Precision in R

for ( i in 1:1000 ) solve(WBtWB - tcrossprod(rnorm(3)))
for ( i in 1:1000 ) solve(WBtWB + tcrossprod(rnorm(3)))

range(replicate( 10000, 1/kappa(dat3-tcrossprod(matrix(rnorm(9),3)))))

sessionInfo()

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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