[R-sig-Debian] Inaccuracy in svd() with R ubuntu package

[Chris Sims]

On two  laptops running 32-bit kubuntu, I have found that svd(), invoked 
within R 2.9.1 as supplied with the current ubuntu package, returns very 
incorrect results when presented with complex-valued input.  One of the 
laptops is a Dell D620, the other a MacBook Pro. I've also verified the 
problem on a 32-bit desktop.  On these same systems, R compiled from 
source provides apparently correct results, so long as the --with-blas 
option is not used or --with-blas is used and an atlas library compiled 
from source is specified as the blas.  The blas that gives incorrect 
results is the ubuntu sse2 atlas package.  On a 64-bit ubuntu  desktop 
system I find the svd() results are correct with the ubuntu packaged R 
as well as with R compiled on the machine.

The error seems not to arise, at least sometimes, with simple 2x2 
complex matrices.  To check for the error, run the  following:

a <- matrix(rnorm(16) + rnorm(16)*1i, 4)
b <- svd(a)
with(b, u %*% t(Conj(u)))

The result should be an identity matrix, by the definition of the 
singular value decomposition.

Below are example runs, first on the 64-bit system where results are 
correct, then on one of the 32-bit systems.

 > version
               _                          
platform       x86_64-pc-linux-gnu        
arch           x86_64                     
os             linux-gnu                  
system         x86_64, linux-gnu          
status                                    
major          2                          
minor          9.1                        
year           2009                       
month          06                         
day            26                         
svn rev        48839                      
language       R                          
version.string R version 2.9.1 (2009-06-26)
 > a <- matrix(rnorm(16) + 1i * rnorm(16),4)
 > a
                    [,1]                  [,2]                  [,3]
[1,]  1.064712-1.343633i -1.6787892-0.7356784i -1.3110026-1.7295312i
[2,] -0.829329-1.538217i  0.6514795+0.8242854i  1.3948013-0.4340075i
[3,]  2.241843+0.297037i  2.9147970+0.2397768i -0.5197081-0.5796579i
[4,]  1.567566-1.154438i -1.0900313+0.0121055i  0.0141203+0.6139178i
                    [,4]
[1,]  1.344998+1.231298i
[2,] -0.190861+1.817582i
[3,]  1.855617-1.244282i
[4,] -1.735007+0.725572i
 > b <- svd(a)
 > with(b, u %*% t(Conj(u)))
                            [,1]                        [,2]
[1,]  1.000000e+00+0.000000e+00i  9.971272e-18-1.092774e-16i
[2,]  9.971272e-18+1.062857e-16i  1.000000e+00-0.000000e+00i
[3,] -9.500311e-17+3.729126e-17i -1.319715e-16-3.354759e-16i
[4,]  1.585713e-16+2.581553e-16i  2.988332e-17+1.814683e-16i
                            [,3]                        [,4]
[1,] -9.500311e-17-2.546774e-17i  1.585713e-16-2.644267e-16i
[2,] -1.319715e-16+3.350337e-16i  2.988332e-17-1.820918e-16i
[3,]  1.000000e+00-0.000000e+00i -2.445638e-16+1.528022e-16i
[4,] -2.445638e-16-1.735266e-16i  1.000000e+00+0.000000e+00i
 >

-----------------------------------------------------
 > version
               _                          
platform       i486-pc-linux-gnu          
arch           i486                       
os             linux-gnu                  
system         i486, linux-gnu            
status                                    
major          2                          
minor          9.1                        
year           2009                       
month          06                         
day            26                         
svn rev        48839                      
language       R                          
version.string R version 2.9.1 (2009-06-26)
 > a <- matrix(rnorm(16) + 1i * rnorm(16), 4)
 > a
                      [,1]                  [,2]                  [,3]
[1,]  1.4465327-1.4747010i  0.7291287-0.3789878i  1.1978147-0.2393877i
[2,]  0.8557766-0.9561998i -1.8390624-0.2263745i  0.1601790+0.8254724i
[3,]  1.1659289+1.3202786i  1.1182754-0.0327039i  0.9901992+0.5903004i
[4,] -0.4728973-0.2885660i -0.2541130+1.5875047i -0.9362061+0.1858397i
                      [,4]
[1,] -0.5949982+1.2969862i
[2,]  0.6272468+1.2662726i
[3,]  0.6722278-0.7768301i
[4,]  0.4064206+0.6788890i
 > b <- svd(a)
 > with(b, u %*% t(Conj(u)))
                      [,1]                  [,2]                  [,3]
[1,]  0.7429858-0.0000000i -0.0890804-0.1273023i -0.1145715-0.3955123i
[2,] -0.0890804+0.1273023i  0.8251623+0.0000000i -0.0217231-0.2699445i
[3,] -0.1145715+0.3955123i -0.0217231+0.2699445i  1.3072318-0.0000000i
[4,] -0.1236460+0.0628505i  0.1937076-0.0101354i -0.1682549+0.0544654i
                      [,4]
[1,] -0.1236460-0.0628505i
[2,]  0.1937076+0.0101354i
[3,] -0.1682549-0.0544654i
[4,]  1.0912424-0.0000000i
 >