[R] impossible to invert a spam-object, but possible when it's a matrix-object

[Uwe Ligges]

On 11.02.2013 15:00, Camarda, Carlo Giovanni wrote:
> Dear Uwe,
>
> thanks for the response.
> I knew my matrix was almost singular, but is there any way to implement the algorithm is solve(base) with a spam-matrix?

Not sure, I think you want another threshold for the error. But I do not 
know if the algorithm is robust enough. Better ask the spam maintainer 
who probably knows much better what is actually used here. There is a 
lot in the documentation, you may find the answer there as well.

>
> As workaround, I might add a ridge penalty:
>
>      ApP <- A+10^-1*diag.spam(nrow(A))
>      solve(ApP)
>
> but this would completely jeopardize other parts of my model.

Well,  just ignoring sensible defaults and relying on numerics that are 
not accurate with such a condition may "jeopardize" the results - just 
in another way.

Best,
Uwe Ligges

>
> Thanks again,
> Giancarlo
>
>
>
> ________________________________________
> From: Uwe Ligges [ligges at statistik.tu-dortmund.de]
> Sent: Saturday, February 09, 2013 8:04 PM
> To: Camarda, Carlo Giovanni
> Cc: r-help at stat.math.ethz.ch
> Subject: Re: [R]  impossible to invert a spam-object, but possible when it's a matrix-object
>
> On 05.02.2013 13:29, Camarda, Carlo Giovanni wrote:
>> Dear R-users,
>>
>> a question concerning sparse matrices in package "spam" (spam_0.29-2).
>>
>> On one hand I have a spam object (n X n) from which I cannot compute the inverse. On the other hand, if I convert this object in a plain matrix, I can find the inverse without any problem.
>>
>> Specifically I get the following error message:
>>     Error in chol.spam(a, ...) :
>>     Singularity problem when calculating the Cholesky factor.
>>
>> Obviously I get similar behaviour when I compute determinants of these objects.
>>
>> Please see below a toy-example which I created based on my actual problem.
>>
>
> Different algorithms are used to compute the inverse - and you are
> rather close to singularity: kappa(A) results in 59638727.
>
> Best,
> Uwe Ligges
>
>
>
>
>
>
>
>
>> Thanks in advance for any help,
>> GC
>>
>>
>> library(spam)
>> ## creating a spam matrix A
>> ent <- c(2312.12324929972,-2000,1000,-2000,1000,-2000,
>>            5031.91011235955,-2000,-2000,1000,-1,1000,-2000,
>>            2049.8595505618,-2000,1000,-1,-2000,5036.89635854342,
>>            -2000,1000,-2000,1,-2000,-2000,8119.66292134831,-2000,
>>            -2000,-2000,1000,-2000,5058.83426966292,-2000,-1,1000,
>>            -2000,2051.85434173669,-2000,1000,1,1000,-2000,-2000,
>>            5043.87640449438,-2000,1,1000,-2000,1000,-2000,
>>            2110.68820224719,-1,1,0,-1,1,-1,1)
>> rr <- as.integer(c(1,6,12,18,24,29,35,41,47,52,55,57,59))
>> cc <- as.integer(c(1,2,3,4,7,1,2,3,5,8,10,1,2,3,6,9,11,1,
>>                      4,5,6,7,10,2,4,5,6,8,3,4,5,6,9,12,1,4,
>>                      7,8,9,11,2,5,7,8,9,12,3,6,7,8,9,2,4,10,3,7,6,8))
>> di <- as.integer(c(12,12))
>> A <-   new("spam",
>>              entries=ent,
>>              colindices=cc,
>>              rowpointers=rr,
>>              dimension=di)
>> ## calculate the determinant
>> det(A)
>> ## computes the inverse
>> solve(A)
>>
>> ## transform A in a plain matrix
>> A1 <- matrix(c(A), di)
>> ## calculate the determinant
>> det(A1)
>> ## computes the inverse
>> solve(A1)
>>
>>
>>> version
>>                  _
>> platform       i686-pc-linux-gnu
>> arch           i686
>> os             linux-gnu
>> system         i686, linux-gnu
>> status
>> major          2
>> minor          14.1
>> year           2011
>> month          12
>> day            22
>> svn rev        57956
>> language       R
>> version.string R version 2.14.1 (2011-12-22)
>>
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>