We document here an extension of the reweighting feature of POWHEG
that can also reweigth the generation of radiation for a new PDF
set and the corresponding change in alpha_S. 

This feature is activated by setting the flag

fullrwgt 1

in the powheg.input file, when running in reweighting mode,
i.e. with the setting

compute_rwgt 1

in the Les Houches file.

The reweighting operates only on the generation of initial
state radiation. It is thus effective for processes as W/Z, H and
t-tbar (with no radiation from top decay) and similar processes (i.e.
W/Z pairs, HW, HZ, etc.). Final
state radiation does not depend directly upon the PDF's;
however, the different value of Lambda_QCD associated with
different PDF's can have an effect on final state radiation.
Furthermore, final state radiation competes with initial state
radiation in POWHEG, thus modifying the Sudakov form factors.
An extension of the procedure to final state radiation may
be possible, but it is not pursued at the moment.

When using the LHAPDF6 package, it is mandatory to use the new
POWHEG interface for LHAPDF6. If not, switching between the two
differen pdf sets will slow down the reweighting procedure by
a considerable amount. 

An example of the procedure is given in the W process, where the newly
added subdirectory test-fullrwgt includes a new Makefile, using the
appropriate interface to the LHAPDF6 package, and a simplified
analysis file at the Les Houches level. In the two run subdirectories,
testrun-wm-lhc-8TeV-ct10 and testrun-wm-lhc-8TeV-MRST, the input files
for parallel runs are included. In the testrun-wm-lhc-8TeV-ct10 run, a
run is performed with the ct10 pdf's, and it is reweighted to the MRST
one's, while the testrun-wm-lhc-8TeV-MRST does the opposite.