[eigen] Blocked QR algorithm - lapack compatible ?

[<vincent.lejeune@xxxxxxxxxx>]

Hi,



I'm trying to implement a blocked QR algorithm, using the code from

HouseholderQR.

I'm using the algorithm used in lapack routine dgeqrf : first I make the

reduction of a panel of the input matrix, then I build the "T" triangular

factor in H=I-VT'V' that defines the blocked householder transformation,

then I apply this transformation to the trailing submatrix by a left

multiplication. Then I iterate the process.



I think that the current implemantation of householderQR does not comply

with lapack routine. The coefficients in hCoeffs() does actually not have

the same meaning than the one in the TAU vector found in dgeqrf. When

applying dlarft and dlarfb with hCoeffs to a partially reduced matrix, I

end with mostly different results than the one furnished by a complete

eigen householder decomposition (strangly the first row is correct).



I suspect that the applyhousolderfrom the left use the coefficient in a

different war than dlarf in lapack does.



Is there some doc on how hcoeffs from eigen and tau from lapack are

related ? 



Thanks, Vincent