subroutine mrstlo(x,q2,mode,upv,dnv,usea,dsea,str,chm,bot,glu)
C***************************************************************C
C C
C This is a package for the new MRST 2001 LO parton C
C distributions. C
C Reference: A.D. Martin, R.G. Roberts, W.J. Stirling and C
C R.S. Thorne, hep-ph/0201xxx C
C C
C There is 1 pdf set corresponding to mode = 1 C
C C
C Mode=1 gives the default set with Lambda(MSbar,nf=4) = 0.220 C
C corresponding to alpha_s(M_Z) of 0.130 C
C This set reads a grid whose first number is 0.02868 C
C C
C This subroutine uses an improved interpolation procedure C
C for extracting values of the pdf's from the grid C
C C
C Comments to : W.J.Stirling@durham.ac.uk C
C C
C***************************************************************C
implicit real*8(a-h,o-z)
character*128 mfile
common/mrinput/mfile
data xmin,xmax,qsqmin,qsqmax/1d-5,1d0,1.25d0,1d7/
if(q2.lt.qsqmin.or.q2.gt.qsqmax) print 99,q2
if(x.lt.xmin.or.x.gt.xmax) print 98,x
if(mode.eq.1) then
call mrst1(x,q2,upv,dnv,usea,dsea,str,chm,bot,glu)
endif
99 format(' WARNING: Q^2 VALUE IS OUT OF RANGE ','q2= ',e10.5)
98 format(' WARNING: X VALUE IS OUT OF RANGE ','x= ',e10.5)
return
end
subroutine mrst1(x,qsq,upv,dnv,usea,dsea,str,chm,bot,glu)
implicit real*8(a-h,o-z)
parameter(nx=49,nq=37,np=8,nqc0=2,nqb0=11,nqc=35,nqb=26)
real*8 f1(nx,nq),f2(nx,nq),f3(nx,nq),f4(nx,nq),f5(nx,nq),
.f6(nx,nq),f7(nx,nq),f8(nx,nq),fc(nx,nqc),fb(nx,nqb)
real*8 qq(nq),xx(nx),cc1(nx,nq,4,4),cc2(nx,nq,4,4),
.cc3(nx,nq,4,4),cc4(nx,nq,4,4),cc6(nx,nq,4,4),cc8(nx,nq,4,4),
.ccc(nx,nqc,4,4),ccb(nx,nqb,4,4)
real*8 xxl(nx),qql(nq),qqlc(nqc),qqlb(nqb)
character*128 mfile
common/mrinput/mfile
data xx/1d-5,2d-5,4d-5,6d-5,8d-5,
. 1d-4,2d-4,4d-4,6d-4,8d-4,
. 1d-3,2d-3,4d-3,6d-3,8d-3,
. 1d-2,1.4d-2,2d-2,3d-2,4d-2,6d-2,8d-2,
. .1d0,.125d0,.15d0,.175d0,.2d0,.225d0,.25d0,.275d0,
. .3d0,.325d0,.35d0,.375d0,.4d0,.425d0,.45d0,.475d0,
. .5d0,.525d0,.55d0,.575d0,.6d0,.65d0,.7d0,.75d0,
. .8d0,.9d0,1d0/
data qq/1.25d0,1.5d0,2d0,2.5d0,3.2d0,4d0,5d0,6.4d0,8d0,1d1,
. 1.2d1,1.8d1,2.6d1,4d1,6.4d1,1d2,
. 1.6d2,2.4d2,4d2,6.4d2,1d3,1.8d3,3.2d3,5.6d3,1d4,
. 1.8d4,3.2d4,5.6d4,1d5,1.8d5,3.2d5,5.6d5,1d6,
. 1.8d6,3.2d6,5.6d6,1d7/
data xmin,xmax,qsqmin,qsqmax/1d-5,1d0,1.25d0,1d7/
data init/0/
save
xsave=x
q2save=qsq
if(init.ne.0) goto 10
open(unit=33,file=mfile,status='old')
do 20 n=1,nx-1
do 20 m=1,nq
read(33,50)f1(n,m),f2(n,m),f3(n,m),f4(n,m),
. f5(n,m),f7(n,m),f6(n,m),f8(n,m)
c notation: 1=uval 2=dval 3=glue 4=usea 5=chm 6=str 7=btm 8=dsea
20 continue
do 40 m=1,nq
f1(nx,m)=0.d0
f2(nx,m)=0.d0
f3(nx,m)=0.d0
f4(nx,m)=0.d0
f5(nx,m)=0.d0
f6(nx,m)=0.d0
f7(nx,m)=0.d0
f8(nx,m)=0.d0
40 continue
do n=1,nx
xxl(n)=dlog(xx(n))
enddo
do m=1,nq
qql(m)=dlog(qq(m))
enddo
call jeppe1(nx,nq,xxl,qql,f1,cc1)
call jeppe1(nx,nq,xxl,qql,f2,cc2)
call jeppe1(nx,nq,xxl,qql,f3,cc3)
call jeppe1(nx,nq,xxl,qql,f4,cc4)
call jeppe1(nx,nq,xxl,qql,f6,cc6)
call jeppe1(nx,nq,xxl,qql,f8,cc8)
emc2=2.045
emb2=18.5
do 44 m=1,nqc
qqlc(m)=qql(m+nqc0)
do 44 n=1,nx
fc(n,m)=f5(n,m+nqc0)
44 continue
qqlc(1)=dlog(emc2)
call jeppe1(nx,nqc,xxl,qqlc,fc,ccc)
do 45 m=1,nqb
qqlb(m)=qql(m+nqb0)
do 45 n=1,nx
fb(n,m)=f7(n,m+nqb0)
45 continue
qqlb(1)=dlog(emb2)
call jeppe1(nx,nqb,xxl,qqlb,fb,ccb)
init=1
10 continue
xlog=dlog(x)
qsqlog=dlog(qsq)
call jeppe2(xlog,qsqlog,nx,nq,xxl,qql,cc1,upv)
call jeppe2(xlog,qsqlog,nx,nq,xxl,qql,cc2,dnv)
call jeppe2(xlog,qsqlog,nx,nq,xxl,qql,cc3,glu)
call jeppe2(xlog,qsqlog,nx,nq,xxl,qql,cc4,usea)
call jeppe2(xlog,qsqlog,nx,nq,xxl,qql,cc6,str)
call jeppe2(xlog,qsqlog,nx,nq,xxl,qql,cc8,dsea)
chm=0.d0
if(qsq.gt.emc2) then
call jeppe2(xlog,qsqlog,nx,nqc,xxl,qqlc,ccc,chm)
endif
bot=0.d0
if(qsq.gt.emb2) then
call jeppe2(xlog,qsqlog,nx,nqb,xxl,qqlb,ccb,bot)
endif
x=xsave
qsq=q2save
return
50 format(8f10.5)
end
c subroutine jeppe1(nx,my,xx,yy,ff,cc)
c implicit real*8(a-h,o-z)
c dimension xx(nx),yy(my),ff(nx,my),ff1(nx,my),ff2(nx,my),
c xff12(nx,my),yy0(4),yy1(4),yy2(4),yy12(4),z(16),wt(16,16),
c xcl(16),cc(nx,my,4,4),iwt(16,16)
subroutine jeppe1(nx,my,xx,yy,ff,cc)
implicit real*8(a-h,o-z)
PARAMETER(NNX=49,MMY=37)
dimension xx(nx),yy(my),ff(nx,my),ff1(NNX,MMY),ff2(NNX,MMY),
xff12(NNX,MMY),yy0(4),yy1(4),yy2(4),yy12(4),z(16),wt(16,16),
xcl(16),cc(nx,my,4,4),iwt(16,16)
data iwt/1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
x 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
x -3,0,0,3,0,0,0,0,-2,0,0,-1,0,0,0,0,
x 2,0,0,-2,0,0,0,0,1,0,0,1,0,0,0,0,
x 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
x 0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
x 0,0,0,0,-3,0,0,3,0,0,0,0,-2,0,0,-1,
x 0,0,0,0,2,0,0,-2,0,0,0,0,1,0,0,1,
x -3,3,0,0,-2,-1,0,0,0,0,0,0,0,0,0,0,
x 0,0,0,0,0,0,0,0,-3,3,0,0,-2,-1,0,0,
x 9,-9,9,-9,6,3,-3,-6,6,-6,-3,3,4,2,1,2,
x -6,6,-6,6,-4,-2,2,4,-3,3,3,-3,-2,-1,-1,-2,
x 2,-2,0,0,1,1,0,0,0,0,0,0,0,0,0,0,
x 0,0,0,0,0,0,0,0,2,-2,0,0,1,1,0,0,
x -6,6,-6,6,-3,-3,3,3,-4,4,2,-2,-2,-2,-1,-1,
x 4,-4,4,-4,2,2,-2,-2,2,-2,-2,2,1,1,1,1/
do 42 m=1,my
dx=xx(2)-xx(1)
ff1(1,m)=(ff(2,m)-ff(1,m))/dx
dx=xx(nx)-xx(nx-1)
ff1(nx,m)=(ff(nx,m)-ff(nx-1,m))/dx
do 41 n=2,nx-1
ff1(n,m)=polderiv(xx(n-1),xx(n),xx(n+1),ff(n-1,m),ff(n,m),
xff(n+1,m))
41 continue
42 continue
do 44 n=1,nx
dy=yy(2)-yy(1)
ff2(n,1)=(ff(n,2)-ff(n,1))/dy
dy=yy(my)-yy(my-1)
ff2(n,my)=(ff(n,my)-ff(n,my-1))/dy
do 43 m=2,my-1
ff2(n,m)=polderiv(yy(m-1),yy(m),yy(m+1),ff(n,m-1),ff(n,m),
xff(n,m+1))
43 continue
44 continue
do 46 m=1,my
dx=xx(2)-xx(1)
ff12(1,m)=(ff2(2,m)-ff2(1,m))/dx
dx=xx(nx)-xx(nx-1)
ff12(nx,m)=(ff2(nx,m)-ff2(nx-1,m))/dx
do 45 n=2,nx-1
ff12(n,m)=polderiv(xx(n-1),xx(n),xx(n+1),ff2(n-1,m),ff2(n,m),
xff2(n+1,m))
45 continue
46 continue
do 53 n=1,nx-1
do 52 m=1,my-1
d1=xx(n+1)-xx(n)
d2=yy(m+1)-yy(m)
d1d2=d1*d2
yy0(1)=ff(n,m)
yy0(2)=ff(n+1,m)
yy0(3)=ff(n+1,m+1)
yy0(4)=ff(n,m+1)
yy1(1)=ff1(n,m)
yy1(2)=ff1(n+1,m)
yy1(3)=ff1(n+1,m+1)
yy1(4)=ff1(n,m+1)
yy2(1)=ff2(n,m)
yy2(2)=ff2(n+1,m)
yy2(3)=ff2(n+1,m+1)
yy2(4)=ff2(n,m+1)
yy12(1)=ff12(n,m)
yy12(2)=ff12(n+1,m)
yy12(3)=ff12(n+1,m+1)
yy12(4)=ff12(n,m+1)
do 47 k=1,4
z(k)=yy0(k)
z(k+4)=yy1(k)*d1
z(k+8)=yy2(k)*d2
z(k+12)=yy12(k)*d1d2
47 continue
do 49 l=1,16
xxd=0.
do 48 k=1,16
xxd=xxd+iwt(k,l)*z(k)
48 continue
cl(l)=xxd
49 continue
l=0
do 51 k=1,4
do 50 j=1,4
l=l+1
cc(n,m,k,j)=cl(l)
50 continue
51 continue
52 continue
53 continue
return
end
subroutine jeppe2(x,y,nx,my,xx,yy,cc,z)
implicit real*8(a-h,o-z)
dimension xx(nx),yy(my),cc(nx,my,4,4)
n=locx(xx,nx,x)
m=locx(yy,my,y)
t=(x-xx(n))/(xx(n+1)-xx(n))
u=(y-yy(m))/(yy(m+1)-yy(m))
z=0.
do 1 l=4,1,-1
z=t*z+((cc(n,m,l,4)*u+cc(n,m,l,3))*u
. +cc(n,m,l,2))*u+cc(n,m,l,1)
1 continue
return
end
integer function locx(xx,nx,x)
implicit real*8(a-h,o-z)
dimension xx(nx)
if(x.le.xx(1)) then
locx=1
return
endif
if(x.ge.xx(nx)) then
locx=nx-1
return
endif
ju=nx+1
jl=0
1 if((ju-jl).le.1) go to 2
jm=(ju+jl)/2
if(x.ge.xx(jm)) then
jl=jm
else
ju=jm
endif
go to 1
2 locx=jl
return
end
real*8 function polderiv(x1,x2,x3,y1,y2,y3)
implicit real*8(a-h,o-z)
polderiv=(x3*x3*(y1-y2)-2.0*x2*(x3*(y1-y2)+x1*
.(y2-y3))+x2*x2*(y1-y3)+x1*x1*(y2-y3))/((x1-x2)*(x1-x3)*(x2-x3))
return
end