ApartIBP.cpp

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#include "HEP.h"
 
namespace HepLib {
 
    namespace {
 
        void AIR2F_Save(string save_dir, exvector air_vec, const lst & IntFs, vector<IBP*> &ibp_vec) {
            auto rc = system(("mkdir -p "+save_dir+"/AIR2F").c_str());
            rc = system(("rm -f "+save_dir+"/AIR2F/*.gar > /dev/null").c_str());
            GiNaC_Parallel(air_vec.size(), [&air_vec,&save_dir](int idx) {
                garWrite(air_vec[idx], save_dir+"/AIR2F/air-"+to_string(idx)+".gar");
                return 0;
            }, "AIR2F_AIR");
            
            GiNaC_Parallel(ibp_vec.size(), [&ibp_vec,&save_dir](int idx) {
                garWrite(ibp_vec[idx]->TO(), save_dir+"/AIR2F/ibp-"+to_string(idx)+".gar");
                return 0;
            }, "AIR2F_IBP");
            
            ostringstream oss;
            oss << air_vec.size() << " " << ibp_vec.size() << " " << IntFs.nops() << endl;
            if(IntFs.nops()>0) {
                oss << IntFs.op(0).op(1).nops() << endl;
                for(auto const & f : IntFs) {
                    oss << f.op(0);
                    for(auto const & n : f.op(1)) oss << " " << n;
                    oss << endl;
                }
            }
            auto oss_str = oss.str();
            fstream ofs(save_dir+"/AIR2F.gar", fstream::out);
            ofs.write(oss_str.c_str(), oss_str.size());
            ofs.close();
        }
 
        void AIR2F_Get(string save_dir, exvector &air_vec, lst &IntFs, vector<IBP*> &ibp_vec, int IBPmethod) {
            fstream ifs(save_dir+"/AIR2F.gar", fstream::in);
            size_t nair, nibp, nf;
            ifs >> nair >> nibp >> nf;
            
            IntFs.remove_all();
            if(nf>0) {
                int nn;
                ifs >> nn;
                for(int i=0; i<nf; i++) {
                    int pn, ni;
                    ifs >> pn;
                    lst ns;
                    for(int j=0; j<nn; j++) {
                        ifs >> ni;
                        ns.append(ni);
                    }
                    IntFs.append(F(pn, ns));
                }
            }
            
            for(int idx=0; idx<nair; idx++) {
                air_vec[idx] = garRead(save_dir+"/AIR2F/air-"+to_string(idx)+".gar");
            }
            
            ibp_vec.resize(nibp);
            for(int idx=0; idx<nibp; idx++) {
                IBP* ibp;
                if(IBPmethod==0) ibp = new IBP();
                else if(IBPmethod==1) ibp = new FIRE();
                else if(IBPmethod==2) ibp = new KIRA();
                else if(IBPmethod==3) ibp = new UKIRA();
                else ibp = new IBP();
                ex ibp_from = garRead(save_dir+"/AIR2F/ibp-"+to_string(idx)+".gar");
                ibp->FROM(ibp_from);
                ibp_vec[idx] = ibp;
            }
        }
 
    }
    
     ex F2ex(const ex & expr_in) {
        ex ret = expr_in;
        ret = MapFunction([](const ex & e, MapFunction &self)->ex{
            if(!e.has(F(w1,w2))) return e;
            else if(e.match(F(w1, w2))) {
                auto ps = e.op(0);
                auto ns = e.op(1);
                ex res = 1;
                for(int i=0; i<ps.nops(); i++) res *= pow(ps.op(i), ex(0)-ns.op(i));
                return res;
            } else return e.map(self);
        })(ret);
        return ret;
     }
 
    void ApartIBP(exvector &air_vec, AIOption aio) {
        
        if(aio.smap.size()<1) aio.init_smap();
        int IBPmethod = aio.IBPmethod;
        int rc;
        
        lst lmom = ex_to<lst>(aio.Internal);
        lst emom = ex_to<lst>(aio.External);
        
        if(aio.SaveDir != "" && file_exists(aio.SaveDir+"/ApartIBP.gar")) {
            if(Verbose > 1) cout << PRE << "\\--Reading ApartIBP" << flush;
            garRead(air_vec, aio.SaveDir+"/ApartIBP.gar");
            return;
        }
        
        string wdir;
        if(aio.SaveDir != "") {
            if(IBPmethod==1) wdir = aio.SaveDir + "/FIRE";
            else if(IBPmethod==2) wdir = aio.SaveDir + "/KIRA";
            else if(IBPmethod==3) wdir = aio.SaveDir + "/UKIRA";
        } else {
            wdir = to_string(getpid());
            if(IBPmethod==1) wdir = wdir + "_FIRE";
            else if(IBPmethod==2) wdir = wdir + "_KIRA";
            else if(IBPmethod==3) wdir = wdir + "_UKIRA";
        }
        
        lst IntFs;
        vector<IBP*> ibp_vec;
        if(aio.SaveDir != "" && file_exists(aio.SaveDir+"/AIR2F.gar")) {
            if(Verbose > 1) cout << PRE << "\\--Reading AIR2F" << flush;
            AIR2F_Get(aio.SaveDir, air_vec, IntFs, ibp_vec, IBPmethod);
            for(auto ibp : ibp_vec) ibp->WorkingDir = wdir; // update working directory
            if(Verbose > 1) cout << " @ " << now(false) << endl; 
            goto AIR2F_Done;
        }
        
        if(aio.SaveDir != "") {
            if(file_exists(aio.SaveDir+"/AP.gar")) {
                if(Verbose > 1) cout << PRE << "\\--Reading AP.gar" << flush;
                garRead(air_vec, aio.SaveDir+"/AP.gar");
                if(Verbose > 1) cout << " @ " << now(false) << endl; 
                goto Apart_Done;
            } else rc = system(("mkdir -p "+aio.SaveDir).c_str());
        }
        
        if(true) {
            int av_size = air_vec.size();
            air_vec = GiNaC_Parallel(av_size, [air_vec,lmom] (int idx) {
                return collect_lst(air_vec[idx], lmom); // o_flint
            }, "ApPre");
            
            exset vset;
            for(int i=0; i<av_size; i++) {
                for(auto cv : ex_to<lst>(air_vec[i])) vset.insert(cv.op(1));
            }
            exvector vvec(vset.begin(), vset.end());
            vset.clear();
 
            exmap v2api;
            for(int i=0; i<vvec.size(); i++) v2api[vvec[i]] = i;
            for(int i=0; i<av_size; i++) {
                lst av_item;
                lst cvs  = ex_to<lst>(air_vec[i]);
                air_vec[i] = av_item;
                for(auto & cv : cvs) av_item.append(lst{cv.op(0), v2api[cv.op(1)]});
                cvs.remove_all();
                air_vec[i] = av_item;
            }
            v2api.clear();
 
            auto ap_vec = GiNaC_Parallel(vvec.size(), [&vvec,lmom,emom,aio] (int idx) {
                auto air = vvec[idx];
                air = Apart(air,lmom,emom,aio.smap);
                air = air.subs(ApartIR(1,w)==aio.apart1);
                air = collect_lst(air, ApartIR(w1,w2), o_flintf);
                return air;
            }, "Apart");
            vvec.clear();
 
            exset ap_set;
            for(auto cvs : ap_vec) for(auto cv : cvs) if(is_a<matrix>(cv.op(1).op(0))) ap_set.insert(cv.op(1));
            exvector ap_ir_vec(ap_set.begin(), ap_set.end());
            ap_set.clear();
            exmap ap_rules;
            if(aio.ap_rules) ap_rules = ApartRules(ap_ir_vec); // including ApartIRC
            ap_ir_vec.clear();
            
            if(false) { // Parallel Version
                ap_vec = GiNaC_Parallel(ap_vec.size(), [&aio,&ap_vec,&ap_rules] (int idx) {
                    auto const & cvs = ap_vec[idx];
                    ex res = 0;
                    if(aio.ap_rules) {
                        for(auto const & cv : cvs) {
                            auto fi = ap_rules.find(cv.op(1));
                            if(fi==ap_rules.end()) res += cv.op(0) * cv.op(1);
                            else res += cv.op(0) * fi->second;
                        }
                    } else {
                        for(auto cv : cvs) res += cv.op(0) * ApartIRC(cv.op(1));
                    }
                    return res;
                }, "ApRule");
            } else {
                int vn = ap_vec.size();
                for(int idx=0; idx<vn; idx++) {
                    lst cvs = ex_to<lst>(ap_vec[idx]);
                    ex res = 0;
                    if(aio.ap_rules) {
                        for(auto const & cv : cvs) {
                            auto fi = ap_rules.find(cv.op(1));
                            if(fi==ap_rules.end()) res += cv.op(0) * cv.op(1);
                            else res += cv.op(0) * fi->second;
                        }
                    } else {
                        for(auto cv : cvs) res += cv.op(0) * ApartIRC(cv.op(1));
                    }
                    ap_vec[idx] = res;
                }
            }
            ap_rules.clear();
            
            if(GiNaC_Parallel_NP.find("ApPost")==GiNaC_Parallel_NP.end() && CpuCores()>8) GiNaC_Parallel_NP["ApPost"] = 8;
            if(GiNaC_Parallel_NB.find("ApPost")==GiNaC_Parallel_NB.end() && CpuCores()>100) GiNaC_Parallel_NB["ApPost"] = 100;
            air_vec = GiNaC_Parallel(av_size, [&air_vec,&ap_vec] (int idx) {
                lst cvs = ex_to<lst>(air_vec[idx]);
                ex res = 0;
                for(auto const & cv : cvs) {
                    int idx = ex_to<numeric>(cv.op(1)).to_int();
                    res += cv.op(0) * ap_vec[idx];
                }
                res = collect_ex(res, ApartIR(w1,w2)); // o_flint
                return res; // air_vec updated to ApartIR
            }, "ApPost");
            ap_vec.clear();
            
            if(aio.SaveDir != "") {
                garWrite(air_vec,aio.SaveDir+"/AP.gar");
                garRead(air_vec,aio.SaveDir+"/AP.gar");
            }
        }
        Apart_Done: ;
        
        if(true) {
        
            exvector AIR;
            if(true) {
                auto ret = GiNaC_Parallel(air_vec.size(), [&air_vec](int idx)->ex {
                    auto air = air_vec[idx];
                    exset airs;
                    find(air, ApartIR(w1,w2), airs);
                    lst ret;
                    for(auto item : airs) ret.append(item);
                    return ret;
                }, "ApIRC");
                exset intg;
                for(auto airs : ret) for(auto air : ex_to<lst>(airs)) intg.insert(air);
                AIR = exvector(intg.begin(), intg.end());
            }
            
            for(auto sp : aio.CSP) SP_map.erase(sp);
            // from here, Vector will be replaced by its name Symbol
            
            lst repls;
            auto sps = sp_map();
            for(auto kv : sps) {
                repls.append(w*kv.first == w*kv.second);
                repls.append(kv.first == kv.second);
            }
                    
            lst loops, exts; // to match FIRE notation, not Vector, just Symbol
            for(auto li : lmom) {
                if(is_a<Vector>(li)) loops.append(ex_to<Vector>(li).name);
                else loops.append(li);
            }
            for(auto li : emom) {
                if(is_a<Vector>(li)) exts.append(ex_to<Vector>(li).name);
                else exts.append(li);
            }
        
            if(Verbose>0) cout <<  PRE << "\\--Prepare " << WHITE << "IBP" << RESET << " reduction @ " << now(false) << flush;
            
            exmap AIR2F;
            std::map<ex, IBP*, ex_is_less> p2IBP;
            int pn=1;
            int ntot = AIR.size();
            for(int i=0; i<ntot; i++) {
                if(Verbose>0 && (((i+1)%1000)==0 || i+1==ntot)) {
                    cout << "\r                                 \r" << flush;
                    cout << PRE << "\\--Prepare " << WHITE << "IBP" << RESET << " reduction [" << (i+1) << "/" << ntot << "] @ " << now(false) << flush;
                }
                auto const & ir = AIR[i];
                auto mat = ex_to<matrix>(ir.op(0));
                auto vars = ex_to<lst>(ir.op(1));
                lst pns;
                int nrow = mat.rows();
                int den_tot = 0;
                for(int c=0; c<mat.cols(); c++) {
                    ex pc = 0;
                    for(int r=0; r<nrow-2; r++) pc += mat(r,c) * vars.op(r);
                    pc += mat(nrow-2,c);
                    pc = SP2sp(pc);
                    ex nc = ex(0)-mat(nrow-1,c);
                    int ncn;
                    if(nc>0) ncn = -1;
                    else ncn = 1;
                    if(ncn==-1) den_tot++;
                    pns.append(lst{ ncn, pc, nc }); // note the convension, ncn just for sorting
                }
                bool pn_sector = false;
                if(aio.pn_sector>0 && den_tot>=aio.pn_sector) pn_sector = true;
                if(!pn_sector) { // back to original format
                    for(int i=0; i<pns.nops(); i++) pns[i] = lst{ pns.op(i).op(1), pns.op(i).op(2) };
                }
                sort_lst(pns);
                if(pn_sector) { // back to original format
                    for(int i=0; i<pns.nops(); i++) pns[i] = lst{ pns.op(i).op(1), pns.op(i).op(2) };
                }
                
                int nCut = aio.Cut.nops();
                if(nCut>0) {
                    ex cuts = aio.Cut;
                    cuts = cuts.subs(SP_map,nopat);
                    if(aio.CutFirst) for(auto cut : cuts) pns.prepend(lst{ SP2sp(cut), 1 });
                    else for(auto cut : cuts) pns.append(lst{ SP2sp(cut), 1 });
                }
                
                lst props, ns;
                for(auto item : pns) {
                    props.append(item.op(0));
                    ns.append(item.op(1));
                }
                
                ex key = props;
                if(pn_sector) {
                    lst nss;
                    for(int i=0; i<ns.nops(); i++) nss.append(ns.op(i)>0 ? 1 : 0);
                    key = lst{props,nss};
                }
 
                auto kv = p2IBP.find(key);
                if(kv==p2IBP.end()) {
                    IBP* ibp;
                    if(IBPmethod==0) ibp = new IBP();
                    else if(IBPmethod==1) ibp = new FIRE();
                    else if(IBPmethod==2) ibp = new KIRA();
                    else if(IBPmethod==3) ibp = new UKIRA();
                    else {
                        ibp = new IBP();
                        IBPmethod = 0;
                    }
                    
                    p2IBP.insert(make_pair(key,ibp));
                    ibp->Propagator = props;
                    ibp->Internal = loops;
                    ibp->External = exts;
                    ibp->Replacement = repls;
                    if(aio.ISP.nops()>0) for(auto item : aio.ISP) ibp->ISP.append(SP2sp(item));
                    if(aio.DSP.nops()>0) {
                        for(auto item : aio.DSP) {
                            lst sp = ex_to<lst>(item);
                            if(is_a<Vector>(sp.op(0))) sp[0] = (ex_to<Vector>(sp.op(0)).name);
                            if(is_a<Vector>(sp.op(1))) sp[1] = (ex_to<Vector>(sp.op(1)).name);
                            ibp->DSP.append(sp);
                        }
                    }
                    if(pn_sector) {
                        lst sector;
                        for(auto const & item : ns) {
                            if(item>0) sector.append(1);
                            else sector.append(0);
                        }
                        ibp->SECTOR = sector;
                    }
                    ibp->WorkingDir = wdir;
                    ibp->ProblemNumber = pn;
                    pn++;
                    if(nCut>0) {
                        if(aio.CutFirst) for(int i=0; i<nCut; i++) ibp->Cut.append(i+1);
                        else for(int i=0; i<nCut; i++) ibp->Cut.append(nCut-i);
                    }
                    ibp_vec.push_back(ibp);
                    ibp->Integral.append(ns);
                    AIR2F[AIR[i]] = F(ibp->ProblemNumber, ns);
                } else {
                    IBP* ibp = kv->second;
                    ibp->Integral.append(ns);
                    AIR2F[AIR[i]] = F(ibp->ProblemNumber, ns);
                }
            }
            if(Verbose>0) cout << endl;
 
            if(Verbose>0) cout << PRE << "\\--Total Ints/Pros: " << WHITE << ntot << "/" << ibp_vec.size() << RESET << " @ " << now(false) << endl;
        
            if(true) {
                //vector<IBP*> ibp_vec2;
                //for(auto ibp : ibp_vec) ibp_vec2.push_back(ibp);
                auto int_fr = FindRules(ibp_vec, false, aio.UF);
                IntFs = int_fr.second;
                if(GiNaC_Parallel_NP.find("AIR2F")==GiNaC_Parallel_NP.end() && CpuCores()>8) GiNaC_Parallel_NP["AIR2F"] = 8;
                if(GiNaC_Parallel_NB.find("AIR2F")==GiNaC_Parallel_NB.end() && CpuCores()>100) GiNaC_Parallel_NB["AIR2F"] = 100;
                air_vec = GiNaC_Parallel(air_vec.size(), [&air_vec,&AIR2F,&int_fr] (int idx) {
                    auto air = air_vec[idx];
                    air = air.subs(AIR2F,nopat);
                    air = air.subs(int_fr.first,nopat);
                    air = collect_ex(air, F(w1,w2)); // o_flint
                    return air;
                }, "AIR2F");
                if(aio.SaveDir != "") AIR2F_Save(aio.SaveDir, air_vec, IntFs, ibp_vec);
            }
        }
        AIR2F_Done: ;
        
        MapFunction _F2ex([&ibp_vec,aio](const ex &e, MapFunction &self)->ex {
            if(!e.has(F(w1,w2))) return e;
            else if(e.match(F(w1,w2))) {
                int pn = ex_to<numeric>(e.op(0)).to_int();
                auto pso = ex_to<lst>(ibp_vec[pn-1]->Propagator);
                auto nso = ex_to<lst>(e.op(1));
                lst ps, ns;
                for(int i=0; i<pso.nops(); i++) {
                    if(!aio.keep0F && nso.op(i).is_zero()) continue;
                    ps.append(pso.op(i));
                    ns.append(nso.op(i));
                }
                return F(ps,ns);
            } else return e.map(self);
        });
        
        if(IBPmethod==0) { // no IBP reduction
            air_vec = GiNaC_Parallel(air_vec.size(), [&air_vec,&_F2ex](int idx)->ex {
                auto res = air_vec[idx];
                return _F2ex(res);
            }, "F2F");
            for(auto fp : ibp_vec) delete fp;
            if(aio.SaveDir == "") rc = system(("rm -rf "+wdir).c_str());
            return;
        }
 
        exmap ibpRules; // IBP rules for problem pn
        if(aio.SaveDir != "" && file_exists(aio.SaveDir+"/MIs.gar")) {
            goto Rules_Done;
        }
        if(true) { 
            vector<IBP*> ibp_vec_re;
            if(true) {
                map<int,lst> pn_ints_map;
                for(auto item : IntFs) {
                    int pn = ex_to<numeric>(item.op(0)).to_int();
                    pn_ints_map[pn].append(item.op(1));
                }
 
                int nints = 0;
                for(auto pi : pn_ints_map) {
                    auto ibp = ibp_vec[pi.first-1];
                    ibp->Integral = pi.second;
                    nints += ibp->Integral.nops();
                    ibp_vec_re.push_back(ibp);
                }
 
                if(Verbose>0) cout << PRE << "\\--Refined Ints/Pros: " << WHITE << nints << "/" << ibp_vec_re.size() << RESET << " @ " << now(false) << endl;
            } 
            
            if(IBPmethod==1) {
                //if(GiNaC_Parallel_NB.find("Expo")==GiNaC_Parallel_NB.end()) GiNaC_Parallel_NB["Expo"] = 1;
                auto pRes = GiNaC_Parallel(ibp_vec_re.size(), [&ibp_vec_re](int idx)->ex {
                    ibp_vec_re[idx]->Export();
                    auto ret = lst{ ibp_vec_re[idx]->IsAlwaysZero ? 1 : 0, ibp_vec_re[idx]->Rules };
                    return ret;
                }, "Expo");
                for(int i=0; i<ibp_vec_re.size(); i++) {
                    ibp_vec_re[i]->IsAlwaysZero = (pRes[i].op(0)==1 ? true : false);
                    ibp_vec_re[i]->Rules = ex_to<lst>(pRes[i].op(1));
                }
                
                int nproc = aio.NIBP;
                if(nproc<1) nproc = 8;
                int cproc = 0;
                if(nproc<1) nproc = 1;
                size_t nibp = ibp_vec_re.size();
                
                //#define using_openMP
                #ifdef using_openMP
                #pragma omp parallel for num_threads(nproc) schedule(dynamic, 1)
                for(int pi=0; pi<nibp; pi++) {
                    if(Verbose>1) {
                        #pragma omp critical
                        {
                        cout << "\r                                        \r" << flush;
                        cout << PRE << "\\--" << WHITE << "FIRE" << RESET << " Reduction [" << (++cproc) << "/" << nibp << "] " << flush;
                        }
                    }
                    ibp_vec_re[pi]->Run();
                }
                if(Verbose>1 && nibp>0) cout << "@" << now(false) << endl;
                #else
                if(nproc>1) {
                    if(GiNaC_Parallel_NP.find("FIRE")==GiNaC_Parallel_NB.end())  GiNaC_Parallel_NP["FIRE"] = nproc;
                    if(GiNaC_Parallel_NB.find("FIRE")==GiNaC_Parallel_NB.end()) GiNaC_Parallel_NB["FIRE"] = 1;
                    GiNaC_Parallel(nibp, [&ibp_vec_re](int idx)->ex {
                        ibp_vec_re[idx]->Run();
                        return 0;
                    }, "FIRE");
                } else {
                    for(int pi=0; pi<nibp; pi++) {
                        if(Verbose>1) cout << "\r                                        \r" << PRE << "\\--" << WHITE << "FIRE" << RESET << " Reduction [" << (++cproc) << "/" << nibp << "] " << flush;
                        ibp_vec_re[pi]->Run();
                    }
                    if(Verbose>1 && nibp>0) cout << "@" << now(false) << endl;
                }
                #endif
                
                if(ibp_vec_re.size()>100) {
                    auto ret = GiNaC_Parallel(ibp_vec_re.size(), [&ibp_vec_re,wdir](int idx)->ex {
                        ibp_vec_re[idx]->Import();
                        return ibp_vec_re[idx]->TO();
                    }, "Impo");
                    for(int i=0; i<ibp_vec_re.size(); i++) ibp_vec_re[i]->FROM(ret[i]);
                } else {
                    cproc = 0;
                    for(auto item : ibp_vec_re) {
                        if(Verbose>1) cout << "\r                                        \r" << PRE << "\\--" << WHITE << "FIRE" << RESET << " Import [" << (++cproc) << "/" << ibp_vec_re.size() << "] " << flush;
                        item->Import();
                    }
                    if(Verbose>1 && ibp_vec_re.size()>0) cout << "@" << now(false) << endl;
                }
                //IBP::ReShare(ibp_vec_re);
                
                if(aio.SaveDir == "") rc = system(("rm -rf "+wdir).c_str());
            } else if(IBPmethod==2 || IBPmethod==3) {
                for(auto ibp : ibp_vec_re) ibp->Reduce();
                if(aio.SaveDir == "") rc = system(("rm -rf "+wdir).c_str());
            }
            
            // Find Rules in MIs
            auto fr = FindRules(ibp_vec_re, true, aio.UF);
            exmap miRules = fr.first;
            if(true) { // scope for ret
                if(aio.SaveDir != "") rc = system(("mkdir -p "+aio.SaveDir+"/Rules").c_str());
                auto rules_vec = GiNaC_Parallel(ibp_vec_re.size(), [&ibp_vec_re,&miRules,&aio](int idx)->ex {
                    lst rules = ex_to<lst>(ibp_vec_re[idx]->Rules);
                    lst res;
                    for(auto ri : rules) res.append(lst { 
                        ri.op(0),  
                        collect_ex(ri.op(1).subs(miRules,nopat),F(w1,w2),o_flint)
                    });
                    for(auto mi : ibp_vec_re[idx]->MIntegral) {
                        auto fi = miRules.find(mi);
                        if(fi!=miRules.end()) res.append(lst{ mi, fi->second });
                    }
                    auto pn = ibp_vec_re[idx]->ProblemNumber;
                    if(aio.SaveDir != "") {
                        garWrite(aio.SaveDir+"/Rules/"+to_string(pn)+".gar", res);
                        return 0;
                    } else return res;
                }, "FR2MI");
                if(aio.SaveDir != "") {
                    garWrite(aio.SaveDir+"/MIs.gar", _F2ex(fr.second));
                } else {
                    for(auto rs : rules_vec) {
                        for(auto ri : rs) if(ri.op(0)!=ri.op(1)) ibpRules[ri.op(0)] = ri.op(1);
                    }
                }
            }
        }
        Rules_Done: ;
        
        if(GiNaC_Parallel_NP.find("F2MI")==GiNaC_Parallel_NP.end() && CpuCores()>16) GiNaC_Parallel_NP["F2MI"] = 16;
        air_vec =
        GiNaC_Parallel(air_vec.size(), [&air_vec,&ibpRules,&_F2ex,&aio](int idx)->ex {
            ex res = air_vec[idx];
            exmap rules;
            if(aio.SaveDir != "") {
                exset fs;
                find(res, F(w1,w2), fs);
                exset pns;
                for(auto fi : fs) pns.insert(fi.op(0));
                for(auto pn : pns) {
                    auto rs = ex_to<lst>(garRead(aio.SaveDir+"/Rules/"+ex2str(pn)+".gar"));
                    for(auto ri : rs) if(ri.op(0)!=ri.op(1)) rules[ri.op(0)] = ri.op(1);
                }
            } else rules = ibpRules;
            res = res.subs(rules,nopat);
            if(aio.pat.nops()>0) {
                auto cvs = collect_lst(res, aio.pat);
                res = 0;
                for(auto cv : cvs) {
                    auto c = cv.op(0);
                    auto v = cv.op(1);
                    if(aio.cv!=nullptr) {
                        auto _cv = aio.cv(c,v);
                        c = _cv.op(0);
                        v = _cv.op(1);
                    }
                    res += c * v;
                }
            }
            return _F2ex(res);
        }, "F2MI");
                                    
        for(auto fp : ibp_vec) delete fp;
        
        if(aio.SaveDir != "") garWrite(air_vec, aio.SaveDir+"/ApartIBP.gar");
    }
    
    void ApartIBP(exvector &air_vec, int IBPmethod, const lst & loops, const lst & exts, const lst & cut_props,
        std::function<lst(const IBP &, const ex &)> uf) {
                
        AIOption aio;
        aio.IBPmethod = IBPmethod;
        //aio.pn_sector = 4;
        aio.Internal = loops;
        aio.External = exts;
        aio.Cut = cut_props;
        if(cut_props.nops()>0) {
            for(auto p1 : loops) {
                for(auto p2 : loops) aio.CSP.append(SP(p1,p2,false));
                for(auto p2 : exts) aio.CSP.append(SP(p1,p2,false));
            }
            aio.CSP.sort();
            aio.CSP.unique();
        }
        for(auto li : loops) aio.smap[SP(li,false)] = 1;
        aio.UF = uf;
        ApartIBP(air_vec, aio);
    }
 
}