outerpdf.F

CMSSW/GeneratorInterface/GenExtensions/bin/BCVEGPY/outerpdf.F

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1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522	`c============================================================================` `c april 10, 2002, v6.01` `c february 23, 2003, v6.1` `c` `c ref[1]: "new generation of parton distributions with uncertainties from global qcd analysis"` `c by: j. pumplin, d.r. stump, j.huston, h.l. lai, p. nadolsky, w.k. tung` `c jhep 0207:012(2002), hep-ph/0201195` `c` `c ref[2]: "inclusive jet production, parton distributions, and the search for new physics"` `c by : d. stump, j. huston, j. pumplin, w.k. tung, h.l. lai, s. kuhlmann, j. owens` `c hep-ph/0303013` `c` `c this package contains` `c (1) 4 standard sets of cteq6 pdf's (cteq6m, cteq6d, cteq6l, cteq6l1) ;` `c (2) 40 up/down sets (with respect to cteq6m) for uncertainty studies from ref[1];` `c (3) updated version of the above: cteq6.1m and its 40 up/down eigenvector sets from ref[2].` `c` `c the cteq6.1m set provides a global fit that is almost equivalent in every respect` `c to the published cteq6m, ref[1], although some parton distributions (e.g., the gluon)` `c may deviate from cteq6m in some kinematic ranges by amounts that are well within the` `c specified uncertainties.` `c the more significant improvements of the new version are associated with some of the` `c 40 eigenvector sets, which are made more symmetrical and reliable in (3), compared to (2).` `c details about calling convention are:` `c ---------------------------------------------------------------------------` `c iset pdf-set description alpha_s(mz)lam4 lam5 table_file` `c ===========================================================================` `c standard, "best-fit", sets:` `c --------------------------` `c 1 cteq6m standard msbar scheme 0.118 326 226 cteq6m.tbl` `c 2 cteq6d standard dis scheme 0.118 326 226 cteq6d.tbl` `c 3 cteq6l leading order 0.118 326 226 cteq6l.tbl` `c 4 cteq6l1 leading order 0.130 215 165 cteq6l1.tbl` `c ============================================================================` `c for uncertainty calculations using eigenvectors of the hessian:` `c ---------------------------------------------------------------` `c central + 40 up/down sets along 20 eigenvector directions` `c -----------------------------` `c original version, ref[1]: central fit: cteq6m (=cteq6m.00)` `c -----------------------` `c 1xx cteq6m.xx +/- sets 0.118 326 226 cteq6m1xx.tbl` `c where xx = 01-40: 01/02 corresponds to +/- for the 1st eigenvector, ... etc.` `c e.g. 100 is cteq6m.00 (=cteq6m),` `c 101/102 are cteq6m.01/02, +/- sets of 1st eigenvector, ... etc.` `c -----------------------` `c updated version, ref[2]: central fit: cteq6.1m (=cteq61.00)` `c -----------------------` `c 2xx cteq61.xx +/- sets 0.118 326 226 ctq61.xx.tbl` `c where xx = 01-40: 01/02 corresponds to +/- for the 1st eigenvector, ... etc.` `c e.g. 200 is cteq61.00 (=cteq6.1m),` `c 201/202 are cteq61.01/02, +/- sets of 1st eigenvector, ... etc.` `c ===========================================================================` `c all fits are obtained by using the same coupling strength` `c \alpha_s(mz)=0.118 and the nlo running \alpha_s formula, except cteq6l1` `c which uses the lo running \alpha_s and its value determined from the fit.` `c for the lo fits, the evolution of the pdf and the hard cross sections are` `c calculated at lo. more detailed discussions are given in the references.` `c` `c the table grids are generated for 10^-6 < x < 1 and 1.3 < q < 10,000 (gev).` `c pdf values outside of the above range are returned using extrapolation.` `c lam5 (lam4) represents lambda value (in mev) for 5 (4) flavors.` `c the matching alpha_s between 4 and 5 flavors takes place at q=4.5 gev,` `c which is defined as the bottom quark mass, whenever it can be applied.` `c` `c the table_files are assumed to be in the working directory.` `c` `c before using the pdf, it is necessary to do the initialization by` `c call setctq6(iset)` `c where iset is the desired pdf specified in the above table.` `c` `c the function ctq6pdf (iparton, x, q)` `c returns the parton distribution inside the proton for parton [iparton]` `c at [x] bjorken_x and scale [q] (gev) in pdf set [iset].` `c iparton is the parton label (5, 4, 3, 2, 1, 0, -1, ......, -5)` `c for (b, c, s, d, u, g, u_bar, ..., b_bar),` `c` `c for detailed information on the parameters used, e.q. quark masses,` `c qcd lambda, ... etc., see info lines at the beginning of the` `c table_files.` `c` `c these programs, as provided, are in double precision. by removing the` `c "implicit double precision" lines, they can also be run in single` `c precision.` `c` `c if you have detailed questions concerning these cteq6 distributions,` `c or if you find problems/bugs using this package, direct inquires to` `c pumplin@pa.msu.edu or tung@pa.msu.edu.` `c` `c===========================================================================` `double precision function ctq6pdf (iparton, x, q)` `implicit double precision (a-h,o-z)` `logical warn` `common` `> / ctqpar2 / nx, nt, nfmx` `> / qcdtable / alambda, nfl, iorder` `data warn /.true./` `save warn` `if (x .lt. 0d0 .or. x .gt. 1d0) then` `print , 'x out of range in ctq6pdf: ', x` `stop` `endif` `if (q .lt. alambda) then` `print , 'q out of range in ctq6pdf: ', q` `stop` `endif` `if ((iparton .lt. -nfmx .or. iparton .gt. nfmx)) then` `if (warn) then` `c put a warning for calling extra flavor.` `warn = .false.` `print , 'warning: iparton out of range in ctq6pdf! '` `print , 'iparton, mxflvn0: ', iparton, nfmx` `endif` `ctq6pdf = 0d0` `return` `endif` `ctq6pdf = partonx6 (iparton, x, q)` `if(ctq6pdf.lt.1.0d-16) ctq6pdf = 0.0d0` `return` `c *******************` `end` `subroutine setctq6 (iset)` `implicit double precision (a-h,o-z)` `parameter (isetmax0=5)` `character flnm(isetmax0)6, nn3, tablefile140` `data (flnm(i), i=1,isetmax0)` `> / 'cteq6m', 'cteq6d', 'cteq6l', 'cteq6l','ctq61.'/` `data isetold, isetmin0, isetmin1, isetmax1 /-987,1,100,140/` `data isetmin2,isetmax2 /200,240/` `save` `c if data file not initialized, do so.` `character cmsdir82` `call getenv('CMSSW_BASE',cmsdir)` `kspace=index(cmsdir,' ')` `if(iset.ne.isetold) then` `iu= nextun()` `if (iset.ge.isetmin0 .and. iset.le.3) then` `tablefile=cmsdir(1:kspace-1)` `$ //'/src/GeneratorInterface/GenExtensions/data/'` `$ //flnm(iset)//'.tbl'` `elseif (iset.eq.4) then` `tablefile=cmsdir(1:kspace-1)` `$ //'/src/GeneratorInterface/GenExtensions/data/'` `$ //flnm(iset)//'1.tbl'` `elseif (iset.ge.isetmin1 .and. iset.le.isetmax1) then` `write(nn,'(i3)') iset` `tablefile=cmsdir(1:kspace-1)` `$ //'/src/GeneratorInterface/GenExtensions/data/'` `$ //flnm(1)//nn//'.tbl'` `elseif (iset.ge.isetmin2 .and. iset.le.isetmax2) then` `write(nn,'(i3)') iset` `tablefile=cmsdir(1:kspace-1)` `$ //'/src/GeneratorInterface/GenExtensions/data/'` `$ //flnm(5)//nn(2:3)//'.tbl'` `else` `print , 'invalid iset number in setctq6 :', iset` `stop` `endif` `c print , 'pdf file ', tablefile` `open(iu, file=tablefile, status='old', err=100)` `call readtbl (iu)` `close (iu)` `isetold=iset` `endif` `return` `100 print , ' data file ', tablefile, ' cannot be opened '` `>//'in setctq6!!'` `stop` `c *******************` `end` `subroutine readtbl (nu)` `implicit double precision (a-h,o-z)` `character line80` `parameter (mxx = 96, mxq = 20, mxf = 5)` `parameter (mxpqx = (mxf + 3) * mxq * mxx)` `common` `> / ctqpar1 / al, xv(0:mxx), tv(0:mxq), upd(mxpqx)` `> / ctqpar2 / nx, nt, nfmx` `> / xqrange / qini, qmax, xmin` `> / qcdtable / alambda, nfl, iorder` `> / masstbl / amass(6)` `read (nu, '(a)') line` `read (nu, '(a)') line` `read (nu, ) dr, fl, al, (amass(i),i=1,6)` `iorder = nint(dr)` `nfl = nint(fl)` `alambda = al` `read (nu, '(a)') line` `read (nu, ) nx, nt, nfmx` `read (nu, '(a)') line` `read (nu, ) qini, qmax, (tv(i), i =0, nt)` `read (nu, '(a)') line` `read (nu, ) xmin, (xv(i), i =0, nx)` `do 11 iq = 0, nt` `tv(iq) = log(log (tv(iq) /al))` `11 continue` `c` `c since quark = anti-quark for nfl>2 at this stage,` `c we read out only the non-redundent data points` `c no of flavors = nfmx (sea) + 1 (gluon) + 2 (valence)` `nblk = (nx+1) * (nt+1)` `npts = nblk * (nfmx+3)` `read (nu, '(a)') line` `read (nu, , iostat=iret) (upd(i), i=1,npts)` `return` `c *************************` `end` `function nextun()` `c returns an unallocated fortran i/o unit.` `logical ex` `c` `do 10 n = 10, 300` `inquire (unit=n, opened=ex)` `if (.not. ex) then` `nextun = n` `return` `endif` `10 continue` `stop ' there is no available i/o unit. '` `c **********************` `end` `c` `subroutine polint (xa,ya,n,x,y,dy)` `implicit double precision (a-h, o-z)` `c adapted from "numerical recipes"` `parameter (nmax=10)` `dimension xa(n),ya(n),c(nmax),d(nmax)` `ns=1` `dif=abs(x-xa(1))` `do 11 i=1,n` `dift=abs(x-xa(i))` `if (dift.lt.dif) then` `ns=i` `dif=dift` `endif` `c(i)=ya(i)` `d(i)=ya(i)` `11 continue` `y=ya(ns)` `ns=ns-1` `do 13 m=1,n-1` `do 12 i=1,n-m` `ho=xa(i)-x` `hp=xa(i+m)-x` `w=c(i+1)-d(i)` `den=ho-hp` `c pause is not supported anymore` `c if(den.eq.0.)pause` `if (den.eq.0.) then` `WRITE (,) 'den is 0'` `READ (,'()')` `endif` `den=w/den` `d(i)=hpden` `c(i)=hoden` `12 continue` `if (2ns.lt.n-m)then` `dy=c(ns+1)` `else` `dy=d(ns)` `ns=ns-1` `endif` `y=y+dy` `13 continue` `return` `end` `double precision function partonx6 (iprtn, xx, qq)` `c given the parton distribution function in the array u in` `c common / pevldt / , this routine interpolates to find` `c the parton distribution at an arbitray point in x and q.` `c` `implicit double precision (a-h,o-z)` `parameter (mxx = 96, mxq = 20, mxf = 5)` `parameter (mxqx= mxq mxx, mxpqx = mxqx * (mxf+3))` `common` `> / ctqpar1 / al, xv(0:mxx), tv(0:mxq), upd(mxpqx)` `> / ctqpar2 / nx, nt, nfmx` `> / xqrange / qini, qmax, xmin` `dimension fvec(4), fij(4)` `dimension xvpow(0:mxx)` `data onep / 1.00001 /` `data xpow / 0.3d0 / !** choice of interpolation variable` `data nqvec / 4 /` `data ientry / 0 /` `save ientry,xvpow` `c store the powers used for interpolation on first call...` `if(ientry .eq. 0) then` `ientry = 1` `xvpow(0) = 0d0` `do i = 1, nx` `xvpow(i) = xv(i)xpow` `enddo` `endif` `x = xx` `q = qq` `tt = log(log(q/al))` `c ------------- find lower end of interval containing x, i.e.,` `c get jx such that xv(jx) .le. x .le. xv(jx+1)...` `jlx = -1` `ju = nx+1` `11 if (ju-jlx .gt. 1) then` `jm = (ju+jlx) / 2` `if (x .ge. xv(jm)) then` `jlx = jm` `else` `ju = jm` `endif` `goto 11` `endif` `c ix 0 1 2 jx jlx nx-2 nx` `c \|---\|---\|---\|...\|---\|-x-\|---\|...\|---\|---\|` `c x 0 xmin x 1` `c` `if (jlx .le. -1) then` `print '(a,1pe12.4)', 'severe error: x <= 0 in partonx6! x = ', x` `stop` `elseif (jlx .eq. 0) then` `jx = 0` `elseif (jlx .le. nx-2) then` `c for interrior points, keep x in the middle, as shown above` `jx = jlx - 1` `elseif (jlx.eq.nx-1 .or. x.lt.onep) then` `c we tolerate a slight over-shoot of one (onep=1.00001),` `c perhaps due to roundoff or whatever, but not more than that.` `c keep at least 4 points >= jx` `jx = jlx - 2` `else` `print '(a,1pe12.4)', 'severe error: x > 1 in partonx6! x = ', x` `stop` `endif` `c ---------- note: jlx uniquely identifies the x-bin; jx does not.` `c this is the variable to be interpolated in` `ss = x*xpow` `const1 = 0.` `const2 = 0.` `const3 = 0.` `const4 = 0.` `const5 = 0.` `const6 = 0.` `sy2 = 0.` `sy3 = 0.` `s23 = 0.` `if (jlx.ge.2 .and. jlx.le.nx-2) then` `c initiation work for "interior bins": store the lattice points in s...` `svec1 = xvpow(jx)` `svec2 = xvpow(jx+1)` `svec3 = xvpow(jx+2)` `svec4 = xvpow(jx+3)` `s12 = svec1 - svec2` `s13 = svec1 - svec3` `s23 = svec2 - svec3` `s24 = svec2 - svec4` `s34 = svec3 - svec4` `sy2 = ss - svec2` `sy3 = ss - svec3` `c constants needed for interpolating in s at fixed t lattice points...` `const1 = s13/s23` `const2 = s12/s23` `const3 = s34/s23` `const4 = s24/s23` `s1213 = s12 + s13` `s2434 = s24 + s34` `sdet = s12s34 - s1213s2434` `tmp = sy2sy3/sdet` `const5 = (s34sy2-s2434sy3)tmp/s12` `const6 = (s1213sy2-s12sy3)tmp/s34` `endif` `c --------------now find lower end of interval containing q, i.e.,` `c get jq such that qv(jq) .le. q .le. qv(jq+1)...` `jlq = -1` `ju = nt+1` `12 if (ju-jlq .gt. 1) then` `jm = (ju+jlq) / 2` `if (tt .ge. tv(jm)) then` `jlq = jm` `else` `ju = jm` `endif` `goto 12` `endif` `if (jlq .le. 0) then` `jq = 0` `elseif (jlq .le. nt-2) then` `c keep q in the middle, as shown above` `jq = jlq - 1` `else` `c jlq .ge. nt-1 case: keep at least 4 points >= jq.` `jq = nt - 3` `endif` `c this is the interpolation variable in q` `tdet = 0.` `t12 = 0.` `t13 = 0.` `t23 = 0.` `t24 = 0.` `t34 = 0.` `ty2 = 0.` `ty3 = 0.` `tmp1 = 0.` `tmp2 = 0.` `if (jlq.ge.1 .and. jlq.le.nt-2) then` `c store the lattice points in t...` `tvec1 = tv(jq)` `tvec2 = tv(jq+1)` `tvec3 = tv(jq+2)` `tvec4 = tv(jq+3)` `t12 = tvec1 - tvec2` `t13 = tvec1 - tvec3` `t23 = tvec2 - tvec3` `t24 = tvec2 - tvec4` `t34 = tvec3 - tvec4` `ty2 = tt - tvec2` `ty3 = tt - tvec3` `tmp1 = t12 + t13` `tmp2 = t24 + t34` `tdet = t12t34 - tmp1tmp2` `endif` `c get the pdf function values at the lattice points...` `if (iprtn .ge. 3) then` `ip = - iprtn` `else` `ip = iprtn` `endif` `jtmp = ((ip + nfmx)(nt+1)+(jq-1))(nx+1)+jx+1` `do it = 1, nqvec` `j1 = jtmp + it(nx+1)` `if (jx .eq. 0) then` `c for the first 4 x points, interpolate x^2f(x,q)` `c this applies to the two lowest bins jlx = 0, 1` `c we can not put the jlx.eq.1 bin into the "interrior" section` `c (as we do for q), since upd(j1) is undefined.` `fij(1) = 0` `fij(2) = upd(j1+1) * xv(1)*2` `fij(3) = upd(j1+2) xv(2)*2` `fij(4) = upd(j1+3) xv(3)2` `c` `c use polint which allows x to be anywhere w.r.t. the grid` `call polint (xvpow(0), fij(1), 4, ss, fx, dfx)` `if (x .gt. 0d0) fvec(it) = fx / x2` `c pdf is undefined for x.eq.0` `elseif (jlx .eq. nx-1) then` `c this is the highest x bin:` `call polint (xvpow(nx-3), upd(j1), 4, ss, fx, dfx)` `fvec(it) = fx` `else` `c for all interior points, use jon's in-line function` `c this applied to (jlx.ge.2 .and. jlx.le.nx-2)` `sf2 = upd(j1+1)` `sf3 = upd(j1+2)` `g1 = sf2const1 - sf3const2` `g4 = -sf2const3 + sf3const4` `fvec(it) = (const5(upd(j1)-g1)` `& + const6(upd(j1+3)-g4)` `& + sf2sy3 - sf3sy2) / s23` `endif` `enddo` `c we now have the four values fvec(1:4)` `c interpolate in t...` `if (jlq .le. 0) then` `c 1st q-bin, as well as extrapolation to lower q` `call polint (tv(0), fvec(1), 4, tt, ff, dfq)` `elseif (jlq .ge. nt-1) then` `c last q-bin, as well as extrapolation to higher q` `call polint (tv(nt-3), fvec(1), 4, tt, ff, dfq)` `else` `c interrior bins : (jlq.ge.1 .and. jlq.le.nt-2)` `c which include jlq.eq.1 and jlq.eq.nt-2, since upd is defined for` `c the full range qv(0:nt) (in contrast to xv)` `tf2 = fvec(2)` `tf3 = fvec(3)` `g1 = ( tf2t13 - tf3t12) / t23` `g4 = (-tf2t34 + tf3t24) / t23` `h00 = ((t34ty2-tmp2ty3)(fvec(1)-g1)/t12` `& + (tmp1ty2-t12ty3)(fvec(4)-g4)/t34)` `ff = (h00ty2ty3/tdet + tf2ty3 - tf3ty2) / t23` `endif` `partonx6 = ff` `return` `end` `double precision function alpcteq(q2, naord)` `********************************************************************` ` ` ` the alpha_s routine. ` ` ` ` input : q2 = scale in gev*2 (not too low, of course); ` `* naord = 1 (lo), 2 (nlo). ` ` ` ` output: alphas_s/(4 pi) for use with the grv(98) partons. ` ` ` `****************************************************i**********` `` `implicit double precision (a - z)` `integer nf, k, i, naord` `dimension lambdal (3:6), lambdan (3:6), q2thr (3)` `` `...heavy quark thresholds and lambda values :` `data q2thr / 1.690, 20.25, 32400. /` `data lambdal / 0.247, 0.215, 0.1650, 0.0847 /` `data lambdan / 0.350, 0.326, 0.2260, 0.151 /` `` `...determination of the appropriate number of flavours :` `nf = 3` `do 10 k = 1, 3` `if (q2 .gt. q2thr (k)) then` `nf = nf + 1` `else` `go to 20` `end if` `10 continue` `` `...lo alpha_s and beta function for nlo calculation :` `20 b0 = 11.- 2./3.* nf` `b1 = 102.- 38./3.* nf` `b10 = b1 / (b0b0)` `if (naord .eq. 1) then` `lam2 = lambdal (nf) lambdal (nf)` `alp = 1./(b0 * dlog (q2/lam2))` `go to 1` `else if (naord .eq. 2) then` `lam2 = lambdan (nf) * lambdan (nf)` `b1 = 102.- 38./3.* nf` `b10 = b1 / (b0b0)` `else` `write (6,91)` `91 format ('invalid choice for order in alpha_s')` `stop` `end if` `` `...start value for nlo iteration :` `lq2 = dlog (q2 / lam2)` `alp = 1./(b0lq2) * (1.- b10dlog(lq2)/lq2)` `` `...exact nlo value, found via newton procedure :` `do 2 i = 1, 6` `xl = dlog (1./(b0alp) + b10)` `xlp = dlog (1./(b0alp1.01) + b10)` `xlm = dlog (1./(b0alp0.99) + b10)` `y = lq2 - 1./ (b0alp) + b10 xl` `y1 = (- 1./ (b0alp1.01) + b10 * xlp` `1 + 1./ (b0alp0.99) - b10 * xlp) / (0.02d0alp)` `alp = alp - y/y1` `2 continue` `` `...output :` `1 alpcteq = alp` `return` `end` `c*****************************************************************` ` * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ` ` ` ` g r v - p r o t o n - p a r a m e t r i z a t i o n s ` ` ` ` 1998 update ` ` ` ` for a detailed explanation see ` ` m. glueck, e. reya, a. vogt : ` ` hep-ph/9806404 = do-th 98/07 = wue-itp-98-019 ` ` (to appear in eur. phys. j. c) ` ` ` ` this package contains subroutines returning the light-parton ` ` distributions in nlo (for the msbar and dis schemes) and lo; ` ` the respective light-parton, charm, and bottom contributions ` ` to f2(electromagnetic); and the scale dependence of alpha_s. ` ` ` ` the parton densities and f2 values are calculated from inter- ` ` polation grids covering the regions ` ` q^2/gev^2 between 0.8 and 1.e6 ( 1.e4 for f2 ) ` ` x between 1.e-9 and 1. ` ` any call outside these regions stops the program execution. ` ` ` ` at q^2 = mz^2, alpha_s reads 0.114 (0.125) in nlo (lo); the ` ` heavy quark thresholds, qh^2 = mh^2, in the beta function are ` ` mc = 1.4 gev, mb = 4.5 gev, mt = 175 gev. ` ` note that the nlo alpha_s running is different from grv(94). ` ` ` ` questions, comments etc to: avogt@physik.uni-wuerzburg.de ` ` ` ` * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ` `` `` `` `` `subroutine grv98pa (iset, x, q2, uv, dv, us, ds, ss, gl)` `*******************************************************************` ` ` ` the parton routine. ` ` __ ` ` input: iset = 1 (lo), 2 (nlo, ms), or 3 (nlo, dis) ` ` x = bjorken-x (between 1.e-9 and 1.) ` ` q2 = scale in gev*2 (between 0.8 and 1.e6) ` `* ` ` output: uv = u - u(bar), dv = d - d(bar), us = u(bar), ` ` ds = d(bar), ss = s = s(bar), gl = gluon. ` ` always x times the distribution is returned. ` ` ` ` common: the main program or the calling routine has to have ` ` a common block common / intinip / iinip , and the ` ` integer variable iinip has always to be zero when ` ` grv98pa is called for the first time or when iset ` ` has been changed. ` ` ` ` grids: 1. grv98lo.grid, 2. grv98nlm.grid, 3. grv98nld.grid, ` ` (1+1809 lines with 6 columns, 4 significant figures) ` ` ` `****************************************************i**********` `` `implicit double precision (a-h, o-z)` `parameter (npart=6, nx=68, nq=27, narg=2)` `dimension xuvf(nx,nq), xdvf(nx,nq), xdef(nx,nq), xudf(nx,nq),` `1 xsf(nx,nq), xgf(nx,nq), parton (npart,nq,nx-1),` `2 qs(nq), xb(nx), xt(narg), na(narg), arrf(nx+nq)` `character80 line` `common /intinip/iinip` `save xuvf, xdvf, xdef, xudf, xsf, xgf, na, arrf` `` `...bjorken-x and q2 values of the grid :` `data qs / 0.8e0,` `1 1.0e0, 1.3e0, 1.8e0, 2.7e0, 4.0e0, 6.4e0,` `2 1.0e1, 1.6e1, 2.5e1, 4.0e1, 6.4e1,` `3 1.0e2, 1.8e2, 3.2e2, 5.7e2,` `4 1.0e3, 1.8e3, 3.2e3, 5.7e3,` `5 1.0e4, 2.2e4, 4.6e4,` `6 1.0e5, 2.2e5, 4.6e5,` `7 1.e6 /` `data xb / 1.0e-9, 1.8e-9, 3.2e-9, 5.7e-9,` `a 1.0e-8, 1.8e-8, 3.2e-8, 5.7e-8,` `b 1.0e-7, 1.8e-7, 3.2e-7, 5.7e-7,` `c 1.0e-6, 1.4e-6, 2.0e-6, 3.0e-6, 4.5e-6, 6.7e-6,` `1 1.0e-5, 1.4e-5, 2.0e-5, 3.0e-5, 4.5e-5, 6.7e-5,` `2 1.0e-4, 1.4e-4, 2.0e-4, 3.0e-4, 4.5e-4, 6.7e-4,` `3 1.0e-3, 1.4e-3, 2.0e-3, 3.0e-3, 4.5e-3, 6.7e-3,` `4 1.0e-2, 1.4e-2, 2.0e-2, 3.0e-2, 4.5e-2, 0.06, 0.08,` `5 0.1, 0.125, 0.15, 0.175, 0.2, 0.225, 0.25, 0.275,` `6 0.3, 0.325, 0.35, 0.375, 0.4, 0.45, 0.5, 0.55,` `7 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.95, 1. /` `` `...check of x and q2 values :` `if ( (x.lt.0.99d-9) .or. (x.gt.1.d0) ) then` `write(6,91)` `91 format (2x,'parton interpolation: x out of range')` `stop` `endif` `if ( (q2.lt.0.799) .or. (q2.gt.1.01e6) ) then` `c write(6,92)` `c 92 format (2x,'parton interpolation: q2 out of range')` `q2=1.0d6` `c stop` `endif` `if (iinip .ne. 0) goto 16` `` `...initialization, if required :` `` `* selection and reading of the grid :` `* (comment: first number in the first line of the grid)` `if (iset .eq. 1) then` `open (11,file='grv98lo.grid',status='old') ! 7.332e-05` `else if (iset .eq. 2) then` `open (11,file='grv98nlm.grid',status='old') ! 1.015e-04` `else if (iset .eq. 3) then` `open (11,file='grv98nld.grid',status='old') ! 1.238e-04` `else` `write(6,93)` `93 format (2x,'no or invalid parton set choice')` `stop` `end if` `iinip = 1` `read(11,89) line` `89 format(a80)` `do 15 m = 1, nx-1` `do 15 n = 1, nq` `read(11,90) parton(1,n,m), parton(2,n,m), parton(3,n,m),` `1 parton(4,n,m), parton(5,n,m), parton(6,n,m)` `90 format (6(1pe10.3))` `15 continue` `close(11)` `` `....arrays for the interpolation subroutine :` `do 10 iq = 1, nq` `do 20 ix = 1, nx-1` `xb0v = xb(ix)0.5` `xb0s = xb(ix)(-0.2)` `xb1 = 1.-xb(ix)` `xuvf(ix,iq) = parton(1,iq,ix) / (xb1*3 xb0v)` `xdvf(ix,iq) = parton(2,iq,ix) / (xb1*4 xb0v)` `xdef(ix,iq) = parton(3,iq,ix) / (xb1*7 xb0v)` `xudf(ix,iq) = parton(4,iq,ix) / (xb1*7 xb0s)` `xsf(ix,iq) = parton(5,iq,ix) / (xb1*7 xb0s)` `xgf(ix,iq) = parton(6,iq,ix) / (xb1*5 xb0s)` `20 continue` `xuvf(nx,iq) = 0.e0` `xdvf(nx,iq) = 0.e0` `xdef(nx,iq) = 0.e0` `xudf(nx,iq) = 0.e0` `xsf(nx,iq) = 0.e0` `xgf(nx,iq) = 0.e0` `10 continue` `na(1) = nx` `na(2) = nq` `do 30 ix = 1, nx` `arrf(ix) = dlog(xb(ix))` `30 continue` `do 40 iq = 1, nq` `arrf(nx+iq) = dlog(qs(iq))` `40 continue` `` `...continuation, if initialization was done previously.` `` `16 continue` `` `...interpolation :` `xt(1) = dlog(x)` `xt(2) = dlog(q2)` `x1 = 1.- x` `xv = x0.5` `xs = x(-0.2)` `uv = fint(narg,xt,na,arrf,xuvf) x1*3 xv` `dv = fint(narg,xt,na,arrf,xdvf) * x1*4 xv` `de = fint(narg,xt,na,arrf,xdef) * x1*7 xv` `ud = fint(narg,xt,na,arrf,xudf) * x1*7 xs` `us = 0.5 * (ud - de)` `ds = 0.5 * (ud + de)` `ss = fint(narg,xt,na,arrf,xsf) * x1*7 xs` `gl = fint(narg,xt,na,arrf,xgf) * x1*5 xs` `` `return` `end` `` `` `` `` `subroutine grv98f2 (iset, x, q2, f2l, f2c, f2b, f2)` `*******************************************************************` ` ` ` the f2 routine. ` ` ` ` input : iset = 1 (lo), 2 (nlo). ` ` x = bjorken-x (between 1.e-9 and 1.) ` ` q2 = scale in gev*2 (between 0.8 and 1.e4) ` `* ` ` output: f2l = f2(light), f2c = f2(charm), f2b = f2(bottom,) ` ` f2 = sum, all given for electromagnetic proton dis. ` ` ` ` common: the main program or the calling routine has to have ` ` a common block common / intinif / iinif , and the ` ` integer variable iinif has always to be zero when ` ` grv98f2 is called for the first time or when iset ` ` has been changed. ` ` ` ` grids: 1. grv98lof.grid, 2. grv98nlf.grid. ` ` (1+1407 lines with 3 columns, 4 significant figures) ` ` ` `****************************************************i**********` `` `implicit double precision (a-h, o-z)` `parameter (nstrf=3, nx=68, nq=21, narg=2)` `dimension xf2lf(nx,nq), xf2cf(nx,nq), xf2bf(nx,nq),` `1 strfct (nstrf,nq,nx-1), qs(nq), xb(nx),` `3 xt(narg), na(narg), arrf(nx+nq)` `character80 line` `common / intinif / iinif` `save xf2lf, xf2cf, xf2bf, na, arrf` `` `...bjorken-x and q2 values of the grid :` `data qs / 0.8e0,` `1 1.0e0, 1.3e0, 1.8e0, 2.7e0, 4.0e0, 6.4e0,` `2 1.0e1, 1.6e1, 2.5e1, 4.0e1, 6.4e1,` `3 1.0e2, 1.8e2, 3.2e2, 5.7e2,` `4 1.0e3, 1.8e3, 3.2e3, 5.7e3,` `5 1.0e4/` `data xb / 1.0e-9, 1.8e-9, 3.2e-9, 5.7e-9,` `a 1.0e-8, 1.8e-8, 3.2e-8, 5.7e-8,` `b 1.0e-7, 1.8e-7, 3.2e-7, 5.7e-7,` `c 1.0e-6, 1.4e-6, 2.0e-6, 3.0e-6, 4.5e-6, 6.7e-6,` `1 1.0e-5, 1.4e-5, 2.0e-5, 3.0e-5, 4.5e-5, 6.7e-5,` `2 1.0e-4, 1.4e-4, 2.0e-4, 3.0e-4, 4.5e-4, 6.7e-4,` `3 1.0e-3, 1.4e-3, 2.0e-3, 3.0e-3, 4.5e-3, 6.7e-3,` `4 1.0e-2, 1.4e-2, 2.0e-2, 3.0e-2, 4.5e-2, 0.06, 0.08,` `5 0.1, 0.125, 0.15, 0.175, 0.2, 0.225, 0.25, 0.275,` `6 0.3, 0.325, 0.35, 0.375, 0.4, 0.45, 0.5, 0.55,` `7 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.95, 1. /` `` `...check of x and q2 values :` `if ( (x.lt.0.99d-9) .or. (x.gt.1.d0) ) then` `write(6,91)` `91 format (2x,'str.fct. interpolation: x out of range')` `stop` `endif` `if ( (q2.lt.0.799) .or. (q2.gt.1.01e4) ) then` `write(6,92)` `92 format (2x,'str.fct. interpolation: q2 out of range')` `stop` `endif` `if (iinif .ne. 0) goto 16` `` `...initialization, if required :` `` `* selection and reading of the grid :` `* (comment: first number in the first line of the grid)` `if (iset .eq. 1) then` `open (11,file='grv98lof.grid',status='old') ! 7.907e-01` `else if (iset.eq.2) then` `open (11,file='grv98nlf.grid',status='old') ! 9.368e-01` `else` `write(6,93)` `93 format (2x,'no or invalid str.fct. set choice')` `stop` `end if` `iinif = 1` `read(11,89) line` `89 format(a80)` `do 15 m = 1, nx-1` `do 15 n = 1, nq` `read(11,90) strfct(1,n,m), strfct(2,n,m), strfct(3,n,m)` `90 format (3(1pe10.3))` `15 continue` `close(11)` `` `....arrays for the interpolation subroutine :` `do 10 iq = 1, nq` `do 20 ix = 1, nx-1` `xbs = xb(ix)0.2` `xb1 = 1.-xb(ix)` `xf2lf(ix,iq) = strfct(1,iq,ix) / xb13 * xbs` `xf2cf(ix,iq) = strfct(2,iq,ix) / xb1*7 xbs` `xf2bf(ix,iq) = strfct(3,iq,ix) / xb1*7 xbs` `20 continue` `xf2lf(nx,iq) = 0.e0` `xf2cf(nx,iq) = 0.e0` `xf2bf(nx,iq) = 0.e0` `10 continue` `na(1) = nx` `na(2) = nq` `do 30 ix = 1, nx` `arrf(ix) = dlog(xb(ix))` `30 continue` `do 40 iq = 1, nq` `arrf(nx+iq) = dlog(qs(iq))` `40 continue` `` `...continuation, if initialization was done previously.` `` `16 continue` `` `...interpolation :` `xt(1) = dlog(x)` `xt(2) = dlog(q2)` `x1 = 1.- x` `xs = x(-0.2)` `f2l = fint(narg,xt,na,arrf,xf2lf) x1*3 xs` `f2c = fint(narg,xt,na,arrf,xf2cf) * x1*7 xs` `f2b = fint(narg,xt,na,arrf,xf2bf) * x1*7 xs` `f2 = f2l + f2c + f2b` `` `return` `end` `` `` `double precision function fint(narg,arg,nent,ent,table)` `*******************************************************************` ` ` ` the interpolation routine (cern library routine e104) ` ` ` `*******************************************************************` `implicit double precision (a-h, o-z)` `dimension arg(narg),nent(narg),ent(),table()` `dimension d(5),ncomb(5),ient(5)` `kd=1` `m=1` `ja=1` `do 5 ii=1,narg` `ncomb(ii)=1` `jb=ja-1+nent(ii)` `do 2 j=ja,jb` `if (arg(ii).le.ent(j)) go to 3` `2 continue` `j=jb` `3 if (j.ne.ja) go to 4` `j=j+1` `4 jr=j-1` `d(ii)=(ent(j)-arg(ii))/(ent(j)-ent(jr))` `ient(ii)=j-ja` `kd=kd+ient(ii)m` `m=mnent(ii)` `ja=jb+1` `5 continue` `fint=0.` `10 fac=1.` `iadr=kd` `ifadr=1` `do 15 i=1,narg` `if (ncomb(i).eq.0) go to 12` `fac=fac(1.-d(i))` `go to 15` `12 fac=facd(i)` `iadr=iadr-ifadr` `ifadr=ifadrnent(i)` `15 continue` `fint=fint+factable(iadr)` `il=narg` `40 if (ncomb(il).eq.0) go to 80` `ncomb(il)=0` `if (il.eq.narg) go to 10` `il=il+1` `do 50 k=il,narg` `50 ncomb(k)=1` `go to 10` `80 il=il-1` `if(il.ne.0) go to 40` `return` `end` `` `` `double precision function alpgrv(q2, naord)` `*******************************************************************` ` ` ` the alpha_s routine. ` ` ` ` input : q2 = scale in gev*2 (not too low, of course); ` `* naord = 1 (lo), 2 (nlo). ` ` ` ` output: alphas_s/(4 pi) for use with the grv(98) partons. ` ` ` `****************************************************i**********` `` `implicit double precision (a - z)` `integer nf, k, i, naord` `dimension lambdal (3:6), lambdan (3:6), q2thr (3)` `` `...heavy quark thresholds and lambda values :` `data q2thr / 1.960, 20.25, 30625. /` `data lambdal / 0.2041, 0.1750, 0.1320, 0.0665 /` `data lambdan / 0.2994, 0.2460, 0.1677, 0.0678 /` `` `...determination of the appropriate number of flavours :` `nf = 3` `do 10 k = 1, 3` `if (q2 .gt. q2thr (k)) then` `nf = nf + 1` `else` `go to 20` `end if` `10 continue` `` `...lo alpha_s and beta function for nlo calculation :` `20 b0 = 11.- 2./3.* nf` `b1 = 102.- 38./3.* nf` `b10 = b1 / (b0b0)` `if (naord .eq. 1) then` `lam2 = lambdal (nf) lambdal (nf)` `alp = 1./(b0 * dlog (q2/lam2))` `go to 1` `else if (naord .eq. 2) then` `lam2 = lambdan (nf) * lambdan (nf)` `b1 = 102.- 38./3.* nf` `b10 = b1 / (b0b0)` `else` `write (6,91)` `91 format ('invalid choice for order in alpha_s')` `stop` `end if` `` `...start value for nlo iteration :` `lq2 = dlog (q2 / lam2)` `alp = 1./(b0lq2) * (1.- b10dlog(lq2)/lq2)` `` `...exact nlo value, found via newton procedure :` `do 2 i = 1, 6` `xl = dlog (1./(b0alp) + b10)` `xlp = dlog (1./(b0alp1.01) + b10)` `xlm = dlog (1./(b0alp0.99) + b10)` `y = lq2 - 1./ (b0alp) + b10 xl` `y1 = (- 1./ (b0alp1.01) + b10 * xlp` `1 + 1./ (b0alp0.99) - b10 * xlp) / (0.02d0alp)` `alp = alp - y/y1` `2 continue` `` `...output :` `1 alpgrv = alp` `return` `end` `c****************************************************************` `subroutine mrstlo(x,q,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 real8(a-h,o-z)` `data xmin,xmax,qsqmin,qsqmax/1d-5,1d0,1.25d0,1d7/` `q2=qq` `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` `c 99 format(' warning: q^2 value is out of range ','q2= ',e10.5)` `c 98 format(' warning: x value is out of range ','x= ',e10.5)` `return` `end` `c******************************************************` `subroutine mrst1(x,qsq,upv,dnv,usea,dsea,str,chm,bot,glu)` `implicit real8(a-h,o-z)` `parameter(nx=49,nq=37,np=8,nqc0=2,nqb0=11,nqc=35,nqb=26)` `real8 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)` `real8 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)` `real8 xxl(nx),qql(nq),qqlc(nqc),qqlb(nqb)` `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='lo2002.dat',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=val 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` `close(33)` `return` `50 format(8f10.5)` `end` `c**********************************************` `subroutine jeppe1(nx,my,xx,yy,ff,cc)` `implicit real8(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),` `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=d1d2` `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` `c*************************************` `subroutine jeppe2(x,y,nx,my,xx,yy,cc,z)` `implicit real8(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=tz+((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` `c*************************************` `integer function locx(xx,nx,x)` `implicit real8(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` `c******************************************` `real8 function polderiv(x1,x2,x3,y1,y2,y3)` `implicit real8(a-h,o-z)` `polderiv=(x3x3(y1-y2)-2.0x2(x3(y1-y2)+x1` `.(y2-y3))+x2x2(y1-y3)+x1x1(y2-y3))/((x1-x2)(x1-x3)(x2-x3))` `return` `end` `c************************************************` `double precision function alpmsrt(scale,lambda,iorder)` `c.` `c. the qcd coupling used in the mrs analysis.` `c. automatically corrects for nf=3,4,5 with thresholds at m_q.` `c. the following parameters must be supplied:` `c. scale = the qcd scale in gev (real)` `c. lambda = the 4 flavour msbar lambda parameter in gev (real)` `c. iorder = 0 for lo, 1 for nlo and 2 for nnlo` `c.` `implicit real8 (a-h,o-z)` `real8 lambda` `data tol,qsct,qsdt/5d-4,74d0,8.18d0/` `c-ap initialize to avoid compiler warnings` `alpmsrt =0.` `pi=4d0datan(1d0)` `iord=iorder` `ith=0` `flav=4d0` `al=lambda` `al2=lambdalambda` `qs=scalescale` `t=dlog(qs/al2)` `tt=t` `c.` `qsctt=qsct/4.` `qsdtt=qsdt/4.` `if(qs.lt.0.5d0) then !! running stops below 0.5` `qs=0.5d0` `t=dlog(qs/al2)` `tt=t` `endif` `alfqc5=0.` `alfqc4=0.` `alfqc3=0.` `if(qs.gt.qsctt) go to 12` `if(qs.lt.qsdtt) go to 312` `11 continue` `b0=11-2.flav/3.` `x1=4.pi/b0` `5 continue` `if(iord.eq.0) then` `alpmsrt=x1/t` `elseif(iord.eq.1) then` `b1=102.-38.flav/3.` `x2=b1/b02` `as2=x1/t(1.-x2dlog(t)/t)` `95 as=as2` `f=-t+x1/as-x2dlog(x1/as+x2)` `fp=-x1/as*2(1.-x2/(x1/as+x2))` `as2=as-f/fp` `del=abs(f/fp/as)` `if((del-tol).gt.0.) go to 95` `alpmsrt=as2` `elseif(iord.eq.2) then` `alpmsrt=qwikalf(t,2,flav)` `endif` `if(ith.eq.0) return` `go to (13,14,15) ith` `print , 'here'` `go to 5` `12 ith=1` `t=dlog(qsctt/al2)` `go to 11` `13 alfqc4=alpmsrt` `flav=5.` `ith=2` `go to 11` `14 alfqc5=alpmsrt` `ith=3` `t=tt` `go to 11` `15 alfqs5=alpmsrt` `alfinv=1./alfqs5+1./alfqc4-1./alfqc5` `alpmsrt=1./alfinv` `return` `311 continue` `b0=11-2.flav/3.` `x1=4.pi/b0` `if(iord.eq.0) then` `alpmsrt=x1/t` `elseif(iord.eq.1) then` `b1=102.-38.flav/3.` `x2=b1/b0*2` `as2=x1/t(1.-x2dlog(t)/t)` `35 as=as2` `f=-t+x1/as-x2dlog(x1/as+x2)` `fp=-x1/as*2(1.-x2/(x1/as+x2))` `as2=as-f/fp` `del=abs(f/fp/as)` `if((del-tol).gt.0.) go to 35` `elseif(iord.eq.2) then` `alpmsrt=qwikalf(t,2,flav)` `endif` `if(ith.eq.0) return` `go to (313,314,315) ith` `312 ith=1` `t=dlog(qsdtt/al2)` `go to 311` `313 alfqc4=alpmsrt` `flav=3.` `ith=2` `go to 311` `314 alfqc3=alpmsrt` `ith=3` `t=tt` `go to 311` `315 alfqs3=alpmsrt` `alfinv=1./alfqs3+1./alfqc4-1./alfqc3` `alpmsrt=1./alfinv` `return` `end` `c**********************************` `double precision function qwikalf(t,iord,flav)` `implicit real8(a-h,o-z)` `dimension z3(6),z4(6),z5(6),zz3(6),zz4(6),zz5(6)` `data z3/ -.161667e+01,0.954244e+01,` `.0.768623e+01,0.101523e+00,-.360127e-02,0.457867e-04/` `data z4/ -.172239e+01,0.831185e+01,` `.0.721463e+01,0.835531e-01,-.285436e-02,0.349129e-04/` `data z5/ -.872190e+00,0.572816e+01,` `.0.716119e+01,0.195884e-01,-.300199e-03,0.151741e-05/` `data zz3/-.155611e+02,0.168406e+02,` `.0.603014e+01,0.257682e+00,-.970217e-02,0.127628e-03/` `data zz4/-.106762e+02,0.118497e+02,0.664964e+01,` `.0.112996e+00,-.317551e-02,0.302434e-04/` `data zz5/-.531860e+01,0.708503e+01,0.698352e+01,` `.0.274170e-01,-.426894e-03,0.217591e-05/` `data pi/3.14159/` `nfm2=flav-2.` `x=dsqrt(t)` `x2=xx` `x3=xx2` `x4=xx3` `x5=xx4` `go to (1,2) iord !!iord change!!` `1 go to (3,4,5) nfm2` `3 y=z3(1)+z3(2)x+z3(3)x2+z3(4)x3+z3(5)x4+z3(6)x5` `go to 10` `4 y=z4(1)+z4(2)x+z4(3)x2+z4(4)x3+z4(5)x4+z4(6)x5` `go to 10` `5 y=z5(1)+z5(2)x+z5(3)x2+z5(4)x3+z5(5)x4+z5(6)x5` `go to 10` `2 go to (6,7,8) nfm2` `6 y=zz3(1)+zz3(2)x+zz3(3)x2+zz3(4)x3+zz3(5)x4+zz3(6)x5` `go to 10` `7 y=zz4(1)+zz4(2)x+zz4(3)x2+zz4(4)x3+zz4(5)x4+zz4(6)x5` `go to 10` `8 y=zz5(1)+zz5(2)x+zz5(3)x2+zz5(4)x3+zz5(5)x4+zz5(6)x5` `go to 10` `10 qwikalf=4.*pi/y` `return` `end`

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c============================================================================
c                             april 10, 2002, v6.01
c                             february 23, 2003, v6.1
c
c   ref[1]: "new generation of parton distributions with uncertainties from global qcd analysis"
c       by: j. pumplin, d.r. stump, j.huston, h.l. lai, p. nadolsky, w.k. tung
c       jhep 0207:012(2002), hep-ph/0201195
c
c   ref[2]: "inclusive jet production, parton distributions, and the search for new physics"
c       by : d. stump, j. huston, j. pumplin, w.k. tung, h.l. lai, s. kuhlmann, j. owens
c       hep-ph/0303013
c
c   this package contains
c   (1) 4 standard sets of cteq6 pdf's (cteq6m, cteq6d, cteq6l, cteq6l1) ;
c   (2) 40 up/down sets (with respect to cteq6m) for uncertainty studies from ref[1];
c   (3) updated version of the above: cteq6.1m and its 40 up/down eigenvector sets from ref[2].
c
c  the cteq6.1m set provides a global fit that is almost equivalent in every respect
c  to the published cteq6m, ref[1], although some parton distributions (e.g., the gluon)
c  may deviate from cteq6m in some kinematic ranges by amounts that are well within the
c  specified uncertainties.
c  the more significant improvements of the new version are associated with some of the
c  40 eigenvector sets, which are made more symmetrical and reliable in (3), compared to (2).

c  details about calling convention are:
c ---------------------------------------------------------------------------
c  iset   pdf-set     description       alpha_s(mz)**lam4  lam5   table_file
c ===========================================================================
c standard, "best-fit", sets:
c --------------------------
c   1    cteq6m   standard msbar scheme   0.118     326   226    cteq6m.tbl
c   2    cteq6d   standard dis scheme     0.118     326   226    cteq6d.tbl
c   3    cteq6l   leading order           0.118**   326** 226    cteq6l.tbl
c   4    cteq6l1  leading order           0.130**   215** 165    cteq6l1.tbl
c ============================================================================
c for uncertainty calculations using eigenvectors of the hessian:
c ---------------------------------------------------------------
c     central + 40 up/down sets along 20 eigenvector directions
c                             -----------------------------
c                original version, ref[1]:  central fit: cteq6m (=cteq6m.00)
c                             -----------------------
c  1xx  cteq6m.xx  +/- sets               0.118     326   226    cteq6m1xx.tbl
c        where xx = 01-40: 01/02 corresponds to +/- for the 1st eigenvector, ... etc.
c        e.g. 100      is cteq6m.00 (=cteq6m),
c             101/102 are cteq6m.01/02, +/- sets of 1st eigenvector, ... etc.
c                              -----------------------
c                updated version, ref[2]:  central fit: cteq6.1m (=cteq61.00)
c                              -----------------------
c  2xx  cteq61.xx  +/- sets               0.118     326   226    ctq61.xx.tbl
c        where xx = 01-40: 01/02 corresponds to +/- for the 1st eigenvector, ... etc.
c        e.g. 200      is cteq61.00 (=cteq6.1m),
c             201/202 are cteq61.01/02, +/- sets of 1st eigenvector, ... etc.
c ===========================================================================
c   ** all fits are obtained by using the same coupling strength
c   \alpha_s(mz)=0.118 and the nlo running \alpha_s formula, except cteq6l1
c   which uses the lo running \alpha_s and its value determined from the fit.
c   for the lo fits, the evolution of the pdf and the hard cross sections are
c   calculated at lo.  more detailed discussions are given in the references.
c
c   the table grids are generated for 10^-6 < x < 1 and 1.3 < q < 10,000 (gev).
c   pdf values outside of the above range are returned using extrapolation.
c   lam5 (lam4) represents lambda value (in mev) for 5 (4) flavors.
c   the matching alpha_s between 4 and 5 flavors takes place at q=4.5 gev,
c   which is defined as the bottom quark mass, whenever it can be applied.
c
c   the table_files are assumed to be in the working directory.
c
c   before using the pdf, it is necessary to do the initialization by
c       call setctq6(iset)
c   where iset is the desired pdf specified in the above table.
c
c   the function ctq6pdf (iparton, x, q)
c   returns the parton distribution inside the proton for parton [iparton]
c   at [x] bjorken_x and scale [q] (gev) in pdf set [iset].
c   iparton  is the parton label (5, 4, 3, 2, 1, 0, -1, ......, -5)
c                            for (b, c, s, d, u, g, u_bar, ..., b_bar),
c
c   for detailed information on the parameters used, e.q. quark masses,
c   qcd lambda, ... etc.,  see info lines at the beginning of the
c   table_files.
c
c   these programs, as provided, are in double precision.  by removing the
c   "implicit double precision" lines, they can also be run in single
c   precision.
c
c   if you have detailed questions concerning these cteq6 distributions,
c   or if you find problems/bugs using this package, direct inquires to
c   pumplin@pa.msu.edu or tung@pa.msu.edu.
c
c===========================================================================

      double precision function ctq6pdf (iparton, x, q)
      implicit double precision (a-h,o-z)
      logical warn
      common
     > / ctqpar2 / nx, nt, nfmx
     > / qcdtable /  alambda, nfl, iorder

      data warn /.true./
      save warn

      if (x .lt. 0d0 .or. x .gt. 1d0) then
        print *, 'x out of range in ctq6pdf: ', x
        stop
      endif
      if (q .lt. alambda) then
        print *, 'q out of range in ctq6pdf: ', q
        stop
      endif
      if ((iparton .lt. -nfmx .or. iparton .gt. nfmx)) then
         if (warn) then
c        put a warning for calling extra flavor.
             warn = .false.
             print *, 'warning: iparton out of range in ctq6pdf! '
             print *, 'iparton, mxflvn0: ', iparton, nfmx
         endif
         ctq6pdf = 0d0
         return
      endif

      ctq6pdf = partonx6 (iparton, x, q)

      if(ctq6pdf.lt.1.0d-16)  ctq6pdf = 0.0d0

      return

c                             ********************
      end

      subroutine setctq6 (iset)
      implicit double precision (a-h,o-z)
      parameter (isetmax0=5)
      character flnm(isetmax0)*6, nn*3, tablefile*140
      data (flnm(i), i=1,isetmax0)
     > / 'cteq6m', 'cteq6d', 'cteq6l', 'cteq6l','ctq61.'/
      data isetold, isetmin0, isetmin1, isetmax1 /-987,1,100,140/
      data isetmin2,isetmax2 /200,240/
      save
c             if data file not initialized, do so.
      character cmsdir*82
      call getenv('CMSSW_BASE',cmsdir)
      kspace=index(cmsdir,' ')
      if(iset.ne.isetold) then
         iu= nextun()
         if (iset.ge.isetmin0 .and. iset.le.3) then
            tablefile=cmsdir(1:kspace-1)
     $           //'/src/GeneratorInterface/GenExtensions/data/'
     $           //flnm(iset)//'.tbl'
         elseif (iset.eq.4) then
            tablefile=cmsdir(1:kspace-1)
     $           //'/src/GeneratorInterface/GenExtensions/data/'
     $           //flnm(iset)//'1.tbl'
         elseif (iset.ge.isetmin1 .and. iset.le.isetmax1) then
            write(nn,'(i3)') iset
            tablefile=cmsdir(1:kspace-1)
     $           //'/src/GeneratorInterface/GenExtensions/data/'
     $           //flnm(1)//nn//'.tbl'
         elseif (iset.ge.isetmin2 .and. iset.le.isetmax2) then
            write(nn,'(i3)') iset
            tablefile=cmsdir(1:kspace-1)
     $           //'/src/GeneratorInterface/GenExtensions/data/'
     $           //flnm(5)//nn(2:3)//'.tbl'
         else
            print *, 'invalid iset number in setctq6 :', iset
            stop
         endif
c        print *, 'pdf file ', tablefile	 
         open(iu, file=tablefile, status='old', err=100)
         call readtbl (iu)
         close (iu)
         isetold=iset
      endif
      return

 100  print *, ' data file ', tablefile, ' cannot be opened '
     >//'in setctq6!!'
      stop
c                             ********************
      end

      subroutine readtbl (nu)
      implicit double precision (a-h,o-z)
      character line*80
      parameter (mxx = 96, mxq = 20, mxf = 5)
      parameter (mxpqx = (mxf + 3) * mxq * mxx)
      common
     > / ctqpar1 / al, xv(0:mxx), tv(0:mxq), upd(mxpqx)
     > / ctqpar2 / nx, nt, nfmx
     > / xqrange / qini, qmax, xmin
     > / qcdtable /  alambda, nfl, iorder
     > / masstbl / amass(6)

      read  (nu, '(a)') line
      read  (nu, '(a)') line
      read  (nu, *) dr, fl, al, (amass(i),i=1,6)
      iorder = nint(dr)
      nfl = nint(fl)
      alambda = al

      read  (nu, '(a)') line
      read  (nu, *) nx,  nt, nfmx

      read  (nu, '(a)') line
      read  (nu, *) qini, qmax, (tv(i), i =0, nt)

      read  (nu, '(a)') line
      read  (nu, *) xmin, (xv(i), i =0, nx)

      do 11 iq = 0, nt
         tv(iq) = log(log (tv(iq) /al))
   11 continue
c
c                  since quark = anti-quark for nfl>2 at this stage,
c                  we read  out only the non-redundent data points
c     no of flavors = nfmx (sea) + 1 (gluon) + 2 (valence)

      nblk = (nx+1) * (nt+1)
      npts =  nblk  * (nfmx+3)
      read  (nu, '(a)') line
      read  (nu, *, iostat=iret) (upd(i), i=1,npts)

      return
c                        ****************************
      end

      function nextun()
c                                 returns an unallocated fortran i/o unit.
      logical ex
c
      do 10 n = 10, 300
         inquire (unit=n, opened=ex)
         if (.not. ex) then
            nextun = n
            return
         endif
 10   continue
      stop ' there is no available i/o unit. '
c               *************************
      end
c

      subroutine polint (xa,ya,n,x,y,dy)

      implicit double precision (a-h, o-z)
c                                        adapted from "numerical recipes"
      parameter (nmax=10)
      dimension xa(n),ya(n),c(nmax),d(nmax)
      ns=1
      dif=abs(x-xa(1))
      do 11 i=1,n
        dift=abs(x-xa(i))
        if (dift.lt.dif) then
          ns=i
          dif=dift
        endif
        c(i)=ya(i)
        d(i)=ya(i)
11    continue
      y=ya(ns)
      ns=ns-1
      do 13 m=1,n-1
        do 12 i=1,n-m
          ho=xa(i)-x
          hp=xa(i+m)-x
          w=c(i+1)-d(i)
          den=ho-hp
c pause is not supported anymore
c          if(den.eq.0.)pause
          if (den.eq.0.) then
            WRITE (*,*) 'den is 0'
            READ (*,'()')
          endif
          den=w/den
          d(i)=hp*den
          c(i)=ho*den
12      continue
        if (2*ns.lt.n-m)then
          dy=c(ns+1)
        else
          dy=d(ns)
          ns=ns-1
        endif
        y=y+dy
13    continue
      return
      end

      double precision function partonx6 (iprtn, xx, qq)

c  given the parton distribution function in the array u in
c  common / pevldt / , this routine interpolates to find
c  the parton distribution at an arbitray point in x and q.
c
      implicit double precision (a-h,o-z)

      parameter (mxx = 96, mxq = 20, mxf = 5)
      parameter (mxqx= mxq * mxx,   mxpqx = mxqx * (mxf+3))

      common
     > / ctqpar1 / al, xv(0:mxx), tv(0:mxq), upd(mxpqx)
     > / ctqpar2 / nx, nt, nfmx
     > / xqrange / qini, qmax, xmin

      dimension fvec(4), fij(4)
      dimension xvpow(0:mxx)
      data onep / 1.00001 /
      data xpow / 0.3d0 /       !**** choice of interpolation variable
      data nqvec / 4 /
      data ientry / 0 /
      save ientry,xvpow

c store the powers used for interpolation on first call...
      if(ientry .eq. 0) then
         ientry = 1

         xvpow(0) = 0d0
         do i = 1, nx
            xvpow(i) = xv(i)**xpow
         enddo
      endif

      x = xx
      q = qq
      tt = log(log(q/al))

c      -------------    find lower end of interval containing x, i.e.,
c                       get jx such that xv(jx) .le. x .le. xv(jx+1)...
      jlx = -1
      ju = nx+1
 11   if (ju-jlx .gt. 1) then
         jm = (ju+jlx) / 2
         if (x .ge. xv(jm)) then
            jlx = jm
         else
            ju = jm
         endif
         goto 11
      endif
c                     ix    0   1   2      jx  jlx         nx-2     nx
c                           |---|---|---|...|---|-x-|---|...|---|---|
c                     x     0  xmin               x                 1
c
      if     (jlx .le. -1) then
        print '(a,1pe12.4)', 'severe error: x <= 0 in partonx6! x = ', x
        stop
      elseif (jlx .eq. 0) then
         jx = 0
      elseif (jlx .le. nx-2) then

c                for interrior points, keep x in the middle, as shown above
         jx = jlx - 1
      elseif (jlx.eq.nx-1 .or. x.lt.onep) then

c                  we tolerate a slight over-shoot of one (onep=1.00001),
c              perhaps due to roundoff or whatever, but not more than that.
c                                      keep at least 4 points >= jx
         jx = jlx - 2
      else
        print '(a,1pe12.4)', 'severe error: x > 1 in partonx6! x = ', x
        stop
      endif
c          ---------- note: jlx uniquely identifies the x-bin; jx does not.

c                       this is the variable to be interpolated in
      ss = x**xpow

      const1 = 0.
      const2 = 0.
      const3 = 0.
      const4 = 0.
      const5 = 0.
      const6 = 0.
      sy2 = 0.
      sy3 = 0.
      s23 = 0.

      if (jlx.ge.2 .and. jlx.le.nx-2) then

c     initiation work for "interior bins": store the lattice points in s...
      svec1 = xvpow(jx)
      svec2 = xvpow(jx+1)
      svec3 = xvpow(jx+2)
      svec4 = xvpow(jx+3)

      s12 = svec1 - svec2
      s13 = svec1 - svec3
      s23 = svec2 - svec3
      s24 = svec2 - svec4
      s34 = svec3 - svec4

      sy2 = ss - svec2
      sy3 = ss - svec3

c constants needed for interpolating in s at fixed t lattice points...
      const1 = s13/s23
      const2 = s12/s23
      const3 = s34/s23
      const4 = s24/s23
      s1213 = s12 + s13
      s2434 = s24 + s34
      sdet = s12*s34 - s1213*s2434
      tmp = sy2*sy3/sdet
      const5 = (s34*sy2-s2434*sy3)*tmp/s12
      const6 = (s1213*sy2-s12*sy3)*tmp/s34

      endif

c         --------------now find lower end of interval containing q, i.e.,
c                          get jq such that qv(jq) .le. q .le. qv(jq+1)...
      jlq = -1
      ju = nt+1
 12   if (ju-jlq .gt. 1) then
         jm = (ju+jlq) / 2
         if (tt .ge. tv(jm)) then
            jlq = jm
         else
            ju = jm
         endif
         goto 12
       endif

      if     (jlq .le. 0) then
         jq = 0
      elseif (jlq .le. nt-2) then
c                                  keep q in the middle, as shown above
         jq = jlq - 1
      else
c                         jlq .ge. nt-1 case:  keep at least 4 points >= jq.
        jq = nt - 3

      endif
c                                   this is the interpolation variable in q

      tdet = 0.
      t12 = 0.
      t13 = 0.
      t23 = 0.
      t24 = 0.
      t34 = 0.
      ty2 = 0.
      ty3 = 0.
      tmp1 = 0.
      tmp2 = 0.

	
      if (jlq.ge.1 .and. jlq.le.nt-2) then
c                                        store the lattice points in t...
      tvec1 = tv(jq)
      tvec2 = tv(jq+1)
      tvec3 = tv(jq+2)
      tvec4 = tv(jq+3)

      t12 = tvec1 - tvec2
      t13 = tvec1 - tvec3
      t23 = tvec2 - tvec3
      t24 = tvec2 - tvec4
      t34 = tvec3 - tvec4

      ty2 = tt - tvec2
      ty3 = tt - tvec3

      tmp1 = t12 + t13
      tmp2 = t24 + t34

      tdet = t12*t34 - tmp1*tmp2

      endif


c get the pdf function values at the lattice points...

      if (iprtn .ge. 3) then
         ip = - iprtn
      else
         ip = iprtn
      endif
      jtmp = ((ip + nfmx)*(nt+1)+(jq-1))*(nx+1)+jx+1

      do it = 1, nqvec

         j1  = jtmp + it*(nx+1)

       if (jx .eq. 0) then
c                          for the first 4 x points, interpolate x^2*f(x,q)
c                           this applies to the two lowest bins jlx = 0, 1
c            we can not put the jlx.eq.1 bin into the "interrior" section
c                           (as we do for q), since upd(j1) is undefined.
         fij(1) = 0
         fij(2) = upd(j1+1) * xv(1)**2
         fij(3) = upd(j1+2) * xv(2)**2
         fij(4) = upd(j1+3) * xv(3)**2
c
c                 use polint which allows x to be anywhere w.r.t. the grid

         call polint (xvpow(0), fij(1), 4, ss, fx, dfx)

         if (x .gt. 0d0)  fvec(it) =  fx / x**2
c                                              pdf is undefined for x.eq.0
       elseif  (jlx .eq. nx-1) then
c                                                this is the highest x bin:

        call polint (xvpow(nx-3), upd(j1), 4, ss, fx, dfx)

        fvec(it) = fx

       else
c                       for all interior points, use jon's in-line function
c                              this applied to (jlx.ge.2 .and. jlx.le.nx-2)
         sf2 = upd(j1+1)
         sf3 = upd(j1+2)

         g1 =  sf2*const1 - sf3*const2
         g4 = -sf2*const3 + sf3*const4

         fvec(it) = (const5*(upd(j1)-g1)
     &               + const6*(upd(j1+3)-g4)
     &               + sf2*sy3 - sf3*sy2) / s23

       endif

      enddo
c                                   we now have the four values fvec(1:4)
c     interpolate in t...

      if (jlq .le. 0) then
c                         1st q-bin, as well as extrapolation to lower q
        call polint (tv(0), fvec(1), 4, tt, ff, dfq)

      elseif (jlq .ge. nt-1) then
c                         last q-bin, as well as extrapolation to higher q
        call polint (tv(nt-3), fvec(1), 4, tt, ff, dfq)
      else
c                         interrior bins : (jlq.ge.1 .and. jlq.le.nt-2)
c       which include jlq.eq.1 and jlq.eq.nt-2, since upd is defined for
c                         the full range qv(0:nt)  (in contrast to xv)
        tf2 = fvec(2)
        tf3 = fvec(3)

        g1 = ( tf2*t13 - tf3*t12) / t23
        g4 = (-tf2*t34 + tf3*t24) / t23

        h00 = ((t34*ty2-tmp2*ty3)*(fvec(1)-g1)/t12
     &    +  (tmp1*ty2-t12*ty3)*(fvec(4)-g4)/t34)

        ff = (h00*ty2*ty3/tdet + tf2*ty3 - tf3*ty2) / t23
      endif

      partonx6 = ff

      return
      end

      double precision function alpcteq(q2, naord)
*********************************************************************
*                                                                   *
*   the alpha_s routine.                                            *
*                                                                   *
*   input :  q2    =  scale in gev**2  (not too low, of course);    *
*            naord =  1 (lo),  2 (nlo).                             *
*                                                                   *
*   output:  alphas_s/(4 pi) for use with the grv(98) partons.      *  
*                                                                   *
*******************************************************i*************
*
      implicit double precision (a - z)
      integer nf, k, i, naord
      dimension lambdal (3:6),  lambdan (3:6), q2thr (3)
*
*...heavy quark thresholds and lambda values :
      data q2thr   /  1.690,  20.25,  32400. /
      data lambdal /  0.247,  0.215,  0.1650, 0.0847  /
      data lambdan /  0.350, 0.326, 0.2260, 0.151 /
*
*...determination of the appropriate number of flavours :
      nf = 3
      do 10 k = 1, 3
      if (q2 .gt. q2thr (k)) then
         nf = nf + 1
      else
          go to 20
       end if
  10   continue
*
*...lo alpha_s and beta function for nlo calculation :
  20   b0 = 11.- 2./3.* nf
       b1 = 102.- 38./3.* nf
       b10 = b1 / (b0*b0)
       if (naord .eq. 1) then
         lam2 = lambdal (nf) * lambdal (nf)
         alp  = 1./(b0 * dlog (q2/lam2))
         go to 1
       else if (naord .eq. 2) then
         lam2 = lambdan (nf) * lambdan (nf)
         b1 = 102.- 38./3.* nf
         b10 = b1 / (b0*b0)
       else
         write (6,91)
  91     format ('invalid choice for order in alpha_s')
         stop
       end if
*
*...start value for nlo iteration :
       lq2 = dlog (q2 / lam2)
       alp = 1./(b0*lq2) * (1.- b10*dlog(lq2)/lq2)
*
*...exact nlo value, found via newton procedure :
       do 2 i = 1, 6
       xl  = dlog (1./(b0*alp) + b10)
       xlp = dlog (1./(b0*alp*1.01) + b10)
       xlm = dlog (1./(b0*alp*0.99) + b10)
       y  = lq2 - 1./ (b0*alp) + b10 * xl
       y1 = (- 1./ (b0*alp*1.01) + b10 * xlp
     1       + 1./ (b0*alp*0.99) - b10 * xlp) / (0.02d0*alp)
       alp = alp - y/y1
  2    continue
*
*...output :
  1    alpcteq = alp
       return
       end
c*******************************************************************
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
*                                                                   *
*     g r v  -  p r o t o n  - p a r a m e t r i z a t i o n s      *
*                                                                   *
*                          1998 update                              *
*                                                                   *
*                  for a detailed explanation see                   *
*                   m. glueck, e. reya, a. vogt :                   *
*        hep-ph/9806404  =  do-th 98/07  =  wue-itp-98-019          *
*                  (to appear in eur. phys. j. c)                   *
*                                                                   *
*   this package contains subroutines returning the light-parton    *
*   distributions in nlo (for the msbar and dis schemes) and lo;    * 
*   the respective light-parton, charm, and bottom contributions    *
*   to f2(electromagnetic); and the scale dependence of alpha_s.    *
*                                                                   *
*   the parton densities and f2 values are calculated from inter-   *
*   polation grids covering the regions                             *
*         q^2/gev^2  between   0.8   and  1.e6 ( 1.e4 for f2 )      *
*            x       between  1.e-9  and   1.                       *
*   any call outside these regions stops the program execution.     *
*                                                                   *
*   at q^2 = mz^2, alpha_s reads  0.114 (0.125) in nlo (lo); the    *
*   heavy quark thresholds, qh^2 = mh^2, in the beta function are   *
*            mc = 1.4 gev,  mb = 4.5 gev,  mt = 175 gev.            *
*   note that the nlo alpha_s running is different from grv(94).    * 
*                                                                   *
*    questions, comments etc to:  avogt@physik.uni-wuerzburg.de     *
*                                                                   *
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
*
*
*
*
      subroutine grv98pa (iset, x, q2, uv, dv, us, ds, ss, gl)
*********************************************************************
*                                                                   *
*   the parton routine.                                             *
*                                     __                            *
*   input:   iset =  1 (lo),  2 (nlo, ms), or  3 (nlo, dis)         *
*            x  =  bjorken-x        (between  1.e-9 and 1.)         *
*            q2 =  scale in gev**2  (between  0.8 and 1.e6)         *
*                                                                   *
*   output:  uv = u - u(bar),  dv = d - d(bar),  us = u(bar),       *
*            ds = d(bar),  ss = s = s(bar),  gl = gluon.            *
*            always x times the distribution is returned.           *
*                                                                   *
*   common:  the main program or the calling routine has to have    *
*            a common block  common / intinip / iinip , and the     *
*            integer variable  iinip  has always to be zero when    *
*            grv98pa is called for the first time or when  iset     *
*            has been changed.                                      *
*                                                                   *
*   grids:   1. grv98lo.grid, 2. grv98nlm.grid, 3. grv98nld.grid,   *
*            (1+1809 lines with 6 columns, 4 significant figures)   *
*                                                                   *
*******************************************************i*************
*
      implicit double precision (a-h, o-z)
      parameter (npart=6, nx=68, nq=27, narg=2)
      dimension xuvf(nx,nq), xdvf(nx,nq), xdef(nx,nq), xudf(nx,nq),
     1          xsf(nx,nq), xgf(nx,nq), parton (npart,nq,nx-1), 
     2          qs(nq), xb(nx), xt(narg), na(narg), arrf(nx+nq) 
      character*80 line
      common /intinip/iinip
	save xuvf, xdvf, xdef, xudf, xsf, xgf, na, arrf
*
*...bjorken-x and q**2 values of the grid :
       data qs / 0.8e0, 
     1           1.0e0, 1.3e0, 1.8e0, 2.7e0, 4.0e0, 6.4e0,
     2           1.0e1, 1.6e1, 2.5e1, 4.0e1, 6.4e1,
     3           1.0e2, 1.8e2, 3.2e2, 5.7e2,
     4           1.0e3, 1.8e3, 3.2e3, 5.7e3,
     5           1.0e4, 2.2e4, 4.6e4,
     6           1.0e5, 2.2e5, 4.6e5, 
     7           1.e6 /
       data xb / 1.0e-9, 1.8e-9, 3.2e-9, 5.7e-9, 
     a           1.0e-8, 1.8e-8, 3.2e-8, 5.7e-8, 
     b           1.0e-7, 1.8e-7, 3.2e-7, 5.7e-7, 
     c           1.0e-6, 1.4e-6, 2.0e-6, 3.0e-6, 4.5e-6, 6.7e-6,
     1           1.0e-5, 1.4e-5, 2.0e-5, 3.0e-5, 4.5e-5, 6.7e-5,
     2           1.0e-4, 1.4e-4, 2.0e-4, 3.0e-4, 4.5e-4, 6.7e-4,
     3           1.0e-3, 1.4e-3, 2.0e-3, 3.0e-3, 4.5e-3, 6.7e-3,
     4           1.0e-2, 1.4e-2, 2.0e-2, 3.0e-2, 4.5e-2, 0.06, 0.08,
     5           0.1, 0.125, 0.15, 0.175, 0.2, 0.225, 0.25, 0.275,
     6           0.3, 0.325, 0.35, 0.375, 0.4,  0.45, 0.5, 0.55,
     7           0.6, 0.65,  0.7,  0.75,  0.8,  0.85, 0.9, 0.95, 1. /
*
*...check of x and q2 values : 
      if ( (x.lt.0.99d-9) .or. (x.gt.1.d0) ) then
         write(6,91) 
  91     format (2x,'parton interpolation: x out of range')
         stop
      endif
      if ( (q2.lt.0.799) .or. (q2.gt.1.01e6) ) then
c         write(6,92) 
c  92     format (2x,'parton interpolation: q2 out of range')
         q2=1.0d6
c	   stop
      endif
      if (iinip .ne. 0) goto 16
*
*...initialization, if required :
*
*    selection and reading of the grid : 
*    (comment: first number in the first line of the grid)
      if (iset .eq. 1) then
        open (11,file='grv98lo.grid',status='old')   ! 7.332e-05
      else if (iset .eq. 2) then
        open (11,file='grv98nlm.grid',status='old')  ! 1.015e-04
      else if (iset .eq. 3) then
        open (11,file='grv98nld.grid',status='old')  ! 1.238e-04
      else
        write(6,93)
  93    format (2x,'no or invalid parton set choice')
        stop
      end if
      iinip = 1
      read(11,89) line
  89  format(a80)
      do 15 m = 1, nx-1 
      do 15 n = 1, nq
      read(11,90) parton(1,n,m), parton(2,n,m), parton(3,n,m), 
     1            parton(4,n,m), parton(5,n,m), parton(6,n,m) 
  90  format (6(1pe10.3))
  15  continue
      close(11)
*
*....arrays for the interpolation subroutine :
      do 10 iq = 1, nq
      do 20 ix = 1, nx-1
        xb0v = xb(ix)**0.5 
        xb0s = xb(ix)**(-0.2) 
        xb1 = 1.-xb(ix)
        xuvf(ix,iq) = parton(1,iq,ix) / (xb1**3 * xb0v)
        xdvf(ix,iq) = parton(2,iq,ix) / (xb1**4 * xb0v)
        xdef(ix,iq) = parton(3,iq,ix) / (xb1**7 * xb0v) 
        xudf(ix,iq) = parton(4,iq,ix) / (xb1**7 * xb0s)
        xsf(ix,iq)  = parton(5,iq,ix) / (xb1**7 * xb0s)
        xgf(ix,iq)  = parton(6,iq,ix) / (xb1**5 * xb0s)
  20  continue
        xuvf(nx,iq) = 0.e0
        xdvf(nx,iq) = 0.e0
        xdef(nx,iq) = 0.e0
        xudf(nx,iq) = 0.e0
        xsf(nx,iq)  = 0.e0
        xgf(nx,iq)  = 0.e0
  10  continue  
      na(1) = nx
      na(2) = nq
      do 30 ix = 1, nx
        arrf(ix) = dlog(xb(ix))
  30  continue
      do 40 iq = 1, nq
        arrf(nx+iq) = dlog(qs(iq))
  40  continue
*
*...continuation, if initialization was done previously.
*
  16  continue
*
*...interpolation :
      xt(1) = dlog(x)
      xt(2) = dlog(q2)
      x1 = 1.- x
      xv = x**0.5
      xs = x**(-0.2)
      uv = fint(narg,xt,na,arrf,xuvf) * x1**3 * xv
      dv = fint(narg,xt,na,arrf,xdvf) * x1**4 * xv
      de = fint(narg,xt,na,arrf,xdef) * x1**7 * xv
      ud = fint(narg,xt,na,arrf,xudf) * x1**7 * xs
      us = 0.5 * (ud - de)
      ds = 0.5 * (ud + de)
      ss = fint(narg,xt,na,arrf,xsf)  * x1**7 * xs
      gl = fint(narg,xt,na,arrf,xgf)  * x1**5 * xs 
*
      return
      end
*
*
*
*
      subroutine grv98f2 (iset, x, q2, f2l, f2c, f2b, f2)
*********************************************************************
*                                                                   *
*   the f2 routine.                                                 *
*                                                                   *
*   input :  iset = 1 (lo),  2 (nlo).                               *
*            x  =  bjorken-x        (between  1.e-9 and 1.)         *
*            q2 =  scale in gev**2  (between  0.8 and 1.e4)         *
*                                                                   *
*   output:  f2l = f2(light), f2c = f2(charm), f2b = f2(bottom,)    *
*            f2  = sum, all given for electromagnetic proton dis.   *
*                                                                   *
*   common:  the main program or the calling routine has to have    *
*            a common block  common / intinif / iinif , and the     *
*            integer variable  iinif  has always to be zero when    *
*            grv98f2 is called for the first time or when  iset     *
*            has been changed.                                      *
*                                                                   *
*   grids:   1. grv98lof.grid, 2. grv98nlf.grid.                    *
*            (1+1407 lines with 3 columns, 4 significant figures)   *
*                                                                   *
*******************************************************i*************
*
      implicit double precision (a-h, o-z)
      parameter (nstrf=3, nx=68, nq=21, narg=2)
      dimension xf2lf(nx,nq), xf2cf(nx,nq), xf2bf(nx,nq), 
     1          strfct (nstrf,nq,nx-1), qs(nq), xb(nx), 
     3          xt(narg), na(narg), arrf(nx+nq) 
      character*80 line
      common / intinif / iinif
      save xf2lf, xf2cf, xf2bf, na, arrf
*
*...bjorken-x and q**2 values of the grid :
       data qs / 0.8e0, 
     1           1.0e0, 1.3e0, 1.8e0, 2.7e0, 4.0e0, 6.4e0,
     2           1.0e1, 1.6e1, 2.5e1, 4.0e1, 6.4e1,
     3           1.0e2, 1.8e2, 3.2e2, 5.7e2,
     4           1.0e3, 1.8e3, 3.2e3, 5.7e3,
     5           1.0e4/ 
       data xb / 1.0e-9, 1.8e-9, 3.2e-9, 5.7e-9, 
     a           1.0e-8, 1.8e-8, 3.2e-8, 5.7e-8, 
     b           1.0e-7, 1.8e-7, 3.2e-7, 5.7e-7, 
     c           1.0e-6, 1.4e-6, 2.0e-6, 3.0e-6, 4.5e-6, 6.7e-6,
     1           1.0e-5, 1.4e-5, 2.0e-5, 3.0e-5, 4.5e-5, 6.7e-5,
     2           1.0e-4, 1.4e-4, 2.0e-4, 3.0e-4, 4.5e-4, 6.7e-4,
     3           1.0e-3, 1.4e-3, 2.0e-3, 3.0e-3, 4.5e-3, 6.7e-3,
     4           1.0e-2, 1.4e-2, 2.0e-2, 3.0e-2, 4.5e-2, 0.06, 0.08,
     5           0.1, 0.125, 0.15, 0.175, 0.2, 0.225, 0.25, 0.275,
     6           0.3, 0.325, 0.35, 0.375, 0.4,  0.45, 0.5, 0.55,
     7           0.6, 0.65,  0.7,  0.75,  0.8,  0.85, 0.9, 0.95, 1. /
*
*...check of x and q2 values : 
      if ( (x.lt.0.99d-9) .or. (x.gt.1.d0) ) then
         write(6,91) 
  91     format (2x,'str.fct. interpolation: x out of range')
         stop
      endif
      if ( (q2.lt.0.799) .or. (q2.gt.1.01e4) ) then
         write(6,92) 
  92     format (2x,'str.fct. interpolation: q2 out of range')
         stop
      endif
      if (iinif .ne. 0) goto 16
*
*...initialization, if required :
*
*    selection and reading of the grid : 
*    (comment: first number in the first line of the grid)
      if (iset .eq. 1) then
        open (11,file='grv98lof.grid',status='old')  !  7.907e-01
      else if (iset.eq.2) then
        open (11,file='grv98nlf.grid',status='old')  !  9.368e-01
      else
        write(6,93)
  93    format (2x,'no or invalid str.fct. set choice')
        stop
      end if
      iinif = 1
      read(11,89) line
  89  format(a80)
      do 15 m = 1, nx-1 
      do 15 n = 1, nq
      read(11,90) strfct(1,n,m), strfct(2,n,m), strfct(3,n,m) 
  90  format (3(1pe10.3))
  15  continue
      close(11)
*
*....arrays for the interpolation subroutine :
      do 10 iq = 1, nq
      do 20 ix = 1, nx-1
        xbs = xb(ix)**0.2 
        xb1 = 1.-xb(ix)
        xf2lf(ix,iq) = strfct(1,iq,ix) / xb1**3 * xbs
        xf2cf(ix,iq) = strfct(2,iq,ix) / xb1**7 * xbs
        xf2bf(ix,iq) = strfct(3,iq,ix) / xb1**7 * xbs 
  20  continue
        xf2lf(nx,iq) = 0.e0
        xf2cf(nx,iq) = 0.e0
        xf2bf(nx,iq) = 0.e0
  10  continue  
      na(1) = nx
      na(2) = nq
      do 30 ix = 1, nx
        arrf(ix) = dlog(xb(ix))
  30  continue
      do 40 iq = 1, nq
        arrf(nx+iq) = dlog(qs(iq))
  40  continue
*
*...continuation, if initialization was done previously.
*
  16  continue
*
*...interpolation :
      xt(1) = dlog(x)
      xt(2) = dlog(q2)
      x1 = 1.- x
      xs = x**(-0.2)
      f2l = fint(narg,xt,na,arrf,xf2lf) * x1**3 * xs
      f2c = fint(narg,xt,na,arrf,xf2cf) * x1**7 * xs
      f2b = fint(narg,xt,na,arrf,xf2bf) * x1**7 * xs
      f2  = f2l + f2c + f2b
*
      return
      end
*
*
      double precision function fint(narg,arg,nent,ent,table)
*********************************************************************
*                                                                   *
*   the interpolation routine (cern library routine e104)           *
*                                                                   *
*********************************************************************
      implicit double precision (a-h, o-z)
      dimension arg(narg),nent(narg),ent(*),table(*)
      dimension d(5),ncomb(5),ient(5)

      kd=1
      m=1
      ja=1

      do 5 ii=1,narg
        ncomb(ii)=1
        jb=ja-1+nent(ii)
        do 2 j=ja,jb
          if (arg(ii).le.ent(j)) go to 3
    2   continue
        j=jb
    3   if (j.ne.ja) go to 4
        j=j+1
    4   jr=j-1
        d(ii)=(ent(j)-arg(ii))/(ent(j)-ent(jr))
        ient(ii)=j-ja
        kd=kd+ient(ii)*m
        m=m*nent(ii)
        ja=jb+1
    5 continue

      fint=0.
   10 fac=1.
      iadr=kd
      ifadr=1

      do 15 i=1,narg
        if (ncomb(i).eq.0) go to 12
        fac=fac*(1.-d(i))
        go to 15
   12   fac=fac*d(i)
        iadr=iadr-ifadr
        ifadr=ifadr*nent(i)
   15 continue

      fint=fint+fac*table(iadr)
      il=narg
   40 if (ncomb(il).eq.0) go to 80
      ncomb(il)=0
      if (il.eq.narg) go to 10
      il=il+1
      do 50  k=il,narg
   50    ncomb(k)=1
      go to 10
   80 il=il-1
      if(il.ne.0) go to 40
      
	return
      end
*
*
      double precision function alpgrv(q2, naord)
*********************************************************************
*                                                                   *
*   the alpha_s routine.                                            *
*                                                                   *
*   input :  q2    =  scale in gev**2  (not too low, of course);    *
*            naord =  1 (lo),  2 (nlo).                             *
*                                                                   *
*   output:  alphas_s/(4 pi) for use with the grv(98) partons.      *  
*                                                                   *
*******************************************************i*************
*
      implicit double precision (a - z)
      integer nf, k, i, naord
      dimension lambdal (3:6),  lambdan (3:6), q2thr (3)
*
*...heavy quark thresholds and lambda values :
      data q2thr   /  1.960,  20.25,  30625. /
      data lambdal / 0.2041, 0.1750, 0.1320, 0.0665 /
      data lambdan / 0.2994, 0.2460, 0.1677, 0.0678 /
*
*...determination of the appropriate number of flavours :
      nf = 3
      do 10 k = 1, 3
      if (q2 .gt. q2thr (k)) then
         nf = nf + 1
      else
          go to 20
       end if
  10   continue
*
*...lo alpha_s and beta function for nlo calculation :
  20   b0 = 11.- 2./3.* nf
       b1 = 102.- 38./3.* nf
       b10 = b1 / (b0*b0)
       if (naord .eq. 1) then
         lam2 = lambdal (nf) * lambdal (nf)
         alp  = 1./(b0 * dlog (q2/lam2))
         go to 1
       else if (naord .eq. 2) then
         lam2 = lambdan (nf) * lambdan (nf)
         b1 = 102.- 38./3.* nf
         b10 = b1 / (b0*b0)
       else
         write (6,91)
  91     format ('invalid choice for order in alpha_s')
         stop
       end if
*
*...start value for nlo iteration :
       lq2 = dlog (q2 / lam2)
       alp = 1./(b0*lq2) * (1.- b10*dlog(lq2)/lq2)
*
*...exact nlo value, found via newton procedure :
       do 2 i = 1, 6
       xl  = dlog (1./(b0*alp) + b10)
       xlp = dlog (1./(b0*alp*1.01) + b10)
       xlm = dlog (1./(b0*alp*0.99) + b10)
       y  = lq2 - 1./ (b0*alp) + b10 * xl
       y1 = (- 1./ (b0*alp*1.01) + b10 * xlp
     1       + 1./ (b0*alp*0.99) - b10 * xlp) / (0.02d0*alp)
       alp = alp - y/y1
  2    continue
*
*...output :
  1    alpgrv = alp
       return
       end
c*******************************************************************
      subroutine mrstlo(x,q,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)
      data xmin,xmax,qsqmin,qsqmax/1d-5,1d0,1.25d0,1d7/
      q2=q*q
      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 
c  99  format('  warning:  q^2 value is out of range   ','q2= ',e10.5)
c  98  format('  warning:   x  value is out of range   ','x= ',e10.5)
      return
      end
c********************************************************
      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)
      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='lo2002.dat',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=val 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

	close(33)

      return
   50 format(8f10.5)
      end
c************************************************ 
      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),
     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
c***************************************
      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
c**************************************
      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
c*******************************************
      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
c**************************************************
      double precision function alpmsrt(scale,lambda,iorder)
c.
c.   the qcd coupling used in the mrs analysis.
c.   automatically corrects for nf=3,4,5 with thresholds at m_q.
c.   the following parameters must be supplied:
c.       scale   =  the qcd scale in gev (real)
c.       lambda  =  the 4 flavour msbar lambda parameter in gev (real)
c.       iorder  =  0 for lo, 1 for nlo and 2 for nnlo
c. 
      implicit real*8 (a-h,o-z)
      real*8 lambda
      data tol,qsct,qsdt/5d-4,74d0,8.18d0/

c-ap initialize to avoid compiler warnings
      alpmsrt =0.

      pi=4d0*datan(1d0)
      iord=iorder
      ith=0
      flav=4d0
      al=lambda
      al2=lambda*lambda
      qs=scale*scale
      t=dlog(qs/al2)
      tt=t
c.
      qsctt=qsct/4.
      qsdtt=qsdt/4.
      if(qs.lt.0.5d0) then   !!  running stops below 0.5
          qs=0.5d0
          t=dlog(qs/al2)
          tt=t
      endif

      alfqc5=0.
      alfqc4=0.
      alfqc3=0.

      if(qs.gt.qsctt) go	to 12  
      if(qs.lt.qsdtt) go	to 312  
   11 continue
      b0=11-2.*flav/3. 
      x1=4.*pi/b0
  5   continue    
      if(iord.eq.0) then
      alpmsrt=x1/t
      elseif(iord.eq.1) then
      b1=102.-38.*flav/3.
      x2=b1/b0**2
      as2=x1/t*(1.-x2*dlog(t)/t)
  95    as=as2
        f=-t+x1/as-x2*dlog(x1/as+x2)
        fp=-x1/as**2*(1.-x2/(x1/as+x2))
        as2=as-f/fp
        del=abs(f/fp/as)
        if((del-tol).gt.0.) go to 95
      alpmsrt=as2
      elseif(iord.eq.2) then
      alpmsrt=qwikalf(t,2,flav)
      endif
      if(ith.eq.0) return
      go to (13,14,15) ith
      print *, 'here'
      go to 5
   12 ith=1
      t=dlog(qsctt/al2)
      go to 11
   13 alfqc4=alpmsrt
      flav=5.   
      ith=2
      go to 11
   14 alfqc5=alpmsrt
      ith=3
      t=tt
      go to 11
   15 alfqs5=alpmsrt
      alfinv=1./alfqs5+1./alfqc4-1./alfqc5
      alpmsrt=1./alfinv
      return

  311 continue
      b0=11-2.*flav/3. 
      x1=4.*pi/b0
      if(iord.eq.0) then
      alpmsrt=x1/t
      elseif(iord.eq.1) then
      b1=102.-38.*flav/3.
      x2=b1/b0**2
      as2=x1/t*(1.-x2*dlog(t)/t)
   35 as=as2
      f=-t+x1/as-x2*dlog(x1/as+x2)
      fp=-x1/as**2*(1.-x2/(x1/as+x2))
      as2=as-f/fp
      del=abs(f/fp/as)
      if((del-tol).gt.0.) go to 35
      elseif(iord.eq.2) then
      alpmsrt=qwikalf(t,2,flav)
      endif
      if(ith.eq.0) return

      go to (313,314,315) ith
  312 ith=1
      t=dlog(qsdtt/al2)
      go to 311
  313 alfqc4=alpmsrt
      flav=3.   
      ith=2
      go to 311
  314 alfqc3=alpmsrt
      ith=3
      t=tt
      go to 311
  315 alfqs3=alpmsrt
      alfinv=1./alfqs3+1./alfqc4-1./alfqc3
      alpmsrt=1./alfinv
      return
      end
c***********************************
      double precision function qwikalf(t,iord,flav)
      implicit real*8(a-h,o-z)
      dimension z3(6),z4(6),z5(6),zz3(6),zz4(6),zz5(6)
      data z3/ -.161667e+01,0.954244e+01,
     .0.768623e+01,0.101523e+00,-.360127e-02,0.457867e-04/
      data z4/ -.172239e+01,0.831185e+01,
     .0.721463e+01,0.835531e-01,-.285436e-02,0.349129e-04/
      data z5/ -.872190e+00,0.572816e+01,
     .0.716119e+01,0.195884e-01,-.300199e-03,0.151741e-05/
      data zz3/-.155611e+02,0.168406e+02,
     .0.603014e+01,0.257682e+00,-.970217e-02,0.127628e-03/
      data zz4/-.106762e+02,0.118497e+02,0.664964e+01,
     .0.112996e+00,-.317551e-02,0.302434e-04/
      data zz5/-.531860e+01,0.708503e+01,0.698352e+01,
     .0.274170e-01,-.426894e-03,0.217591e-05/
      data pi/3.14159/
      nfm2=flav-2.
      x=dsqrt(t)
      x2=x*x
      x3=x*x2
      x4=x*x3
      x5=x*x4
      go to (1,2) iord  !!iord change!!
    1 go to (3,4,5) nfm2
    3 y=z3(1)+z3(2)*x+z3(3)*x2+z3(4)*x3+z3(5)*x4+z3(6)*x5
      go to 10
    4 y=z4(1)+z4(2)*x+z4(3)*x2+z4(4)*x3+z4(5)*x4+z4(6)*x5
      go to 10
    5 y=z5(1)+z5(2)*x+z5(3)*x2+z5(4)*x3+z5(5)*x4+z5(6)*x5
      go to 10
    2 go to (6,7,8) nfm2
    6 y=zz3(1)+zz3(2)*x+zz3(3)*x2+zz3(4)*x3+zz3(5)*x4+zz3(6)*x5
      go to 10
    7 y=zz4(1)+zz4(2)*x+zz4(3)*x2+zz4(4)*x3+zz4(5)*x4+zz4(6)*x5
      go to 10
    8 y=zz5(1)+zz5(2)*x+zz5(3)*x2+zz5(4)*x3+zz5(5)*x4+zz5(6)*x5
      go to 10
   10 qwikalf=4.*pi/y
      return
      end