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From: Eddie Vedder (Eddie.Vedder_at_[hidden])
Date: 2005-12-20 05:39:27

Hello list,

I'm using the function geqrf from the LAPACK bindings to compute a QR
factorisation. I need to know the matrix Q from this factorisation. As there
is no binding to orgqr I have to do this on my own. The problem is, I don't
understand what is ment by "matrix Q is represented as a product of
elementary reflectors" in the LAPACK help.

The following is from the documentation of geqrf:

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 real scalar, and v is a real 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).

Does anybody known:
Is H a matrix, vector or scalar?
Does v*v' result in a scalar or a matrix?
What does the : in v(1:i-1) mean?
How is the vector v constructed?
Is there a good paper about elementary reflectors?
Did anyone else ever tried to extract matrix Q?

I would appreciate any help ...
Thanks Ed

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