmetric(tcrossprod(x))
[1] TRUE
> tcrossprod(x)
     [,1] [,2] [,3]
[1,]    1    2    3
[2,]    2    4    6
[3,]    3    6    9