From: "M. Edward (Ed) Borasky" <znmeb@...>
Date: 2006-07-31T07:58:05+09:00
Subject: Re: Setting precision in Ruby-GSL calculations ?

Nuralanur@aol.com wrote:
> Dear Ed,
>  
> thank you for responding.
> Well, I tried transposing as you said too, but then I lost
> confidence in the algorithm implemented there, because
>  
> for m=[[10,5,-10],[2,-11,10]].to_gsl_matrix, I then get
> a matrix u of size (3,2), (it should be 3,3), and u*u.transposed
> is 
>  
> [  8.889e-001 -2.222e-001 -2.222e-001 
> -2.222e-001   5.556e-001 -4.444e-001 
> -2.222e-001 -4.444e-001  5.556e-001  ],
>  
> so nowhere near a unit matrix, either ...
>  
> With respect to the sizes, I am expecting to be able to keep
> (m1,m2) somewhere in the range of 50 or below each.
>  
> Best regards,
>  
> Axel 
>   

Here's what I get from R:

 > m=matrix(c(10, 5 ,-10 ,2 ,-11 ,10), nrow=3, ncol=2)
 > m
     [,1] [,2]
[1,]   10    2
[2,]    5  -11
[3,]  -10   10
 > svd(m)
$d
[1] 18.973666  9.486833

$u
           [,1]          [,2]
[1,] -0.2981424  8.944272e-01
[2,] -0.5962848 -4.472136e-01
[3,]  0.7453560 -1.489694e-16

$v
           [,1]      [,2]
[1,] -0.7071068 0.7071068
[2,]  0.7071068 0.7071068



 > m=t(m)
 > m
     [,1] [,2] [,3]
[1,]   10    5  -10
[2,]    2  -11   10
 > svd(m)
$d
[1] 18.973666  9.486833

$u
           [,1]      [,2]
[1,] -0.7071068 0.7071068
[2,]  0.7071068 0.7071068

$v
           [,1]          [,2]
[1,] -0.2981424  8.944272e-01
[2,] -0.5962848 -4.472136e-01
[3,]  0.7453560 -1.859678e-16