Available functions

EvolutionParams

Struct for holding all QCDNUM Parameters.

GridParams

Struct for holding the QCDNUM grid parameters.

InputPDF(; func::Function, map::AbstractArray{<:Real})

Struct containing all necessary info to pass a PDF (parton distribution function) into QCDNUM.

SPLINTParams

Struct for storage of parameters used with SPLINT package of QCDNUM.

SplineAddresses

Lookup table for addresses of different structure function splines.

const WrappedPDF = FunctionWrappers.FunctionWrapper{Float64, Tuple{Int32, Float64}}

const WrappedSpFun = FunctionWrappers.FunctionWrapper{Float64, Tuple{Int32, Float64}}

allfij(iset, ix, iq, n, ichk)

Get all flavour-pdf values for given ix and iq grid points.

Arguments

• iset::Integer: pdf set id (1-24).
• ix::Integer: x grid point.
• iq::Integer: q2 grid point.
• n::Integer: number of additional pdfs to be returned.
• ichk::Integer: flag to steer error checking. See QCDNUM

docs. ichk = -1 makes code faster, at the risk of not checking certain things.

Returns

• pdf::Array{Float64,2}: pdf values over flavours.

allfxq(iset, x, qmu2, n, ichk)

Get all flavour-pdf values for a given x and mu^2.

Arguments

• iset::Integer: pdf set id (1-24).
• x::Float64: input value of x.
• qmu2::Float64: input value of qmu2.
• n::Integer: number of additional pdfs to be returned.
• ichk::Integer: flag to steer error checking. See QCDNUM

docs. ichk = -1 makes code faster, at the risk of not checking certain things.

Returns

• pdf::Array{Float64,2}: pdf values over flavours.

altabn(iset, iq, n)

Returns the value of (alphaS / 2pi)^n, properly truncated, at the factorisation scale muF^2.

Arguments

• iset::Integer: identifier of tha active alpha_S table (0) or pdf set (1-24).
• iq::Integer: index of q2 grid point
• n::Integer: power of alpha_S for the different perturbative series.

Returns

• asn::Float64: value of (alpha_S / 2pi)^n, 0 if error.
• ierr::Integer: set, on exit, to 1 if iq is close to or below the value of

Lambda^2, and to 2 if iq is outside the grid boundaries.

asfunc(r2)

Evolve alpha_S(mu_R^2). Does not use mu^2 grid or weight tables.

Returns

• alphas::FLoat64: alpha_S value.
• nf::Integer: number of flavours at scale r2.
• ierr::Integer: error code

bvalij(iset, id, ix, iq, ichk)

Get the value of a basis pdf at a given point (ix, iq).

Arguments

• iset::Integer: pdf set id (1-24)
• id::Integer: basis pdf identifier from 0 to 12+n,

where n is the number of additional pdfs in iset.

• ix::Integer: x index.
• iq::Integer: qq index.
• ichk::Integer: flag to steer error checking.

See allfxq().

Returns

• pdf::Float64: pdf values.

bvalxq(iset, id, x, qq, ichk)

Get the value of a basis pdf at a given point (x, qq).

Arguments

• iset::Integer: pdf set id (1-24)
• id::Integer: basis pdf identifier from 0 to 12+n,

where n is the number of additional pdfs in iset.

• x::Float64: x value.
• qq::Float64: qq value.
• ichk::Integer: flag to steer error checking.

See allfxq().

Returns

• pdf::Float64: pdf values.

cpypar(iset)

Copy the evolution parameters of a pdf set to a local array. The array has the following param values:

• 1: iord
• 2: alfas
• 3: r2alf
• 4: nfix
• 5: q2c
• 6: q2b
• 7: q2t
• 8: ar
• 9: br
• 10:xmin
• 11:qmin
• 12:qmax

In addition to the evolution parameters is given the pdf type in array(13): 1 = unpolarised, 2 = polarised, 3 = time-like, 4 = external, 5 = user.

Arguments

• iset::Integer: pdf set identifier.

Returns

• array::Vector{Float64}

dmpwgt(itype, lun, filename)

Dump weight tables of a given itype to filename.

dsp_funs1(ia, u, ichk)

Evaluate function for 1D spline.

Possible values of ichk:

• -1: extrapolate the spline
• 0: return 0
• 1: throw an error message

Arguments

• ia::Integer: address of spline
• u::Float64: x or qq
• ichk::Integer: defines behaviour when outside

spline range

dsp_funs2(ia, x, q, ichk)

Evaluate function for 2D spline.

Possible values of ichk:

• -1: extrapolate the spline
• 0: return 0
• 1: throw an error message

Arguments

• ia::Integer: address of spline
• x::Float64: x value
• q::Float64: qq value
• ichk::Integer: defines behaviour when outside

spline range

dsp_ints1(ia, u1, u2)

Evaluate integral of spline between u1 and u2.

The integration limits must lie inside the spline range.

dsp_ints2(ia, x1, x2, q1, q2, rs, np)

Evaluate integral of spline between x1, x2, q1 and q2. Also takes care of rscut and integrations makes use of N-point Gauss quadrature, as defined by the choice of np.

The integration limits must lie inside the spline range.

dsp_rscut(ia)

Get the root(s) cut for the spline at ia.

dsp_rsmax(ia, rsc)

Get the root(s) cut limit for the spline at ia and cut rsc.

dsp_spsgtval(ia, i)

Get some extra info, val, from the spline ia.

Arguments

• ia::Integer: spline address.
• i::Integer: storage index, runs from 1-100.

Returns

• val::Float64: value to store.

dsp_uread(i)

Read something from the reserved user space.

Arguments

• i::Integer: where to read, from 1 to nuser

Returns

• val::Float64: what is read

evolfg(itype::Integer, func::Union{Base.CFunction, Ptr{Nothing}}, def::Array{Float64}, iq0::Integer)
evolfg(itype::Integer, func::WrappedPDF, def::Array{Float64}, iq0::Integer)
evolfg(itype::Integer, func::InputPDF, iq0::Integer)

Evolve the flavour pdf set.

Arguments

• itype::Integer: select un-polarised (1), polarised (2) or

time-like (3) evolution.

• func::Union{Base.CFunction, Ptr{Nothing}}: User-defined function

that returns input x * f_j(x) at iq0. j is from 0 to 2 * nf.

• def::Array{Float64}: input array containing the contribution of

quark species i to the input distribution j.

• iq0::Integer: grid index of the starting scale mu_0^2.

Returns

• epsi::Float64: max deviation of the quadratic spline interpolation

from linear interpolation mid-between grid points.

evolve(input_pdf, qcdnum_params)

High-level interface to QCD evolution with QCDNUM.

evsgns(itype::Integer, func::Union{Base.CFunction, Ptr{Nothing}}, isns::Array{Int32,1}, n::Integer, iq0::Integer)
evsgns(itype::Integer, func::WrappedPDF, isns::Array{Int32,1}, n::Integer, iq0::Integer)

Evolve an arbitrary set of single/non-singlet pdfs. The evolution can only run in FFNS or MFNS mode, as it is not possible to correctly match at the thresholds as in evolfg.

Arguments

The arguments are as for evolfg, expect def::Array{Float64} is replaced with:

• isns::Array{Int32,1}: Input int array specifing the

evolution type. Entries can be (+1, -1, +-2) corresponding to singlet, valence non-singlet and +/- q_ns singlets respectively.

• n::Integer: Number of singlet/non-singlet pdfs to evolve

Returns

• epsi::Float64: Maximum deviation of the quadratic spline from

linear interpolation mid-between the grid points.

extpdf(fun, iset, n, offset)

Import a pdfset from an external source.

Arguments

• fun::Union{Base.CFunction, Ptr{Nothing}}: User-defined function with the signature

fun(ipdf::Integer, x::Float64, qq::Float64, first::UInt8)::Float64 specifying the values at x and qq of pdfset ipdf.

• iset::Integer: Pdfset identifier, between 1 and 24.
• n::Integer: Number of pdf tables in addition to gluon tables.
• offset::Float64: Relative offset at the thresholds mu_h^2, used

to catch matching discontinuities.

Returns

• epsi::Float64: Maximum deviation of the quadratic spline from

linear interpolation mid-between the grid points.

fflist(iset, c, isel, x, q, ichk)

A fast routine to generate a list of interpolated pdfs.

Arguments

• iset::Integer: pdf set identifier [1-24]
• c::Array{Float64}: coefficients of quarks/anti-quarks
• isel::Integer: selection flag
• x::Array{Float64}: list of x values.
• q::Array{Float64}: list of q2 values.
• ichk::Integer: flag to steer error checking. See allfxq().

Returns

• f::Array{Float64}: output list of pdf values.

rfromf(fscale2)

Convert the renormalisation scale, muR^2, to the factorisation scale, muF^2.

fillwt(itype)

Fill weight tables for all order and number of flavours. itype is used to select un-polarised pdfs (1), polarised pdfs (2) or fragmentation functions (3).

Returns

• nwds::Integer: number of words used in memory.

fsplne(iset, id, x, iq)

Spline interpolation of a basis PDF in x, at the grid point iq. Provided as a diagnostic tool to investigate possible quadratic spline oscillations.

Arguments

iset::Integer: PDF set identifier [1-24] id::Integer: Identifier of a basis pdf |e^±| x::Float64: x value iq::Integer: Index of a Q^2 grid point

Returns

pdf::Float64: pdf value

fftabl(ist, c, isel, x, q, n, ichk)

A fast routine to generate a table of interpolated pdfs.

• iset::Integer: pdf set identifier [1-24]
• c::Array{Float64}: coefficients of quarks/anti-quarks
• isel::Integer: selection flag
• x::Array{Float64}: list of x values.
• q::Array{Float64}: list of q2 values.
• ichk::Integer: flag to steer error checking. See allfxq().

Returns

• table::Matrix{Float64}: output table of pdf values.

fvalij(iset, id, ix, iq, ichk)

Get the value of a flavour momentum density at a given point (ix, iq).

Arguments

• iset::Integer: pdf set id (1-24)
• id::Integer: basis pdf identifier from -6 to 6+n,

where n is the number of additional pdfs in iset.

• ix::Integer: x index.
• iq::Intger: qq index.
• ichk::Integer: flag to steer error checking.

See allfxq().

Returns

• pdf::Float64: pdf values.

fvalxq(iset, id, x, qq, ichk)

Get the value of a flavour momentum density at a given point (x, qq).

Arguments

• iset::Integer: pdf set id (1-24)
• id::Integer: basis pdf identifier from -6 to 6+n,

where n is the number of additional pdfs in iset.

• x::Float64: x value.
• qq::Float64: qq value.
• ichk::Integer: flag to steer error checking.

See allfxq().

Returns

• pdf::Float64: pdf values.

getabr()

Get the relation between the factorisation scale muF^2 and the renormalisation scale muR^2.

muR^2 = ar muF^2 + br.

getalf()

Set the starting value of alpha_S and the starting renormalisation scale r2. By default alpha_S(m_Z^2) = 0.118.

getcbt()

Return the current threshold settings for the FFNS or VFNS.

Returns

• nfix::Integer: number of flavours in the FFNS. For VNFS set

nfix = 0.

• qc/b/t::Float64: q2 values of the heavy flavour thresholds

in the VFNS. Ignored if FFNS.

getint(param)

Get QCDNUM integer parameters.

Arguments

• param::String: Name of parameter. Can be "iter" (number of

evolutions in backwards iteration), "tlmc" (time-like matching conditions), "nopt" (number of perturbative terms) or "edbg" (evolution loop debug printout).

Returns

• ival::Int32: Integer value that is read

getlim(iset)

Read current grid boundary values for a pdf set iset.

Returns

• xmin::Float64: min x boundary
• qmin::Float64: min q2 boundary
• qmax::Float64: max q2 boundary

getord()

Get order of perturbative QCD calculations. iord = 1, 2, 3 for LO, NLO and NNLO respectively. By default, iord = 2.

getval(param)

Get QCDNUM parameters.

Arguments

• param::String: Name of parameter. Can be "null" (result of

calc that cannot be performed), "epsi" (tolerance level in float comparison |x-y| < epsi), "epsg" (numerical accuracy of Gauss integration in weight table calc), "elim" (allowed diff between quadratic and linear spline interpolation mid-between x grid points - to disable, set elim<=0), "alim" (Max allowed value of alpha_s(mu^2)), "qmin" (smallest possible boundary of mu^2 grid) "qmax" (largest possible boundary of mu^2 grid).

Returns

• val::Float64: Value.

gqcopy(n)

Copy the current mu^2 grid into an array of length n.

gqmake(qarr, wgt, n, nqin)

Define a logarithmically-spaced mu_F^2 grid on which the parton densities are evolved.

Arguments

• qarr::Array{Float64,1}: input array containing n values of mu^2

in ascending order. The lower edge of the grid should be above 0.1 GeV^2.

• wgt::Array{Float64,1}: relative grip point density in each region

defined by qarr.

• n::Integer: number of values in qarr and wgt (n>=2).
• nqin::Integer: requested number of grid points.

Returns

• nqout::Integer: number of generated grid points.

grpars()

Get the current grid definitions.

Returns

nx::Integer: number of points in x grid. xmi::Float64: lower boundary of x grid. xma::Float64: upper boundary of x grid. nq::Integer: number of points in qq grid. qmi::Float64: lower boundary of qq grid. qma::Float64: upper boundary of qq grid. iord::Integer: order of spline interpolation.

gxcopy(n)

Copy the current x grid into an array of length n.

gxmake(xmin, iwt, n, nxin, iord)

Define a logarithmically-spaced x grid.

Arguments

• xmin::Array{Float64,1}: an input array containitn n values

of x in ascending order. xmin[1] defines the lower end of the grid and other values define approx positions where the point density will change according to the values set in iwt.

• iwt::Array{Int32,1}: input integer weights given in ascending order

and must always be an integer multiple of the previous weight.

• n::Integer: number of values specified in xmin and iwt.
• nxin::Integer: Requested number of grid points.
• iord::Integer: iord = 2(3) for linear(quadratic) spline interpolation.

Returns

• nxout::Integer: the number of generated grid points.

ievtype(iset)

Get the pdf evolution type for set iset::Integer.

init()

High-level default initialisation for QCDNUM.

iqfrmq(q2)

Get grid point index of the closest grid point at or below q2 value.

isp_s2make(istepx, istepq)

Create a spline object in memory, and return the address. Every istep-th grid point is taken as a node point of the spline and the grid boundaries are always included as node points.

Arguments

• istepx::Integer: steps taken in sampling the QCDNUM x grid
• istepq::Integer: steps taken in sampling the QCDNUM qq grid

isp_s2user(xarr, nx, qarr, nq)

Set your own node points in the spline in case the automatic sampling fails.

The routine will discard points outside the x-qq evolution grid, round the remaining nodes down to the nearest grid-point and then sort them in ascending order, discarding equal values. Thus you are allowed to enter un-sorted scattered arrays.

Arguments

• xarr::Array{Float64}: array of x values
• nx::Integer: length of xarr
• qarr::Array{Float64}: array of qq values
• nq::Integer: length of qarr

Returns

• iasp::Integer: address of the spline object

isp_splinetype(ia)

Get the type of spline at address ia.

Possible types are:

• -1: x spline
• 0: not a spline
• 1: qq spline
• 2: x-qq spline

ssp_spread(filename)

Read spline from filename and return address ia.

isp_spsize(ia)

Get used space for spline ia, or total memory size when ia = 0.

isp_spvers()

SPLINT version as a date.

isp_sqmake(istepq)

Create a 1D qq spline object in memory, and return the address. Every istep-th grid point is taken as a node point of the spline and the grid boundaries are always included as node points.

Arguments

• istepq::Integer: steps taken in sampling the QCDNUM qq grid

isp_squser(qarr, nq)

Set your own node points in the 1D qq spline in case the automatic sampling fails.

Arguments

• qarr::Array{Float64}: array of qq values
• nq::Integer: length of qarr

Returns

• iasp::Integer: address of the spline object

isp_sxmake(istepx)

Create a 1D x spline object in memory, and return the address. Every istep-th grid point is taken as a node point of the spline and the grid boundaries are always included as node points.

Arguments

• istepx::Integer: steps taken in sampling the QCDNUM x grid

isp_sxuser(xarr, nx)

Set your own node points in the 1D x spline in case the automatic sampling fails.

Arguments

• xarr::Array{Float64}: array of x values
• nx::Integer: length of xarr

Returns

• iasp::Integer: address of the spline object

ixfrmx(x)

Get grid point index of closest grid point at or below x value.

keygrp(iset, igroup)

Returns the parameter key of the pdf group in iset. Useful to check if parameters match. Like a more specific keypar.

igroup can be:

• 1: order
• 2: alpha_S
• 3: fnsandthresholds
• 4: scale
• 5: cutes
• 6: all

keypar(iset)

Returns the parameter key of the pdf in iset. Useful to check if parameters match with.

QCDNUM.load_params(file_name::String)
QCDNUM.load_params(::Type{HDF5.File}, file_name::String)
QCDNUM.load_params(src::HDF5.H5DataStore)

Load stored QCDNUM or SPLINT parameters.

make_grid(grid_params)

High-level interface to build QCDNUM grid from GridParams.

mixfns(nfix, r2c, r2b, r2t)

Select the MFNS mode and set thresholds on mu_R^2.

Arguments

• nfix::Integer: Fixed number of flavours for MFNS. Can be

in the range [3, 6].

• r2c/b/t::Float64: Thresholds defined on the renormalisation scale

mu_R^2 for c, b and t.

nfrmiq(iset, iq)

Returns the number of active flavours nf at a q2 grid point iq.

Arguments

• iset::Integer: pdf set identifier.
• iq::Integer: q2 grid point.

Returns

• nf::Integer: number of active flavours. 0 if iq is

outside the q2 grid.

• ithresh::Integer: threshold indicator that is set to

+1(-1) if iq is at a threshold with the larger (smaller) number of flavours, 0 otherwise.

nptabs(iset)

Get the number of pdf tables in set iset::Integer.

nwused()

Returns the szie nwtot of the QCDNUM store (the parameter nwf0 in qcdnum.inc) and the number of words used, nwuse.

The output argument ndummy is not used at present.

nxtlun(lmin)

Get next free logical unit number above max(lmin, 10). Returns 0 if there is no free logical unit. Can be called before or after qcinit. Handy if you want to open a file on a unit that is guaranteed to be free.

pdfcpy(iset1, iset2)

Copy pdf set.

pushcp()

Pull the current parameters from LIFO stack (load stashed parameters).

pushcp()

Push the current parameters to LIFO stack (temporarily stash them).

qcdnum_lock()::AbstractLock

Get the global lock for QCDNUM operations.

The QCDNUM Fortran package itself is not thread-safe, so QCDNUM.jl uses a global lock do guard against parallel calls to the Fortran library.

qcinit(lun, filename)

Initialise QCDNUM - should be called before anything else.

Arguments

• lun::Integer: the output logical unit number. When set to 6,

the QCDNUM messages appear on the standard output. When set to -6, the QCDNUM banner printout is suppressed.

• filename::String: the output filename to store log. Irrelevant

when lun is set to 6/-6

qfrmiq(iq)

Get q2 value at grid point iq.

qqatiq(q, iq)

Check if q2 coincides with a grid point iq.

Returns

out::Bool: true or false

qstore(action, i, val)

QCDNUM reserves 500 words of memory for user use.

Arguments

• action::String: Can be "write", "read", "lock" or "unlock".
• i::Integer: Where to read/write in the store.
• val::Float64: What to write in the store.

qstore(action, i)

QCDNUM reserves 500 words of memory for user use.

Arguments

• action::String: Can be "write", "read", "lock" or "unlock".
• i::Integer: Where to read/write in the store.

Returns

• val::Float64: What is read from the store.

readwt(lun, filename)

Read weight tables from filename.

rfromf(fscale2)

Convert the factorisation scale, muF^2, to the renormalisation scale, muR^2.

QCDNUM.save_params(file_name::String, params::Union{EvolutionParams,SPLINTParams})
QCDNUM.save_params(::Type{HDF5.File}, file_name::String, params::Union{EvolutionParams,SPLINTParams})
QCDNUM.save_params(trg::HDF5.H5DataStore, params::Union{EvolutionParams,SPLINTParams})

Store the QCDNUM or SPLINT parameters for reproducibility.

setabr(ar, br)

Define the relation between the factorisation scale muF^2 and the renormalisation scale muR^2.

muR^2 = ar muF^2 + br.

setalf(alfs, r2)

Set the starting value of alpha_S and the starting renormalisation scale r2. By default alpha_S(m_Z^2) = 0.118.

setcbt(nfix, iqc, iqb, iqt)

Select FFNS or VFNS, and thresholds on mu_F^2 if necessary.

Arguments

• nfix::Integer: number of flavours in the FFNS. For VNFS set

nfix = 0.

• iqc/b/t::Integer: grid indices of the heavy flavour thresholds

in the VFNS. Ignored if FFNS.

setint(param, ival)

Set QCDNUM integer parameters.

Arguments

• param::String: Name of parameter. Can be "iter" (number of

evolutions in backwards iteration), "tlmc" (time-like matching conditions), "nopt" (number of perturbative terms) or "edbg" (evolution loop debug printout).

• ival::Integer: Value to set.

setlim(ixmin, iqmin, iqmax)

Restrict the range of a pdf evolution or import to only part of the x-q2 grid.

ixmin, iqmin and iqmax re-define the range of the grid. To release a cut, eneter a value of 0. Fatal error if the cuts result in a kinematic domain that is too small or empty.

setlun(lun, filename)

Redirect the QCDNUM messages. Arguments are the same as for qcinit, but it can be called at any point in the program after qcinit.

Arguments

• lun::Integer: the output logical unit number. When set to 6,

the QCDNUM messages appear on the standard output. When set to -6, the QCDNUM banner printout is suppressed.

• filename::String: the output filename to store log. Irrelevant

when lun is set to 6/-6

setord(iord)

Set order of perturbative QCD calculations. iord = 1, 2, 3 for LO, NLO and NNLO respectively. By default, iord = 2.

setval(param, val)

Set QCDNUM parameters.

Arguments

• param::String: Name of parameter. Can be "null" (result of

calc that cannot be performed), "epsi" (tolerance level in float comparison |x-y| < epsi), "epsg" (numerical accuracy of Gauss integration in weight table calc), "elim" (allowed diff between quadratic and linear spline interpolation mid-between x grid points - to disable, set elim<=0), "alim" (Max allowed value of alpha_s(mu^2)), "qmin" (smallest possible boundary of mu^2 grid) "qmax" (largest possible boundary of mu^2 grid).

• val::Float64: Value to set.

splchk(iset, id, iq)

Return for a basis pdf at a given Q^2 grid point the maximum deviation between a linear interpolation and the spline interpolation used by QCDNUM.

To be used if having issues with evolfg or extpdf.

Arguments

iset::Integer: PDF set identifier [1-24] id::Integer: Identifier of a basis PDF |e^±| iq::Integer: Index of a Q^2 grid point

Returns

epsi::Float64: Value of the max deviation

splint_init()

High-level interface to splint initialisation.

ssp_erase(ia)

Clear the memory from ia onwards. ia=0 can also be used to erase all spline objects in memory.

ssp_extrapu(ia, n)

Define the extrapolation at the kinematic limit for a spline at address ia.

The extrapolation index n can be:

• 0: constant
• 1: linear
• 2: quadratic
• 3: cubic

ssp_extrapv(ia, n)

Define the extrapolation at the kinematic limit for a spline at address ia.

The extrapolation index n can be:

• 0: constant
• 1: linear
• 2: quadratic
• 3: cubic

ssp_nprint(ia)

Print a list of nodes and grids for the spline at address ia.

ssp_s2f123(ia, iset, def, istf, rs)

Fast structure function input for 2D splines over x and qq.

Arguments

• ia::Integer: address of the spline object
• iset::Integer: QCDNUM pdf-set index
• def::Array{Float64}: Array of (anti-)quark

coefficients

• istf::Integer: structure function index

1<=>FL, 2<=>F2, 3<=>xF3, 4<=>FL'

• rs::Float64: sqrt(s) cut - 0 for no kinematic cut

ssp_s2fill(iasp::Integer, fun::Union{Base.CFunction, Ptr{Nothing}}, rs::Float64)
ssp_s2fill(iasp::Integer, fun::WrappedSpFun, rs::Float64)

Fill the spline object by passing a function. The function must have the signature fun(ix::Integer, iq::Integer, first::Bool).

Arguments

• iasp::Integer: address of the spline object
• fun::Union{Base.CFunction, Ptr{Nothing}}: function to be splined
• rs::Float64: set a sqrt(s) cut - 0 for no kinematic cut

ssp_spdump(ia, filename)

Dump spline at address ia to filename.

ssp_spinit(nuser)

Initialise SPLINT - should be called before other SPLINT functions.

Arguments

• nuser::Integer: the number of words reserved for user storage

ssp_splims(ia)

Get node limits of spline at address ia.

Here, u and v refer to the x and qq dimensions respectively.

Returns tuple containing

• nu::Integer: number of nodes in u direction
• u1::Float64: lower u limit
• u2::Float64: upper u limit
• nv::Integer: number of nodes in v direction
• v1::Float64: lower v limit
• v2::Float64: upper v limit
• n::Integer: number of active nodes below kinematic limit

ssp_spsetval(ia, i, val)

Store some extra info, val, along with the spline at ia.

Arguments

• ia::Integer: spline address.
• i::Integer: storage index, runs from 1-100.
• val::Float64: value to store.

ssp_sq123(ia, iset, def, istf, ix)

Fast structure function input for splines over qq.

Arguments

• ia::Integer: address of the spline object
• iset::Integer: QCDNUM pdf-set index
• def::Array{Float64}: Array of (anti-)quark

coefficients

• istf::Integer: structure function index

1<=>FL, 2<=>F2, 3<=>xF3, 4<=>FL'

• ix::Integer: index of x value

ssp_sqfill(iasp, fun, ix)

Fill the 1D qq spline object by passing a function. The function must have the signature fun(ix::Integer, iq::Integer, first::Bool).

Arguments

• iasp::Integer: address of the spline object
• fun::Union{Base.CFunction, Ptr{Nothing}}: function to be splined
• ix::Integer: fixed ix value to pass to fun

ssp_sxf123(ia, iset, def, istf, iq)

Fast structure function input for splines over x.

Arguments

• ia::Integer: address of the spline object
• iset::Integer: QCDNUM pdf-set index
• def::Array{Float64}: Array of (anti-)quark

coefficients

• istf::Integer: structure function index

1<=>FL, 2<=>F2, 3<=>xF3, 4<=>FL'

• iq::Integer: index of qq value

ssp_sxfill(iasp, fun, iq)

Fill the 1D x spline object by passing a function. The function must have the signature fun(ix::Integer, iq::Integer, first::Bool).

Arguments

• iasp::Integer: address of the spline object
• fun::Union{Base.CFunction, Ptr{Nothing}}: function to be splined
• iq::Integer: fixed iq value to pass to fun

ssp_unodes(ia, n, nu)

Copy u-nodes from spline at address ia to local array.

Arguments

• ia::Integer: address of spline
• n::Integer: dimension of array to copy to
• nu::Integer: number of u-nodes copied

Returns

• array::Array{Float64}: array of u-nodes

ssp_uwrite(i, val)

Write something to the reserved user space.

Arguments

• i::Integer: where to write, from 1 to nuser
• val::Float: what to write

ssp_vnodes(ia, n, nv)

Copy v-nodes from spline at address ia to local array.

Arguments

• ia::Integer: address of spline
• n::Integer: dimension of array to copy to
• nv::Integer: number of v-nodes copied

Returns

• array::Array{Float64}: array of v-nodes

sumfij(iset, c, isel, ix, iq, ichk)

Return the gluon or a weighted sum of quark densities, depending on the selection flag, isel.

isel values:

0: Gluon density |xg> 1: Linear combination c summed over active flavours 2-8: Specific singlet/non-singlet quark component 9: Intrinsic heavy flavours 12+i: Additional pdf |xf_i> in iset

See QCDNUM manual for more information.

Arguments

• iset::Integer: pdf set id (1-24).
• c::Array{Float64}: Coefficients of quarks/anti-quarks
• isel::Integer: Selection flag
• ix::Integer: x grid point.
• iq::Integer: q2 grid point.
• n::Integer: number of additional pdfs to be returned.
• ichk::Integer: flag to steer error checking. See QCDNUM

docs. ichk = -1 makes code faster, at the risk of not checking certain things.

Returns

• pdf::Float64: pdf value.

sumfxq(iset, c, isel, x, qmu2, ichk)

Return the gluon or a weighted sum of quark densities, depending on the selection flag, isel.

isel values:

0: Gluon density |xg> 1: Linear combination c summed over active flavours 2-8: Specific singlet/non-singlet quark component 9: Intrinsic heavy flavours 12+i: Additional pdf |xf_i> in iset

See QCDNUM manual for more information.

Arguments

• iset::Integer: pdf set id (1-24).
• c::Array{Float64}: Coefficients of quarks/anti-quarks
• isel::Integer: Selection flag
• x::Float64: input value of x.
• qmu2::Float64: input value of qmu2.
• n::Integer: number of additional pdfs to be returned.
• ichk::Integer: flag to steer error checking. See QCDNUM

docs. ichk = -1 makes code faster, at the risk of not checking certain things.

Returns

• pdf::Float64: pdf value.

usepar(iset)

Activate the parameters of iset, ie. copy them to iset = 0 and re-initialise the active look-up tables.

usrpdf(fun, iset, n, offset)

Create a user-defined type-5 pdfset (same type as the output of evsgns).

Arguments

• fun::Union{Base.CFunction, Ptr{Nothing}}: User-defined function with the signature

fun(ipdf::Integer, x::Float64, qq::Float64, first::UInt8)::Float64 specifying the values at x and qq of pdfset ipdf.

• iset::Integer: Pdfset identifier, between 1 and 24.
• n::Integer: Number of pdf tables in addition to gluon tables.
• offset::Float64: Relative offset at the thresholds mu_h^2, used

to catch matching discontinuities.

Returns

• epsi::Float64: Maximum deviation of the quadratic spline from

linear interpolation mid-between the grid points.

wtfile(itype, filename)

Maintains an up-to-date weight table in filename.

xfrmix(ix)

Get x value at grid point ix.

xxatix(x, ix)

Check if x coincides with a grid point ix.

Returns

out::Bool: true or false

zmfillw()

Fill weight tables for zero-mass structure function calculations.

zmstfun()

Calculate a structure function from a linear combination of parton densities.

Arguments

• istf::Integer: structure function index

where (1,2,3,4) = (FL, F2, xF3, fL^').

• def::Array{Float64}: coeffs of the quark linear combination

for which the structure function is to be calculated.

• x::Array{Float64}: list of x values.
• Q2::Array{Float64}: list of Q2 values.
• n::Integer: number of items in x, Q2 and f.
• ichk::Integer: flag for grid boundary checks. See QCDNUM docs.

Returns

• f::Array{Float64}: list of structure functions.

zmwords()

Check the number of words available in the ZMSTF workspace and the number of words used.

QCDNUM.@qlccall expr

Equivalent to @lock qcdnum_lock() @ccall ....