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new_as.f90
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module new_as
use types; use consts_dp
use assertions; use warnings_and_errors
implicit none
private
type na_segment
real(dp) :: tlo, thi, dt
real(dp) :: beta0, beta1, beta2
real(dp), pointer :: ra(:)
!-- above iflip we evolve upwards, below iflip we evolve downwards
integer :: iflip, dummy
end type na_segment
type na_handle
private
type(na_segment), pointer :: seg(:)
integer :: nlo, nhi
integer :: nloop, fixnf
!--- these are startoff parameters
real(dp) :: alfas, Q
real(dp) :: quark_masses(1:6)
real(dp) :: muMatch_mQuark
end type na_handle
!-- this seems to give reasonable results (c. 10^-9 precision
! almost everywhere if we start at Z peak)
real(dp) :: dt_base = 0.2_dp
!real(dp), parameter :: dt_base = 0.1_dp
!--------- go from 0.5 GeV to over 10^20 GeV
real(dp), parameter :: tlo = -1.3862944 !-3.2188758_dp
real(dp), parameter :: thi = 93.0_dp
integer, parameter :: nofixnf = -1000000045
public :: na_handle
public :: na_Init, na_Value, na_Del, na_NumberOfLoops
public :: na_nfRange, na_nfAtQ, na_QrangeAtNf, na_QuarkMass
public :: na_Set_dt_base
type(na_segment), pointer :: seg
contains
!======================================================================
!! Set the value of dt_base (used to decide spacings for new coupling
!! instances).
subroutine na_Set_dt_base(new_dt_base)
real(dp) :: new_dt_base
dt_base = new_dt_base
end subroutine na_Set_dt_base
!---------------------------------------------------
subroutine na_Init(nah, alfas, Q, nloop, fixnf, quark_masses, muMatch_mQuark)
use qcd;
type(na_handle), intent(out), target :: nah
real(dp), intent(in), optional :: alfas, Q
integer, intent(in), optional :: nloop, fixnf
real(dp), intent(in), optional :: quark_masses(4:6)
real(dp), intent(in), optional :: muMatch_mQuark
!---------------------------------------------
!real(dp) :: alfas_lcl, Q_lcl
!integer :: nloop_lcl, fixnf_lcl
!-------------------------------
real(dp) :: alfas_here, lnmatch
real(dp) :: tstart, t, ra
integer :: nf_store
integer :: nbin, i, j, nseg, istart
integer :: nbin_total
!-- we may well play with nf, so need to be able to reset it
nf_store = nf_int
nah%alfas = default_or_opt(0.118_dp, alfas)
nah%Q = default_or_opt(91.2_dp, Q)
nah%nloop = default_or_opt(2, nloop)
nah%fixnf = default_or_opt(nofixnf, fixnf)
nah%muMatch_mQuark = default_or_opt(one, muMatch_mQuark)
nah%quark_masses(1:3) = quark_masses_def(1:3)
if (present(quark_masses)) then
nah%quark_masses(4:6) = quark_masses(4:6)
else
nah%quark_masses(4:6) = quark_masses_def(4:6)
end if
!-- work out which ranges are needed
! even in the fixnf case these are used as guides
! for when to switch dt?
do i = lbound(nah%quark_masses, dim=1), ubound(nah%quark_masses, dim=1)
if (tlo > tOfQ(nah%muMatch_mQuark*nah%quark_masses(i))) nah%nlo = i
if (thi > tOfQ(nah%muMatch_mQuark*nah%quark_masses(i))) nah%nhi = i
end do
!-- now set up the parameters of the segments
allocate(nah%seg(nah%nlo:nah%nhi))
nbin_total = 0
do i = nah%nlo, nah%nhi
seg => nah%seg(i)
nah%seg(i)%tlo = max(tlo, tOfQ(nah%muMatch_mQuark*nah%quark_masses(i)))
if (i < nah%nhi) then
seg%thi = tOfQ(nah%muMatch_mQuark*nah%quark_masses(i+1))
else
seg%thi = thi
end if
!-- now fix running coupling
if (nah%fixnf == nofixnf) then
call qcd_SetNf(i)
else
call qcd_SetNf(nah%fixnf)
end if
!-- lazy person's option for getting number of loops automatically
! in derivative calculation
seg%beta0 = beta0
select case(nah%nloop)
case(1)
seg%beta1 = zero
seg%beta2 = zero
case(2)
seg%beta1 = beta1
seg%beta2 = zero
case(3)
seg%beta1 = beta1
seg%beta2 = beta2
case default
call wae_Error('na_init: unsupported number of loops requested')
end select
!-- first guess, which then needs to be "adapted" to the range
seg%dt = dt_base * half**(6-i)
nbin = ceiling((seg%thi - seg%tlo)/seg%dt)
nbin_total = nbin_total + nbin
seg%dt = (seg%thi - seg%tlo) / nbin
allocate(seg%ra(0:nbin))
end do
!write(0,*) 'new_as: used total bins ', nbin_total
!-- find out in which segment we start
tstart = tOfQ(nah%Q)
do i = nah%nlo, nah%nhi
if (tstart <= nah%seg(i)%thi .and. tstart >= nah%seg(i)%tlo) exit
end do
if (i > nah%nhi) &
&call wae_Error('na_init: Specified Q in not in supported range')
nseg = i
!-- fill up the starting segment
ra = one/nah%alfas
seg => nah%seg(nseg)
istart = nint((tstart-seg%tlo)/seg%dt)
t = tstart
seg%ra(istart) = na_evolve(ra, seg%tlo+istart*seg%dt - tstart)
do i = istart+1, ubound(seg%ra,dim=1)
seg%ra(i) = na_evolve(seg%ra(i-1), seg%dt)
end do
do i = istart-1, lbound(seg%ra,dim=1), -1
seg%ra(i) = na_evolve(seg%ra(i+1), -seg%dt)
end do
seg%iflip = istart
!-- fill up the segments above
do j = nseg+1, nah%nhi
seg => nah%seg(j)
alfas_here = one/nah%seg(j-1)%ra(ubound(nah%seg(j-1)%ra,dim=1))
if (mass_steps_on .and. nah%fixnf == nofixnf) then
!write(0,*) '------ changing as from ',j-1,' to ',j
!write(0,*) j-1, alfas_here
lnmatch = two*log(nah%muMatch_mQuark)
select case (nah%nloop)
case(2)
alfas_here = alfas_here*(1 + alphastep11 * lnmatch * alfas_here)
case(3)
alfas_here = alfas_here*(1 + alphastep11 * lnmatch * alfas_here&
& + (alphastep22 * lnmatch**2 + alphastep21 * lnmatch&
& + alphastep20_pole)*alfas_here**2)
!alfas_here = alfas_here*(1 + alphastep20_pole*alfas_here**2)
end select
!write(0,*) j, alfas_here
end if
seg%ra(0) = one/alfas_here
! recall that this is the reciprocal of alpha!
do i = 1, ubound(seg%ra,dim=1)
seg%ra(i) = na_evolve(seg%ra(i-1), seg%dt)
end do
seg%iflip = -1
end do
!-- fill up the segments below
do j = nseg-1, nah%nlo, -1
seg => nah%seg(j)
alfas_here = one/nah%seg(j+1)%ra(0)
if (mass_steps_on .and. nah%fixnf == nofixnf) then
!write(0,*) '------ changing as from ',j+1,' to ',j
!write(0,*) j+1, alfas_here
lnmatch = two*log(nah%muMatch_mQuark)
select case (nah%nloop)
case(2)
alfas_here = alfas_here*(1 - alphastep11 * lnmatch * alfas_here)
case(3)
alfas_here = alfas_here*(1 - alphastep11 * lnmatch * alfas_here&
& + (alphastep22 * lnmatch**2 - alphastep21 * lnmatch&
& - alphastep20_pole)*alfas_here**2)
!alfas_here = alfas_here*(1 - alphastep20_pole*alfas_here**2)
end select
!write(0,*) j, alfas_here
end if
seg%ra(ubound(seg%ra,dim=1)) = one/alfas_here
do i = ubound(seg%ra,dim=1)-1, 0, -1
seg%ra(i) = na_evolve(seg%ra(i+1), -seg%dt)
end do
seg%iflip = ubound(seg%ra,dim=1)+1
end do
!--- set things back to their origins
call qcd_SetNf(nf_store)
end subroutine na_init
!-------------------------------------------------------------------------
! If fixnf is present, then the program will force (within limits of +-dt)
! the alpha that is returned to be that corresponding to fixnf flavours.
!
! With smooth matching conditions, this is not a big deal, but with
! steps at alpha_s thresholds, it is important so that certain D.E.
! routines (e.g. for PDF evolution) do not give alpha values at end
! points that give non-smoothness.
function na_Value(nah, Q, fixnf) result(res)
type(na_handle), intent(in), target :: nah
real(dp), intent(in) :: Q
integer, intent(in), optional :: fixnf
real(dp) :: res
!-------------------------------------
real(dp) :: t, trescaled, ra, delta_t
integer :: nseg, i, n
integer, save :: warn_id = warn_id_INIT
integer, parameter :: max_warn = 1
t = tOfQ(Q)
if (present(fixnf) .and. nah%fixnf == nofixnf) then
if (fixnf < nah%nlo .or. fixnf > nah%nhi) then
call wae_error('na_Value:', 'the fixnf requested is&
& outside the range supported this na_handle')
end if
if (t < tlo .or. t > thi) then
call wae_error('na_Value:', 'the Q value is&
& outside the range supported this na_handle')
end if
nseg = fixnf
!if (t > nah%seg(nseg)%thi+ nah%seg(nseg)%dt .or.&
! & t < nah%seg(nseg)%tlo-nah%seg(nseg)%dt) then
! call wae_error('na_Value:', &
! & 'With fixnf, Q is too far outside supported range.')
!end if
else
if (present(fixnf) .and. nah%fixnf /= nofixnf) then
if (fixnf /= nah%fixnf) then
call wae_error('na_Value:', 'the fixnf requested is &
&different from that supported by na_handle')
end if
end if
do nseg = nah%nlo, nah%nhi
if (t <= nah%seg(nseg)%thi .and. t >= nah%seg(nseg)%tlo) exit
end do
if (nseg > nah%nhi) &
&call wae_Error('na_Value: Specified Q is not in supported range'&
&,dbleval=Q)
end if
seg => nah%seg(nseg)
trescaled = (t - seg%tlo)/seg%dt
if (trescaled > seg%iflip) then
i = floor(trescaled)
else
i = ceiling(trescaled)
end if
i = max(0,min(ubound(seg%ra,dim=1),i))
!-- support going well beyond supported limits of this nf, even
! if the procedure is not particularly recommended.
delta_t = t - (seg%tlo+i*seg%dt)
if (abs(delta_t) <= 1.3_dp*seg%dt) then
res = one/na_evolve(seg%ra(i), delta_t)
else
call wae_warn(max_warn,warn_id,'na_Value: will evolve &
&fixed-nf alpha_s beyond precalculated range.',&
&'This procedure may be very slow')
write(0,*) Qoft(seg%tlo),Qoft(seg%thi),Q
n = ceiling(abs(delta_t/seg%dt))
delta_t = delta_t/n
ra = seg%ra(i)
do i = 1, n
ra = na_evolve(ra,delta_t)
end do
res = one/ra
end if
!write(0,'(f15.10,i,f15.12)') t, nseg, res ! HOPPER TESTING
end function na_Value
!======================================================================
!! Returns the number of loops in this coupling
integer function na_NumberOfLoops(nah)
type(na_handle), intent(in) :: nah
na_NumberOfLoops = nah%nloop
end function na_NumberOfLoops
!-------------------------------------------------------------
!! Do all the necessary cleaning up
subroutine na_Del(nah)
type(na_handle), intent(inout) :: nah
integer :: i, status
do i = nah%nlo, nah%nhi
deallocate(nah%seg(i)%ra, stat=status)
end do
deallocate(nah%seg, stat=status)
end subroutine na_Del
!======================================================================
!! Return the mass of the quark specified by iflv
real(dp) function na_QuarkMass(nah,iflv) result(mass)
type(na_handle), intent(in) :: nah
integer, intent(in) :: iflv
if (iflv > 6 .or. iflv < 1) call wae_error('na_QuarkMass', &
&'illegal value for iflv', intval=iflv)
mass = nah%quark_masses(iflv)
end function na_QuarkMass
!-------------------------------------------------------------
!! Indicate the range of nf values supported by this handle.
subroutine na_nfRange(nah,nflo,nfhi)
type(na_handle), intent(in) :: nah
integer, intent(out) :: nflo, nfhi
if (nah%fixnf == nofixnf) then
nflo = nah%nlo
nfhi = nah%nhi
else
nflo = nah%fixnf
nfhi = nah%fixnf
end if
end subroutine na_nfRange
!-------------------------------------------------------------
!! Returns the number of flavours relevant for scale Q
!! Also returns the range of Qvalues (Qlo, Qhi) for which
!! this value of nf remains the same.
subroutine na_nfAtQ(nah, Q, nfAtQ, Qlo, Qhi, muM_mQ)
type(na_handle), intent(in) :: nah
real(dp), intent(in) :: Q
integer, intent(out) :: nfAtQ
real(dp), intent(out), optional :: Qlo, Qhi
real(dp), intent(in), optional :: muM_mQ
!-----------------------------
real(dp) :: deltat_match
real(dp) :: t
integer :: nseg
real(dp) :: mtlo(nah%nlo:nah%nhi), mthi(nah%nlo:nah%nhi)
deltat_match = tofQ(default_or_opt(&
&nah%muMatch_mQuark, muM_mQ)/nah%muMatch_mQuark)
!-- redefine limits so as to account for requested matching
! thresholds muM_mQ. Outer limits should not be modified
! since they are rigidly fixed?
!
! What happens if one of these intervals becomes negative?
mtlo(nah%nlo+1:nah%nhi) = nah%seg(nah%nlo+1:nah%nhi)%tlo + deltat_match
mthi(nah%nlo:nah%nhi-1) = nah%seg(nah%nlo:nah%nhi-1)%thi + deltat_match
mtlo(nah%nlo) = nah%seg(nah%nlo)%tlo
mthi(nah%nhi) = nah%seg(nah%nhi)%thi
t = tOfQ(Q)
if (nah%fixnf == nofixnf) then
do nseg = nah%nlo, nah%nhi
if (t <= mthi(nseg) .and. t >= mtlo(nseg)) exit
end do
if (nseg > nah%nhi) &
&call wae_Error('na_nfAtQ: Specified Q is not in supported range:'&
&,dbleval=Q)
nfAtQ = nseg
if (present(Qlo) .and. present(Qhi)) then
Qlo = QOft(mtlo(nseg))
Qhi = QOft(mthi(nseg))
end if
else
if (t > thi .or. t < tlo) then
call wae_Error('na_nfAtQ: Specified Q is not in supported range'&
&,dbleval=Q)
end if
nfAtQ = nah%fixnf
if (present(Qlo) .and. present(Qhi)) then
Qlo = QOft(tlo)
Qhi = QOft(thi)
end if
end if
end subroutine na_nfAtQ
!-------------------------------------------------------------
! returns the Q range for a given value of nf. If supported.
subroutine na_QRangeAtNf(nah, nflcl, Qlo, Qhi, muM_mQ)
type(na_handle), intent(in) :: nah
integer, intent(in) :: nflcl
real(dp), intent(out) :: Qlo, Qhi
real(dp), optional, intent(in) :: muM_mQ
!---------------------------------------
real(dp) :: deltat_match
character(len=60) :: string
deltat_match = tofQ(default_or_opt(&
&nah%muMatch_mQuark, muM_mQ)/nah%muMatch_mQuark)
if (nah%fixnf == nofixnf) then
if (nflcl < nah%nlo .or. nflcl > nah%nhi) then
write(string,'(a,i2,a)') 'nf value ',nflcl,' not supported'
call wae_Error('QrangeAtNf', trim(string))
end if
if (nflcl == nah%nlo) then
Qlo = QOft(nah%seg(nflcl)%tlo)
else
Qlo = QOft(nah%seg(nflcl)%tlo + deltat_match)
end if
if (nflcl == nah%nhi) then
Qhi = QOft(nah%seg(nflcl)%thi)
else
Qhi = QOft(nah%seg(nflcl)%thi + deltat_match)
end if
else
if (nflcl /= nah%fixnf) then
write(string,'(a,i2,a)') 'nf value ',nflcl,' not supported'
call wae_Error('QrangeAtNf', trim(string))
end if
Qlo = QOft(tlo)
Qhi = QOft(thi)
end if
end subroutine na_QRangeAtNf
!------------------------------------------------------------
! given ra return the value evolve by dt
function na_evolve(ra,dt) result(res)
use runge_kutta
real(dp), intent(in) :: ra, dt
!----------------------------------
real(dp) :: res,t
t = zero
res = ra
call rkstp(dt,t,res,na_deriv)
end function na_evolve
!---------------------------------------------------------
! derivative of 1/alpha
subroutine na_deriv(t, ra, dra)
real(dp), intent(in) :: t, ra
real(dp), intent(out) :: dra
dra = seg%beta0 + seg%beta1/ra + seg%beta2/ra**2
end subroutine na_deriv
!-- avoid risk of errors when forgetting factor of two
function tOfQ(Q)
real(dp), intent(in) :: Q
real(dp) :: tOfQ
tOfQ = two * log(Q)
end function tOfQ
function QOft(t)
real(dp), intent(in) :: t
real(dp) :: QOft
QOft = exp(half*t)
end function QOft
end module new_as

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