From: Nuralanur@...
Date: 2006-07-31T06:36:40+09:00
Subject: Setting precision in Ruby-GSL calculations ?

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Dear all,
 
I'd like to use ruby-gsl for some singular value decompositions, i.e.
a matrix m should be decomposed into a product of three  matrices,
 
m=u*s*v.transposed,
 
now,as the documentation says that this algorithm is not implemented
if the dimensions of m (m1 x m2) are such that m1<m2, I've  implemented
my own version, re-reading some long-forgotten linear algebra book.
In the process, I need to find the eigenvectors and the eigenvalues of  
m*m.transposed,
but these are printed out and apparently also calculated only to three  
decimal digits
by the command
 
     eigval, eigvec =  Eigen::symmv(m*m.transposed).
 
This causes the matrix u, which is constructed from the values  eigval,
to have quite strange values for its determinant  (I get values of  1.06, 
0.96  for u*u.transpose.det, but u is unitary by definition, i.e.,  
u*u.transpose.det=1).
 
Then, of course, m isn't remotely equal to u*s*v.transposed ....
 
 
Is there a way of setting the precision of the eigenvalue and eigenvector  
calculations
any higher ? 
 
Thank you very much,
 
Best regards,
 
Axel    

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