SecDec/loop/src/deco/SDroutines.m [ Mathematica Files ]

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NAME

  SDroutines.m

USAGE

  called from decomposition.m

PURPOSE

  Contains routines to perform iterated SD, and to output files created by
  decomposition.m

FUNCTIONS

 for the decomposition:
  countvars[cvf,cfv,np]: finds the maximum power of a set of variables cfv 
   in a function cvf from primary sector np.
  findpossset[fexpr,np]: finds all minimal sets (wrt length) of the
   integration variables which nullify a function fexpr from primary
   sector np. 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,np]: finds the 'best' set which nullifies 
   function n from the list of integrands, derived from primary sector
   np. '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. The prefactor 
   maxinv^(expoU+expoF)is put into the numerator.
  
 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 and
   which primary sector it derives from. increments the counter
   polecount[polestruct,np] for this classification, and adds a pointer to
   sector in a list seclist[polestruct,np] 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.
   for each primary sector, 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 [graph]sec[np]P[polestruct].out. The information
   on number of sectors from each primary sector with this pole structure is
   added to the string poleinfostring
  writeinfo: writes the necessary information to file [graph]OUT.info, or
   [graph]Sec[npmax]OUT.info if primary sectors are treated individually.
   this info includes number of propagators Nn, exponents expoU and expoF,
   total number of sectors produced allcount, maximum poles maxlogpole,
   maxlinpole, maxhpole, the order of the default prefactor prefacord, and
   the default prefactor itself prefac.
  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.
  
  variables:
   maxinv: is a symbolic variable which will be replaced by the biggest kinematic
    invariant during numerical integration
  from decompose.pl:
   indflag: Indflag states if special primary sectors were indicated in the 
    paramloop.input file. If indflag=1, the integrand info is written to 
    [graph]Sec[npmax]OUT.info, else it is written to [graph]OUT.info.