[R] Schur decomposition?

[Spencer Graves]

Hi, Doug: 

      What about returning list(T., Z) or list(quT, Z), where T. or quT 
is quasi-upper triangular and Z is orthogonal, consistent with the 
documentation?  This would make it easier for people like me to build an 
intuition for its properties by playing with it.  If it finds 
substantial use, someone may later suggest a special storage format for 
the quasi-upper-triangular part. 

      Thank for your work on this. 
      Spencer Graves

Douglas Bates wrote:

> Spencer Graves wrote:
>
>>      Does R have a function for the Schur decomposition?  The 
>> documentation for library(Matrix) describes a function "Schur", but 
>> it seems to be missing from the Windows version 0.8-14 (2004-09-14) 
>> and 0.8-15 (2004-10-02).
>>      The R 2.0.0 pat documentation for "eigen" refers to 
>> "http://www.netlib.org/lapack/lug/lapack_lug.html", and the 
>> description there for eigen analysis of a non-symmetric matrix says, 
>> "This problem can be solved via the Schur factorization of A, defined 
>> in the real case as
>> A = ZTZT,
>>
>> where Z is an orthogonal matrix and T is an upper quasi-triangular 
>> matrix with 1-by-1 and 2-by-2 diagonal blocks, the 2-by-2 blocks 
>> corresponding to complex conjugate pairs of eigenvalues of A."
>>      Thanks,
>>      Spencer Graves
>
>
> That documentation entry was a note to myself to add the Schur 
> factorization to the Matrix package but I have not yet done so.  If 
> anyone can suggest a reasonable data structure for the result, it 
> would be fairly easy to add the Schur decomposition.
>
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-- 
Spencer Graves, PhD, Senior Development Engineer
O:  (408)938-4420;  mobile:  (408)655-4567