Hello,

I would like to use dlarf to apply an elementary Householder reflector to a vector rather than to a matrix, how can I do that?

My context is that of updating a QR decomposition after deleting columns. I'm reusing the Fortran routines from the links:

http://www.maths.manchester.ac.uk/~cluc ... /delcols.f

http://www.maths.manchester.ac.uk/~cluc ... delcolsq.f

I

can apply and test the delcols QR update correctly using delcols.f, I

then use a modified version of delcolsq.f as test to apply the update to

the Q_B'*C i.e. Q_delcols*Q_B'*C and this works fine I get my new R

upper triangular. I don't know why the authors of those functions

decided to provide a delcolsq.f that requires generating explicitly the Q

since no one in practice ever expensively generate the Q explicitly but

well ... my version of their delcolsq to be able to apply it to my

Q_B'*C is included below and this works fine ... I can test that it

annihilates the offending non zero terms under the diagonal. However,

when I try to apply the same transformation to my vector c solving an

overdetermined system (the c of the solve Ax=b, c=Q_B'*b and I need to

do c=Q_delcols*c on top) it doesn't work. I have tried modifying the

Fortran code below to take Q as a vector rather than a matrix but it

doesn't produce the correct results. I have also tried to fool the DLARF

setting the ldc=1 (or LDQ below) but doesn't work either. Can anyone

shed some light into how to do this?

Many thanks in advance,

Best regards,

Giovanni

LAST = MIN( M-1, N )

*

DO 10 J = K, LAST

*

LENH = MIN( P+1, M-J+1 )

*

* Apply H(J) to trailing matrix from left

*

AJJ = A( J, J )

A( J, J ) = ONE

CALL DLARF( 'L', LENH, M-J, A( J, J ), 1, TAU( J-K+1 ),

$ Q( J, J ), LDQ, WORK )

*

A( J, J ) = AJJ

*

10 CONTINUE