On Thu, 15 Jan 2009, dos Reis, Marlon wrote:
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?
Thanks for posting your data, Marlon.
This is what I get on windows XP:
tcp1-tcp2
[,1] [,2] [,3]
[1,] -2.861023e-06 -4.768372e-07 -4.768372e-07
[2,] -4.768372e-07 -3.814697e-06 2.622604e-06
[3,] -4.768372e-07 2.622604e-06 -5.960464e-08
but on my Gentoo Linux Intel Core 2 Duo:
print(tcp1-tcp2,digits=20)
[,1] [,2] [,3]
[1,] 0 0 0
[2,] 0 0 0
[3,] 0 0 0
So, it would seem to be that the floating point calcs on my Windows
box, David's Mac, and whatever system you are using are not as
accurate as they might be.
It is well known that rounding error can play havoc with crossproducts
(particularly when the range of magnitudes of the numbers is wide as it is
here), which is why matrix decompositions are generally used for solving
least squares problems.
The internal code for crossprod and tcrossprod is different, so the
computations are likely done in a different order, which would account
for the difference in tcp1 and tcp2 . Ultimately, array.c and blas.f SUBROUTINE
DSYRK have the code if you want to dig into it.
So to summarize: the difference is not due to R per se, but in the
limited accuracy of floating point calcs on the system used.
HTH,
Chuck
Marlon.
-----Original Message-----
From: David Winsemius [mailto:dwinsem...@comcast.net]
Sent: Thursday, 15 January 2009 6:04 p.m.
To: Charles C. Berry
Cc: dos Reis, Marlon; r-help@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)
}
}
}
=
=
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Charles C. Berry (858) 534-2098
Dept of Family/Preventive
Medicine
E mailto:cbe...@tajo.ucsd.edu UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/ La Jolla, San Diego
92093-0901
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