[R] Symmetric Matrix classes

[David Winsemius]

On Nov 26, 2009, at 11:00 PM, Gad Abraham wrote:

> On Fri, Nov 27, 2009 at 2:22 PM, David Winsemius <dwinsemius at comcast.net 
> > wrote:
>>
>> On Nov 26, 2009, at 9:45 PM, Gad Abraham wrote:
>>
>>> Hi,
>>>
>>> I'd like to store large covariance matrices using Matrix classes.
>>>
>>> dsyMatrix seems like the right one, but I want to specify just the
>>> upper/lower triangle and diagonal and not have to instantiate a huge
>>> n^2 vector just for the sake of having half of it ignored:
>>>
>>> Dumb example:
>>> M <- new("dsyMatrix", uplo="U", x=rnorm(1e4),  
>>> Dim=as.integer(c(100, 100)))
>>> diag(M) <- 1
>>>
>>> This doesn't work:
>>> M <- new("dsyMatrix", uplo="U", x=0, Dim=as.integer(c(100, 100)))
>>
>> Per help
>> Slots
>>
>> uplo:A character object indicating if the upper triangle ("U") or  
>> the lower
>> triangle ("L") is stored. At present only the lower triangle form is
>> allowed.
>>
>> This "works" ( at least to the extent of not producing an error  
>> message)
>> after addressing a couple of other error messages that were helpful.
>>
>> M <- new("dsyMatrix", uplo="L", x=as.double(1:(100*100)),
>> Dim=as.integer(c(100, 100)))
>>
>> I'm not sure that I would have expected the result, though it makes a
>> certain amount of sense after considering the contradictory  
>> requirements:
>>
>>> M <- new("dsyMatrix", uplo="L", x=as.double(1:(10*10)),
>>> Dim=as.integer(c(10, 10)))
>>> M
>> 10 x 10 Matrix of class "dsyMatrix"
>>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
>>  [1,]    1    2    3    4    5    6    7    8    9    10
>>  [2,]    2   12   13   14   15   16   17   18   19    20
>>  [3,]    3   13   23   24   25   26   27   28   29    30
>>  [4,]    4   14   24   34   35   36   37   38   39    40
>>  [5,]    5   15   25   35   45   46   47   48   49    50
>>  [6,]    6   16   26   36   46   56   57   58   59    60
>>  [7,]    7   17   27   37   47   57   67   68   69    70
>>  [8,]    8   18   28   38   48   58   68   78   79    80
>>  [9,]    9   19   29   39   49   59   69   79   89    90
>> [10,]   10   20   30   40   50   60   70   80   90   100
>>
>
> But I don't want to specify x=foo where foo is of length n^2, because
> that uses a lot of memory (I have 20000 by 20000 matrices).
>
> I just want to be able to fill in one triangle and diagonal, like you
> can with regular non-Matrix matrices:
> M <- matrix(0, m, n)
> gdata::lowerTriangle(M) <- x
> diag(M) <- y

Then maybe you should pick a Matrix class that suits your desires. You  
are the one who said he wanted a symmetric class. There is a  
triangular sparse class.

I doubt you will get the lowerTriangle function to work on these  
instances of Matrix. When I use the base function lower.tri to index  
that 10 x 10 sparse matrix I get an error message that makes me think  
you will need to populate these Matrices element by element.

M[lower.tri] <- 0
Error in .local(x, i, j, ..., value) :
   not-yet-implemented 'Matrix[<-' method

diag(M) <- 1    # did work.

>
> -- 
> Gad Abraham
> PhD Student, Dept. CSSE and NICTA
> The University of Melbourne
> Parkville 3010, Victoria, Australia
> email: gabraham at csse.unimelb.edu.au
> web: http://www.csse.unimelb.edu.au/~gabraham

David Winsemius, MD
Heritage Laboratories
West Hartford, CT