[R] Precision in R
dos Reis, Marlon
Marlon.dosReis at agresearch.co.nz
Thu Jan 15 07:32:42 CET 2009
I'm using:
"solve(a, b, tol, LINPACK = FALSE, ...)"
Therefore,tol ==.Machine$double.eps
>.Machine$double.eps
[1] 2.220446e-16
It explains why 'solve' works for 'tcp1' but not for 'tcp2':
eigen(tcp1)$values
[1] 5.208856e+09 2.585816e+08 -3.660671e-06
-3.660671e-06/5.208856e+09
[1] -7.027783e-16
eigen(tcp2)$values
[1] 5.208856e+09 2.585816e+08 -6.416393e-08
-6.416393e-08/5.208856e+09
[1] -1.231824e-17
My question would be why 'tcrossprod' and 'crossprod' leads to such
difference?
Marlon.
-----Original Message-----
From: David Winsemius [mailto:dwinsemius at comcast.net]
Sent: Thursday, 15 January 2009 6:04 p.m.
To: Charles C. Berry
Cc: dos Reis, Marlon; r-help at r-project.org
Subject: Re: [R] Precision in R
I am seeing different behavior than don Reis on my installation as well:
mtx is the same as his WBtWB
> mtx <- matrix(c(1916061939, 2281366606, 678696067, 2281366606,
3098975504, 1092911209, 678696067, 1092911209, 452399849), ncol=3)
>
> mtx
[,1] [,2] [,3]
[1,] 1916061939 2281366606 678696067
[2,] 2281366606 3098975504 1092911209
[3,] 678696067 1092911209 452399849
> eigen(mtx)
$values
[1] 5.208856e+09 2.585816e+08 -4.276959e-01
$vectors
[,1] [,2] [,3]
[1,] -0.5855545 -0.7092633 0.3925195
[2,] -0.7678140 0.3299775 -0.5491599
[3,] -0.2599763 0.6229449 0.7378021
> rcond(mtx)
[1] 5.33209e-11
Despite a very ill-conditioned matrix, solve still proceeds
>
> solve(mtx)
[,1] [,2] [,3]
[1,] -0.3602361 0.5039933 -0.6771204
[2,] 0.5039933 -0.7051189 0.9473348
[3,] -0.6771204 0.9473348 -1.2727543
>
> sessionInfo()
R version 2.8.1 Patched (2009-01-07 r47515)
i386-apple-darwin9.6.0
locale:
en_US.UTF-8/en_US.UTF-8/C/C/en_US.UTF-8/en_US.UTF-8
snipped package info
--
David Winsemius
On Jan 14, 2009, at 11:15 PM, Charles C. Berry wrote:
>
> 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)
>> }
>> }
>> }
>>
>>
>> =
>> =
>> =====================================================================
>> Attention: The information contained in this message and...
>> {{dropped:15}}
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
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>> PLEASE do read the posting guide
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>> and provide commented, minimal, self-contained, reproducible code.
>>
>
> 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
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
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