Re: [Help-gsl] Re: QR Decomposition for a matrix with complex values

[Brian Gough]

At Tue, 29 Jan 2008 11:46:17 +0000,
Jonny Taylor wrote:
> With that taken into account, I've got it working. Source file is  
> attached in case it is of use to anybody. I have not included  
> equivalents of some of the functions in qr.c because I did not test  
> them since I don't need them. I have no idea whether it's more  
> "correct" to store tau or its conjugate in the tau vector; I have  
> chosen to store the conjugate.

It's best to follow LAPACK (routine CGEQRF) which stores tau.

       The matrix Q is represented as a product of elementary reflectors

          Q = H(1) H(2) . . . H(k), where k = min(m,n).

       Each H(i) has the form

          H(i) = I - tau * v * v'

       where  tau is a complex scalar, and v is a complex vector with v(1:i-1)
       = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau  in
       TAU(i).