[Rd] eigen in beta

[Paul Gilbert]

Here is the example. Pehaps others could check on other platforms. It is 
only the first eigenvalue that is different.  I am relatively sure the 
old values are correct, since I compare with an alternate calculation 
using the expansion of a polynomial determinant.


z <- t(matrix(c(
 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.0064083373167516857, 
-0.14786612501440565826,  0.368411802235074137,
 0, 0, 0, 0, 0, 0, 0, 0, 0,  0.0568624483195125444,  
0.08575928008564302762, -0.101993668348446601,
 0, 0, 0, 0, 0, 0, 0, 0, 0,  0.0039684327579889069, 
-0.00002857482925046247,  0.202241897806646448,
 1, 0, 0, 0, 0, 0, 0, 0, 0, -0.0222834092601282285, 
-0.09126708346036176145,  0.644249961695308682,
 0, 1, 0, 0, 0, 0, 0, 0, 0, -0.0032676036920228878,  
0.16985862929849462888,  0.057282326361118636,
 0, 0, 1, 0, 0, 0, 0, 0, 0,  0.0148488735227452068, 
-0.06175528918915401677,  0.109566197834008949,
 0, 0, 0, 1, 0, 0, 0, 0, 0, -0.0392756265125193960,  
0.04921079262665441212,  0.078176878215115805,
 0, 0, 0, 0, 1, 0, 0, 0, 0, -0.0013937451966661973,  
0.02009823693764142133, -0.207228935136287512,
 0, 0, 0, 0, 0, 1, 0, 0, 0,  0.0273358858605219357,  
0.03830466468488327725,  0.224426004034737836,
 0, 0, 0, 0, 0, 0, 1, 0, 0, -0.1456426235151105919,  
0.28688029213315069388,  0.326933845656016908,
 0, 0, 0, 0, 0, 0, 0, 1, 0,  0.0164670122082246559, 
-0.21966261349875662590,  0.036404179329694988,
 0, 0, 0, 0, 0, 0, 0, 0, 1,  0.0146156940584119890,  
0.07505490943478997090,  0.077660578370038813
 ), 12, 12))
 

R-2.5.0 gives
 >  eigen(z, symmetric = FALSE, only.values = TRUE)$values
 [1]  0.8465266+0.0000000i -0.0280087+0.6244992i -0.0280087-0.6244992i
 [4] -0.2908409+0.5522274i -0.2908409-0.5522274i -0.6228929+0.0000000i
 [7]  0.6177419+0.0000000i -0.5604582+0.1958709i -0.5604582-0.1958709i
[10]  0.1458799+0.4909300i  0.1458799-0.4909300i  0.3378356+0.0000000i

R-2.4.1 and many, many previous versions gave
 >  eigen(z, symmetric = FALSE, only.values = TRUE)$values
 [1]  0.8794798+0.0000000i -0.0280087+0.6244992i -0.0280087-0.6244992i
 [4] -0.2908409+0.5522274i -0.2908409-0.5522274i -0.6228929+0.0000000i
 [7] -0.5604582+0.1958709i -0.5604582-0.1958709i  0.5847887+0.0000000i
[10]  0.1458799+0.4909300i  0.1458799-0.4909300i  0.3378356+0.0000000i
 
Sys.info()
                             sysname                              release
                             "Linux"                    "2.4.21-40.ELsmp"
                             version                             nodename
"#1 SMP Thu Feb 2 22:13:55 EST 2006"                           "mfa04559"
                             machine                               
                            "x86_64" 

Paul Gilbert

Prof Brian Ripley wrote:

> We are only aware of better behaviour from LAPACK 3.1 (which is what I 
> suppose you are talking about, that is R compiled with its internal 
> LAPACK).
>
> But in at least one case that means finding a complex set of 
> eigenvalues where previously a real one was found.
>
> On Tue, 10 Apr 2007, Paul Gilbert wrote:
>
>> I am having some trouble with a case where  eigen in R-beta  gives a
>> different largest value than in previous versions of R. Other values
>> seem to be the same. Before I spend too much time, is anyone aware of a
>> problem (symmetric = FALSE, only.values = TRUE).
>>
>> Paul Gilbert
>> ==================================================================================== 
>>
>>
>> La version française suit le texte anglais.
>>
>> ------------------------------------------------------------------------------------ 
>>
>>
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>
====================================================================================

La version française suit le texte anglais.

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