[R] Precision in R
dos Reis, Marlon
Marlon.dosReis at agresearch.co.nz
Thu Jan 15 06:47:48 CET 2009
Hi,
I attached the files I'm using, it may help.
I'm using Windows XP
> sessionInfo()
R version 2.6.0 (2007-10-03)
i386-pc-mingw32
locale: LC_COLLATE=English_New Zealand.1252;LC_CTYPE=English_New
Zealand.1252;LC_MONETARY=English_New
Zealand.1252;LC_NUMERIC=C;LC_TIME=English_New Zealand.1252
attached base packages:
[1] stats graphics grDevices utils datasets methods base
Try for example:
WB<-as.matrix(read.table("WB.dat"))
tcp1 <- tcrossprod(WB)
tcp2 <- crossprod(t(WB))
solve(tcp1)
[,1] [,2] [,3]
[1,] -41692.80 58330.89 -78368.17
[2,] 58330.89 -81608.66 109642.09
[3,] -78368.17 109642.09 -147305.32
solve(tcp2)
Error in solve.default(tcp2) :
system is computationally singular: reciprocal condition number =
2.17737e-17
Marlon.
-----Original Message-----
From: Charles C. Berry [mailto:cberry at tajo.ucsd.edu]
Sent: Thursday, 15 January 2009 5:16 p.m.
To: dos Reis, Marlon
Cc: r-help at r-project.org
Subject: Re: [R] Precision in R
Marlon,
Are you using a current version of R? sessionInfo()?
It would help if you had something we could _fully_ reproduce.
Taking the _printed_ values you have below (WBtWB) and adding or
subtracting what you have printed as the difference of the two visually
equal matrices ( say Delta ) , I am able to run
solve( dat3 )
solve( WBtWB + Delta )
solve( WBtWB - Delta )
solve( WBtWB + 2*Delta )
solve( WBtWB - 2*Delta )
and get the results to agree to 3 significant digits. And perturbing
things even more I still get solve() to return a value:
> for ( i in 1:1000 ) solve(WBtWB - tcrossprod(rnorm(3)))
> for ( i in 1:1000 ) solve(WBtWB + tcrossprod(rnorm(3)))
And I cannot get condition numbers anything like what you report:
> range(replicate( 10000, 1/kappa(dat3-tcrossprod(matrix(rnorm(9),3)))))
[1] 5.917764e-11 3.350445e-09
>
So I am very curious that you got the results that you print below.
I suppose that it is possible that the difference between what you
report
and what I see lies in the numerical libraries (LINPACK/LAPACK) that R
calls upon.
This was done on a windows XP PC. Here is my sessionInfo()
> sessionInfo()
R version 2.8.1 Patched (2008-12-22 r47296)
i386-pc-mingw32
locale:
LC_COLLATE=English_United States.1252;LC_CTYPE=English_United
States.1252;LC_MONETARY=English_United
States.1252;LC_NUMERIC=C;LC_TIME=English_United States.1252
attached base packages:
[1] stats graphics grDevices utils datasets methods base
>
HTH,
Chuck
On Thu, 15 Jan 2009, dos Reis, Marlon wrote:
> Dear All,
> I'm preparing a simple algorithm for matrix multiplication for a
> specific purpose, but I'm getting some unexpected results.
> If anyone could give a clue, I would really appreciate.
> Basically what I want to do is a simple matrix multiplication:
> (WB) %*% t(WB).
> The WB is in the disk so I compared to approaches:
> - Load 'WB' using 'read.table' (put it in WB.tmp) and then to the
> simple matrix multiplication
> WB.tmp%*%t(WB.tmp)
>
> - Scan each row of WB and do the cross products 'sum(WB.i*WB.i)'
> and 'sum(WB.i*WB.j)', which proper arrangement leads to WBtWB.
>
> Comparing these two matrices, I get the very similar values, however
> when I tried their inverse, WBtWB leads to a singular system.
> I've tried different tests and my conclusion is that my precision
> problem is related to cross products 'sum(WB.i*WB.i)' and
> 'sum(WB.i*WB.j)'.
> Does it makes sense?
> Thanks,
> Marlon
>
>
>> WB.tmp%*%t(WB.tmp)
> WB.i WB.i WB.i
> WB.i 1916061939 2281366606 678696067
> WB.i 2281366606 3098975504 1092911209
> WB.i 678696067 1092911209 452399849
>
>> WBtWB
> [,1] [,2] [,3]
> [1,] 1916061939 2281366606 678696067
> [2,] 2281366606 3098975504 1092911209
> [3,] 678696067 1092911209 452399849
>
>
>> WBtWB-WB.tmp%*%t(WB.tmp)
> WB.i WB.i WB.i
> WB.i 2.861023e-06 4.768372e-07 4.768372e-07
> WB.i 4.768372e-07 3.814697e-06 -2.622604e-06
> WB.i 4.768372e-07 -2.622604e-06 5.960464e-08
>
>> solve(WB.tmp%*%t(WB.tmp))
> WB.i WB.i WB.i
> WB.i -41692.80 58330.89 -78368.17
> WB.i 58330.89 -81608.66 109642.09
> WB.i -78368.17 109642.09 -147305.32
>
>> solve(WBtWB)
> Error in solve.default(WBtWB) :
> system is computationally singular: reciprocal condition number =
> 2.17737e-17
>
>
>
>
> WB.tmp<-NULL
> WBtWB<-matrix(NA,n,n)
> for (i in 1:n)
> {
> setwd(Home.dir)
> WB.i<-scan("WB.dat", skip = (i-1), nlines = 1)
> WB.tmp<-rbind(WB.tmp,WB.i)
> WBtWB[i,i]<-sum(WB.i*WB.i)
> if (i<n)
> {
> for (j in (i+1):n)
> {
> setwd(Home.dir)
> WB.j<-scan("WB.dat", skip = (j-1), nlines = 1)
> WBtWB[i,j]<-sum(WB.i*WB.j)
> WBtWB[j,i]<-sum(WB.i*WB.j)
> }
> }
> }
>
>
>
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Charles C. Berry (858) 534-2098
Dept of Family/Preventive
Medicine
E mailto:cberry at tajo.ucsd.edu UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/ La Jolla, San Diego
92093-0901
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