[R-SIG-Mac] Erroneous zeros in results using Matrix package

[Simon Urbanek]

On Oct 15, 2013, at 3:10 PM, Braun, Michael wrote:

> I suppose that is true.  But the problem does not occur in smaller examples.  It only occurs when working with very large matrices.  That's the whole point.  And to be fair, I did warn the members of the list that this is a memory-intensive example.
> 

Isn't this related to the mysterious issue with 32-bit overflow in matrices on some OS X systems? Unfortunately I can't seem to find that thread - I recall Brian committing a work-around, so can you test more recent R? In addition, which BLAS implementation are you using?

Thanks,
Simon



> On Oct 15, 2013, at 1:26 PM, Roger Koenker <rkoenker at illinois.edu> wrote:
> 
>> You would be much more likely to get a response to this if you had a _smaller_ reproducible example.
>> 
>> url:    www.econ.uiuc.edu/~roger            Roger Koenker
>> email    rkoenker at uiuc.edu            Department of Economics
>> vox:     217-333-4558                University of Illinois
>> fax:       217-244-6678                Urbana, IL 61801
>> 
>> On Oct 15, 2013, at 11:36 AM, Braun, Michael wrote:
>> 
>>> I've come across some interesting behavior using the Matrix package, and I cannot seem to explain it.  I have sent this issue to the Matrix maintainers, and Martin Maechler was unable to replicate it on his Linux system.  Since it might be something Mac-specific, he suggested that I post here.  The complete code is pasted at the bottom of this email, along with my sessionInfo() output.
>>> 
>>> The function f takes 3 parameters:  p, k and N.  First, it creates A,  a lower triangle of a sparse block diagonal matrix with p blocks, and each block being k x k.  I then let S = AA', and have L be the lower Cholesky decomposition of L. (I use Cholesky instead of chol because, for my "real" application, because I need the permutation matrix also).  I then multiply L by a matrix z, where each column in z is a standard MVN sample.
>>> 
>>> None of the elements should be zero.  However, if z becomes very large, I get lots of zero entries.
>>> 
>>> Additionally, you will see that when I try to coerce a large identity matrix to a dtCMatrix, some of the ones are lost. 
>>> 
>>> A word of warning:  this script does consume a lot of RAM, and it will take several minutes to run.  But it would be helpful if someone with a Mac Pro with 32GB of RAM could try to replicate the problem.
>>> 
>>> Thanks in advance for your help.
>>> 
>>> Michael
>>> 
>>> 
>>> library(Matrix)
>>> 
>>> f <- function(p,k,N) {
>>> A <- tril(kronecker(Diagonal(p),Matrix(1:(k^2),k,k)))
>>> S <- tcrossprod(A)
>>> CH <- Cholesky(S)
>>> L <- expand(CH)$L
>>> z <- rnorm(N*k*p)
>>> dim(z) <- c(p*k,N)
>>> y <- L %*% z
>>> return(sum(y==0))
>>> }
>>> 
>>> system.time(small   <- f(p=  100, k=3, N=  200) )
>>> system.time(medium  <- f(p=  200, k=3, N= 5000) )
>>> 
>>> print(small ) ## 0
>>> print(medium)  ## 0
>>> 
>>> print( system.time(large.p <- f(p=50000, k=3, N= 5000) ))
>>> print( system.time(large.N <- f(p=10000, k=3, N=20000) ))
>>> 
>>> print(large.p) ## I get 536870912, but it should be 0
>>> print(large.N) ## I get 536870912, but it should be 0
>>> 
>>> system.time( W1 <- as(diag(10000),"dtCMatrix") )
>>> print(sum(diag(W1)))  ## should be 10000, and that's what I get
>>> 
>>> system.time( W3 <- as(diag(30000),"dtCMatrix") )
>>> print(sum(diag(W3)))## should be 30000, I get  12104 
>>> 
>>> sessionInfo()
>>> R version 3.0.1 (2013-05-16)
>>> Platform: x86_64-apple-darwin12.3.0/x86_64 (64-bit)
>>> 
>>> locale:
>>> [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
>>> 
>>> attached base packages:
>>> [1] stats     graphics  grDevices utils     datasets  methods   base     
>>> 
>>> other attached packages:
>>> [1] Matrix_1.0-14   lattice_0.20-15
>>> 
>>> loaded via a namespace (and not attached):
>>> [1] grid_3.0.1  tools_3.0.1
>>> 
>>> --------------------------
>>> Michael Braun
>>> Associate Professor of Marketing
>>> Cox School of Business
>>> Southern Methodist University
>>> Dallas, TX 75275
>>> braunm _at_ smu.edu
>>> 
>>> _______________________________________________
>>> R-SIG-Mac mailing list
>>> R-SIG-Mac at r-project.org
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mac
>> 
> 
> _______________________________________________
> R-SIG-Mac mailing list
> R-SIG-Mac at r-project.org
> https://stat.ethz.ch/mailman/listinfo/r-sig-mac
>