SecDec/loop/src/deco/NSDroutines.m [ Mathematica Files ]
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NAME
NSDroutines.m
USAGE
called from deconoprimary.m
PURPOSE
Contains routines to perform iterated SD, and to output files created by deconoprimary.m
FUNCTIONS
for the decomposition: countvars[cvf,cfv]: finds the maximum power of a set of variables cfv in a function cvf. findpossset[fexpr]: finds all minimal sets (wrt length) of the integration variables which nullify a function fexpr. returns these sets, together with an integer which is the maximum power of these integration variables in the function. howmanynullify[posset,integrands]: counts the number of integrands a given set posset nullifies. findbestset[integrands,n]: finds the 'best' set which nullifies function n from the list of integrands. 'best' is the set which nullifies the most integrands, and has the lowest maximum power of integration variables in integrand n paralleldecompose[allsecs]: maps 'decompose' onto each sector in allsecs, uses parallel processing where available/appropriate. allsecs is a list of sectors to be decomposed. Returns a list of fully decomposed sectors. exdecompose[esec,set,varnum]: performs the explicit replacements needed for decomposition. Factorizes the integrands and recalculates the exponents of the integration variables. Returns a sector which may require further decomposition. factorizeintegrand[{integ,expo,flag},tt,var]: pulls out any factors of tt[var] in int, recalculates the exponent of tt[var] and returns {factorized int, expo, new flag}. flag/new flag = A or B. decompose[dsec]: Checks whether dsec needs decomposition. If not (ie all flags = A), returns {dsec}. Otherwise the set of variables to decompose is selected by findbestset, and exdecompose is mapped onto this set. newsecs is the list of transformed sectors, and then this list of sectors is further decomposed by paralleldecompose[newsecs]. when this process terminates, decompose returns a list of fully decomposed sectors. rescalesecs[sector]: The function F and U are rescaled for each sector by symbolic parameter maxinv, which will be replaced by the biggest kinematic invariant during the numerical integration for preparing and writing output: polecheck[expos]: classifies a a list of exponents by number of logarithmic, linear and higher poles. makesectoroutput[sector]: classifies a sector by its pole structure. increments the counter polecount[polestruct] for this classification, and adds a pointer to sector in a list seclist[polestruct] linked to this classification. If polestruct is the first of this structure, it is added to the list structlist of observed pole structures. writeoutput[polestruct]: Updates the values of maxpoles where applicable. the list of pointers is used to form the final list of sectors for this polestruct to write for output. The output is written to the appropriate [integral]P[polestruct].out. The information on number of sectors with this pole structure is added to the string poleinfostring writeinfo: writes the necessary information to file *graph*Func[number]OUT.info which is later read by the Perl module getinfo.pm. The number in Func[number] corresponds to first entry in primseclist that the user puts in by hand. The info files include number of integration variables nmax, total number of sectors produced allcount, maximum poles maxlogpole, common exponent expoU and expoF of the functions with number [number], maxlinpole, maxhpole, and the order of the constant prefactor prefacord. Note: If functions written to the primseclist have different exponents for U and F, their function number should be different. makeoutput: calculates the total number of sectors, performs makesecoutput to each sector, reformats the sectors to be in the desired output format, sorts the structlist into order of complexity, performs writeoutput for each pole structure, then performs writeinfo. from *graph*.m: lengthprimseclist: checks template file for first entry in primseclist. lengthprimseclist is set to the highest number in the first entry. This is comparable to the number of sectors which is used for usual sector decomposition, where the number of sectors is defined by the number of propagators written to *param*.input. variables: nf: short for number of function, is first entry in every element of primseclist maxinv: is a symbolic variable which will be replaced by the biggest kinematic invariant during numerical integration global variables set here: expsuf[number]: exponents U and F of functions with function number [number] (first entry in primseclist)