ktclusdble.f

CMSSW/GeneratorInterface/PartonShowerVeto/src/ktclusdble.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 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571	`C-----------------------------------------------------------------------` `C-----------------------------------------------------------------------` `C-----------------------------------------------------------------------` `C KTCLUS: written by Mike Seymour, July 1992.` `C Last modified November 2000.` `C Please send comments or suggestions to Mike.Seymour@rl.ac.uk` `C` `C This is a general-purpose kt clustering package.` `C It can handle ee, ep and pp collisions.` `C It is loosely based on the program of Siggi Bethke.` `C` `C The time taken (on a 10MIP machine) is (0.2microsec)N3` `C where N is the number of particles.` `C Over 90 percent of this time is used in subroutine KTPMIN, which` `C simply finds the minimum member of a one-dimensional array.` `C It is well worth thinking about optimization: on the SPARCstation` `C a factor of two increase was obtained simply by increasing the` `C optimization level from its default value.` `C` `C The approach is to separate the different stages of analysis.` `C KTCLUS does all the clustering and records a merging history.` `C It returns a simple list of the y values at which each merging` `C occured. Then the following routines can be called to give extra` `C information on the most recently analysed event.` `C KTCLUR is identical but includes an R parameter, see below.` `C KTYCUT gives the number of jets at each given YCUT value.` `C KTYSUB gives the number of sub-jets at each given YCUT value.` `C KTBEAM gives same info as KTCLUS but only for merges with the beam` `C KTJOIN gives same info as KTCLUS but for merges of sub-jets.` `C KTRECO reconstructs the jet momenta at a given value of YCUT.` `C It also gives information on which jets at scale YCUT belong to` `C which macro-jets at scale YMAC, for studying sub-jet properties.` `C KTINCL reconstructs the jet momenta according to the inclusive jet` `C definition of Ellis and Soper.` `C KTISUB, KTIJOI and KTIREC are like KTYSUB, KTJOIN and KTRECO,` `C except that they only apply to one inclusive jet at a time,` `C with the pt of that jet automatically used for ECUT.` `C KTWICH gives a list of which particles ended up in which jets.` `C KTWCHS gives the same thing, but only for subjets.` `C Note that the numbering of jets used by these two routines is` `C guaranteed to be the same as that used by KTRECO.` `C` `C The collision type and analysis type are indicated by the first` `C argument of KTCLUS. IMODE=<TYPE><ANGLE><MONO><RECOM> where` `C TYPE: 1=>ee, 2=>ep with p in -z direction, 3=>pe, 4=>pp` `C ANGLE: 1=>angular kt def., 2=>DeltaR, 3=>f(DeltaEta,DeltaPhi)` `C where f()=2(cosh(eta)-cos(phi)) is the QCD emission metric` `C MONO: 1=>derive relative pseudoparticle angles from jets` `C 2=>monotonic definitions of relative angles` `C RECOM: 1=>E recombination scheme, 2=>pt scheme, 3=>pt2 scheme` `C` `C There are also abbreviated forms for the most common combinations:` `C IMODE=1 => E scheme in e+e- (=1111)` `C 2 => E scheme in ep (=2111)` `C 3 => E scheme in pe (=3111)` `C 4 => E scheme in pp (=4111)` `C 5 => covariant E scheme in pp (=4211)` `C 6 => covariant pt-scheme in pp (=4212)` `C 7 => covariant monotonic pt2-scheme in pp (=4223)` `C` `C KTRECO no longer needs to reconstruct the momenta according to the` `C same recombination scheme in which they were clustered. Its first` `C argument gives the scheme, taking the same values as RECOM above.` `C` `C Note that unlike previous versions, all variables which hold y` `C values have been named in a consistent way:` `C Y() is the output scale at which jets were merged,` `C YCUT is the input scale at which jets should be counted, and` `C jet-momenta reconstructed etc,` `C YMAC is the input macro-jet scale, used in determining whether` `C or not each jet is a sub-jet.` `C The original scheme defined in our papers is equivalent to always` `C setting YMAC=1.` `C Whenever a YCUT or YMAC variable is used, it is rounded down` `C infinitesimally, so that for example, setting YCUT=Y(2) refers` `C to the scale where the event is 2-jet, even if rounding errors` `C have shifted its value slightly.` `C` `C An R parameter can be used in hadron-hadron collisions by` `C calling KTCLUR instead of KTCLUS. This is as suggested by` `C Ellis and Soper, but implemented slightly differently,` `C as in M.H. Seymour, LU TP 94/2 (submitted to Nucl. Phys. B.).` `C R2 multiplies the single Kt everywhere it is used.` `C Calling KTCLUR with R=1 is identical to calling KTCLUS.` `C R plays a similar role to the jet radius in a cone-type algorithm,` `C but is scaled up by about 40% (ie R=0.7 in a cone algorithm is` `C similar to this algorithm with R=1).` `C Note that R.EQ.1 must be used for the e+e- and ep versions,` `C and is strongly recommended for the hadron-hadron version.` `C However, R values smaller than 1 have been found to be useful for` `C certain applications, particularly the mass reconstruction of` `C highly-boosted colour-singlets such as high-pt hadronic Ws,` `C as in M.H. Seymour, LU TP 93/8 (to appear in Z. Phys. C.).` `C Situations in which R<1 is useful are likely to also be those in` `C which the inclusive reconstruction method is more useful.` `C` `C Also included is a set of routines for doing Lorentz boosts:` `C KTLBST finds the boost matrix to/from the cm frame of a 4-vector` `C KTRROT finds the rotation matrix from one vector to another` `C KTMMUL multiplies together two matrices` `C KTVMUL multiplies a vector by a matrix` `C KTINVT inverts a transformation matrix (nb NOT a general 4 by 4)` `C KTFRAM boosts a list of vectors between two arbitrary frames` `C KTBREI boosts a list of vectors between the lab and Breit frames` `C KTHADR boosts a list of vectors between the lab and hadronic cmf` `C The last two need the momenta in the +z direction of the lepton` `C and hadron beams, and the 4-momentum of the outgoing lepton.` `C` `C The main reference is:` `C S. Catani, Yu.L. Dokshitzer, M.H. Seymour and B.R. Webber,` `C Nucl.Phys.B406(1993)187.` `C The ep version was proposed in:` `C S. Catani, Yu.L. Dokshitzer and B.R. Webber,` `C Phys.Lett.285B(1992)291.` `C The inclusive reconstruction method was proposed in:` `C S.D. Ellis and D.E. Soper,` `C Phys.Rev.D48(1993)3160.` `C` `C-----------------------------------------------------------------------` `C-----------------------------------------------------------------------` `C-----------------------------------------------------------------------` `SUBROUTINE KTCLUS(IMODE,PP,NN,ECUT,Y,)` `IMPLICIT NONE` `C---DO CLUSTER ANALYSIS OF PARTICLES IN PP` `C` `C IMODE = INPUT : DESCRIBED ABOVE` `C PP(I,J) = INPUT : 4-MOMENTUM OF Jth PARTICLE: I=1,4 => PX,PY,PZ,E` `C NN = INPUT : NUMBER OF PARTICLES` `C ECUT = INPUT : DENOMINATOR OF KT MEASURE. IF ZERO, ETOT IS USED` `C Y(J) = OUTPUT : VALUE OF Y FOR WHICH EVENT CHANGES FROM BEING` `C J JET TO J-1 JET` `C LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT` `C COULD NOT BE PROCESSED (MOST LIKELY DUE TO TOO MANY PARTICLES)` `C` `C NOTE THAT THE MOMENTA ARE DECLARED DOUBLE PRECISION,` `C AND ALL OTHER FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION` `C` `INTEGER IMODE,NN` `DOUBLE PRECISION PP(4,)` `DOUBLE PRECISION ECUT,Y(),ONE` `ONE=1` `CALL KTCLUR(IMODE,PP,NN,ONE,ECUT,Y,999)` `RETURN` `999 RETURN 1` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTCLUR(IMODE,PP,NN,R,ECUT,Y,)` `IMPLICIT NONE` `C---DO CLUSTER ANALYSIS OF PARTICLES IN PP` `C` `C IMODE = INPUT : DESCRIBED ABOVE` `C PP(I,J) = INPUT : 4-MOMENTUM OF Jth PARTICLE: I=1,4 => PX,PY,PZ,E` `C NN = INPUT : NUMBER OF PARTICLES` `C R = INPUT : ELLIS AND SOPER'S R PARAMETER, SEE ABOVE.` `C ECUT = INPUT : DENOMINATOR OF KT MEASURE. IF ZERO, ETOT IS USED` `C Y(J) = OUTPUT : VALUE OF Y FOR WHICH EVENT CHANGES FROM BEING` `C J JET TO J-1 JET` `C LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT` `C COULD NOT BE PROCESSED (MOST LIKELY DUE TO TOO MANY PARTICLES)` `C` `C NOTE THAT THE MOMENTA ARE DECLARED DOUBLE PRECISION,` `C AND ALL OTHER FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION` `C` `INTEGER NMAX,IM,IMODE,TYPE,ANGL,MONO,RECO,N,I,J,NN,` `& IMIN,JMIN,KMIN,NUM,HIST,INJET,IABBR,NABBR` `PARAMETER (NMAX=512,NABBR=7)` `DOUBLE PRECISION PP(4,)` `DOUBLE PRECISION R,ECUT,Y(),P,KT,ETOT,RSQ,KTP,KTS,KTPAIR,KTSING,` `& KTMIN,ETSQ,KTLAST,KTMAX,KTTMP` `LOGICAL FIRST` `CHARACTER TITLE(4,4)10` `C---KT RECORDS THE KT2 OF EACH MERGING.` `C---KTLAST RECORDS FOR EACH MERGING, THE HIGHEST ECUT2 FOR WHICH THE` `C RESULT IS NOT MERGED WITH THE BEAM (COULD BE LARGER THAN THE` `C KT2 AT WHICH IT WAS MERGED IF THE KT VALUES ARE NOT MONOTONIC).` `C THIS MAY SOUND POINTLESS, BUT ITS USEFUL FOR DETERMINING WHETHER` `C SUB-JETS SURVIVED TO SCALE Y=YMAC OR NOT.` `C---HIST RECORDS MERGING HISTORY:` `C N=>DELETED TRACK N, MNMAX+N=>MERGED TRACKS M AND N (M<N).` `COMMON /KTCOMM/ETOT,RSQ,P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX),` `& KT(NMAX),KTLAST(NMAX),HIST(NMAX),NUM` `DIMENSION INJET(NMAX),IABBR(NABBR)` `DATA FIRST,TITLE,IABBR/.TRUE.,` `& 'e+e- ','ep ','pe ','pp ',` `& 'angle ','DeltaR ','f(DeltaR) ','********',` `& 'no ','yes ','******','******',` `& 'E ','Pt ','Pt2 ','*********',` `& 1111,2111,3111,4111,4211,4212,4223/` `C---CHECK INPUT` `IM=IMODE` `IF (IM.GE.1.AND.IM.LE.NABBR) IM=IABBR(IM)` `TYPE=MOD(IM/1000,10)` `ANGL=MOD(IM/100 ,10)` `MONO=MOD(IM/10 ,10)` `RECO=MOD(IM ,10)` `IF (NN.GT.NMAX.OR.NN.LT.1.OR.(NN.LT.2.AND.TYPE.EQ.1))` `& CALL KTWARN('KTCLUS',100,999)` `IF (TYPE.LT.1.OR.TYPE.GT.4.OR.ANGL.LT.1.OR.ANGL.GT.4.OR.` `& MONO.LT.1.OR.MONO.GT.2.OR.RECO.LT.1.OR.RECO.GT.3)` `& CALL KTWARN('KTCLUS',101,999)` `IF (FIRST) THEN` `WRITE (6,'(/,1X,54('''')/A)')` `& ' KTCLUS: written by Mike Seymour, July 1992.'` `WRITE (6,'(A)')` `& ' Last modified November 2000.'` `WRITE (6,'(A)')` `& ' Please send comments or suggestions to Mike.Seymour@rl.ac.uk'` `WRITE (6,'(/A,I2,2A)')` `& ' Collision type =',TYPE,' = ',TITLE(TYPE,1)` `WRITE (6,'(A,I2,2A)')` `& ' Angular variable =',ANGL,' = ',TITLE(ANGL,2)` `WRITE (6,'(A,I2,2A)')` `& ' Monotonic definition =',MONO,' = ',TITLE(MONO,3)` `WRITE (6,'(A,I2,2A)')` `& ' Recombination scheme =',RECO,' = ',TITLE(RECO,4)` `IF (R.NE.1) THEN` `WRITE (6,'(A,F5.2)')` `& ' Radius parameter =',R` `IF (TYPE.NE.4) WRITE (6,'(A)')` `& ' R.NE.1 is strongly discouraged for this collision type!'` `ENDIF` `WRITE (6,'(1X,54('''')/)')` `FIRST=.FALSE.` `ENDIF` `C---COPY PP TO P` `N=NN` `NUM=NN` `CALL KTCOPY(PP,N,P,(RECO.NE.1))` `ETOT=0` `DO 100 I=1,N` `ETOT=ETOT+P(4,I)` `100 CONTINUE` `IF (ETOT.EQ.0) CALL KTWARN('KTCLUS',102,999)` `IF (ECUT.EQ.0) THEN` `ETSQ=1/ETOT2` `ELSE` `ETSQ=1/ECUT2` `ENDIF` `RSQ=R*2` `C---CALCULATE ALL PAIR KT's` `DO 210 I=1,N-1` `DO 200 J=I+1,N` `KTP(J,I)=-1` `KTP(I,J)=KTPAIR(ANGL,P(1,I),P(1,J),KTP(J,I))` `200 CONTINUE` `210 CONTINUE` `C---CALCULATE ALL SINGLE KT's` `DO 230 I=1,N` `KTS(I)=KTSING(ANGL,TYPE,P(1,I))` `230 CONTINUE` `KTMAX=0` `C---MAIN LOOP` `300 CONTINUE` `C---FIND MINIMUM MEMBER OF KTP` `CALL KTPMIN(KTP,NMAX,N,IMIN,JMIN)` `C---FIND MINIMUM MEMBER OF KTS` `CALL KTSMIN(KTS,NMAX,N,KMIN)` `C---STORE Y VALUE OF TRANSITION FROM N TO N-1 JETS` `KTMIN=KTP(IMIN,JMIN)` `KTTMP=RSQKTS(KMIN)` `IF ((TYPE.GE.2.AND.TYPE.LE.4).AND.` `& (KTTMP.LE.KTMIN.OR.N.EQ.1))` `& KTMIN=KTTMP` `KT(N)=KTMIN` `Y(N)=KT(N)ETSQ` `C---IF MONO.GT.1, SEQUENCE IS SUPPOSED TO BE MONOTONIC, IF NOT, WARN` `IF (KTMIN.LT.KTMAX.AND.MONO.GT.1) CALL KTWARN('KTCLUS',1,999)` `IF (KTMIN.GE.KTMAX) KTMAX=KTMIN` `C---IF LOWEST KT IS TO A BEAM, THROW IT AWAY AND MOVE LAST ENTRY UP` `IF (KTMIN.EQ.KTTMP) THEN` `CALL KTMOVE(P,KTP,KTS,NMAX,N,KMIN,1)` `C---UPDATE HISTORY AND CROSS-REFERENCES` `HIST(N)=KMIN` `INJET(N)=KMIN` `DO 400 I=N,NN` `IF (INJET(I).EQ.KMIN) THEN` `KTLAST(I)=KTMAX` `INJET(I)=0` `ELSEIF (INJET(I).EQ.N) THEN` `INJET(I)=KMIN` `ENDIF` `400 CONTINUE` `C---OTHERWISE MERGE JETS IMIN AND JMIN AND MOVE LAST ENTRY UP` `ELSE` `CALL KTMERG(P,KTP,KTS,NMAX,IMIN,JMIN,N,TYPE,ANGL,MONO,RECO)` `CALL KTMOVE(P,KTP,KTS,NMAX,N,JMIN,1)` `C---UPDATE HISTORY AND CROSS-REFERENCES` `HIST(N)=IMINNMAX+JMIN` `INJET(N)=IMIN` `DO 600 I=N,NN` `IF (INJET(I).EQ.JMIN) THEN` `INJET(I)=IMIN` `ELSEIF (INJET(I).EQ.N) THEN` `INJET(I)=JMIN` `ENDIF` `600 CONTINUE` `ENDIF` `C---THATS ALL THERE IS TO IT` `N=N-1` `IF (N.GT.1 .OR. N.GT.0.AND.(TYPE.GE.2.AND.TYPE.LE.4)) GOTO 300` `IF (N.EQ.1) THEN` `KT(N)=1D20` `Y(N)=KT(N)ETSQ` `ENDIF` `RETURN` `999 RETURN 1` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTYCUT(ECUT,NY,YCUT,NJET,)` `IMPLICIT NONE` `C---COUNT THE NUMBER OF JETS AT EACH VALUE OF YCUT, FOR EVENT WHICH HAS` `C ALREADY BEEN ANALYSED BY KTCLUS.` `C` `C ECUT = INPUT : DENOMINATOR OF KT MEASURE. IF ZERO, ETOT IS USED` `C NY = INPUT : NUMBER OF YCUT VALUES` `C YCUT(J) = INPUT : Y VALUES AT WHICH NUMBERS OF JETS ARE COUNTED` `C NJET(J) =OUTPUT : NUMBER OF JETS AT YCUT(J)` `C LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT` `C COULD NOT BE PROCESSED` `C` `C NOTE THAT ALL FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION` `C` `INTEGER NY,NJET(NY),NMAX,HIST,I,J,NUM` `PARAMETER (NMAX=512)` `DOUBLE PRECISION YCUT(NY),ETOT,RSQ,P,KT,KTP,KTS,ETSQ,ECUT,KTLAST,` `& ROUND` `PARAMETER (ROUND=0.99999D0)` `COMMON /KTCOMM/ETOT,RSQ,P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX),` `& KT(NMAX),KTLAST(NMAX),HIST(NMAX),NUM` `IF (ETOT.EQ.0) CALL KTWARN('KTYCUT',100,999)` `IF (ECUT.EQ.0) THEN` `ETSQ=1/ETOT2` `ELSE` `ETSQ=1/ECUT2` `ENDIF` `DO 100 I=1,NY` `NJET(I)=0` `100 CONTINUE` `DO 210 I=NUM,1,-1` `DO 200 J=1,NY` `IF (NJET(J).EQ.0.AND.KT(I)ETSQ.GE.ROUNDYCUT(J)) NJET(J)=I` `200 CONTINUE` `210 CONTINUE` `RETURN` `999 RETURN 1` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTYSUB(ECUT,NY,YCUT,YMAC,NSUB,)` `IMPLICIT NONE` `C---COUNT THE NUMBER OF SUB-JETS AT EACH VALUE OF YCUT, FOR EVENT WHICH` `C HAS ALREADY BEEN ANALYSED BY KTCLUS.` `C REMEMBER THAT A SUB-JET IS DEFINED AS A JET AT Y=YCUT WHICH HAS NOT` `C YET BEEN MERGED WITH THE BEAM AT Y=YMAC.` `C` `C ECUT = INPUT : DENOMINATOR OF KT MEASURE. IF ZERO, ETOT IS USED` `C NY = INPUT : NUMBER OF YCUT VALUES` `C YCUT(J) = INPUT : Y VALUES AT WHICH NUMBERS OF SUB-JETS ARE COUNTED` `C YMAC = INPUT : Y VALUE USED TO DEFINE MACRO-JETS, TO DETERMINE` `C WHICH JETS ARE SUB-JETS` `C NSUB(J) =OUTPUT : NUMBER OF SUB-JETS AT YCUT(J)` `C LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT` `C COULD NOT BE PROCESSED` `C` `C NOTE THAT ALL FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION` `C` `INTEGER NY,NSUB(NY),NMAX,HIST,I,J,NUM` `PARAMETER (NMAX=512)` `DOUBLE PRECISION YCUT(NY),YMAC,ETOT,RSQ,P,KT,KTP,KTS,ETSQ,ECUT,` `& KTLAST,ROUND` `PARAMETER (ROUND=0.99999D0)` `COMMON /KTCOMM/ETOT,RSQ,P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX),` `& KT(NMAX),KTLAST(NMAX),HIST(NMAX),NUM` `IF (ETOT.EQ.0) CALL KTWARN('KTYSUB',100,999)` `IF (ECUT.EQ.0) THEN` `ETSQ=1/ETOT2` `ELSE` `ETSQ=1/ECUT2` `ENDIF` `DO 100 I=1,NY` `NSUB(I)=0` `100 CONTINUE` `DO 210 I=NUM,1,-1` `DO 200 J=1,NY` `IF (NSUB(J).EQ.0.AND.KT(I)ETSQ.GE.ROUNDYCUT(J)) NSUB(J)=I` `IF (NSUB(J).NE.0.AND.KTLAST(I)ETSQ.LT.ROUNDYMAC)` `& NSUB(J)=NSUB(J)-1` `200 CONTINUE` `210 CONTINUE` `RETURN` `999 RETURN 1` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTBEAM(ECUT,Y,)` `IMPLICIT NONE` `C---GIVE SAME INFORMATION AS LAST CALL TO KTCLUS EXCEPT THAT ONLY` `C TRANSITIONS WHERE A JET WAS MERGED WITH THE BEAM JET ARE RECORDED` `C` `C ECUT = INPUT : DENOMINATOR OF KT MEASURE. IF ZERO, ETOT IS USED` `C Y(J) =OUTPUT : Y VALUE WHERE Jth HARDEST JET WAS MERGED WITH BEAM` `C LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT` `C COULD NOT BE PROCESSED` `C` `C NOTE THAT ALL FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION` `C` `INTEGER NMAX,HIST,NUM,I,J` `PARAMETER (NMAX=512)` `DOUBLE PRECISION ETOT,RSQ,P,KT,KTP,KTS,ECUT,ETSQ,Y(),KTLAST` `COMMON /KTCOMM/ETOT,RSQ,P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX),` `& KT(NMAX),KTLAST(NMAX),HIST(NMAX),NUM` `IF (ETOT.EQ.0) CALL KTWARN('KTBEAM',100,999)` `IF (ECUT.EQ.0) THEN` `ETSQ=1/ETOT2` `ELSE` `ETSQ=1/ECUT2` `ENDIF` `J=1` `DO 100 I=1,NUM` `IF (HIST(I).LE.NMAX) THEN` `Y(J)=ETSQKT(I)` `J=J+1` `ENDIF` `100 CONTINUE` `DO 200 I=J,NUM` `Y(I)=0` `200 CONTINUE` `RETURN` `999 RETURN 1` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTJOIN(ECUT,YMAC,Y,)` `IMPLICIT NONE` `C---GIVE SAME INFORMATION AS LAST CALL TO KTCLUS EXCEPT THAT ONLY` `C TRANSITIONS WHERE TWO SUB-JETS WERE JOINED ARE RECORDED` `C REMEMBER THAT A SUB-JET IS DEFINED AS A JET AT Y=YCUT WHICH HAS NOT` `C YET BEEN MERGED WITH THE BEAM AT Y=YMAC.` `C` `C ECUT = INPUT : DENOMINATOR OF KT MEASURE. IF ZERO, ETOT IS USED` `C YMAC = INPUT : VALUE OF Y USED TO DEFINE MACRO-JETS` `C Y(J) =OUTPUT : Y VALUE WHERE EVENT CHANGED FROM HAVING` `C N+J SUB-JETS TO HAVING N+J-1, WHERE N IS` `C THE NUMBER OF MACRO-JETS AT SCALE YMAC` `C LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT` `C COULD NOT BE PROCESSED` `C` `C NOTE THAT ALL FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION` `C` `INTEGER NMAX,HIST,NUM,I,J` `PARAMETER (NMAX=512)` `DOUBLE PRECISION ETOT,RSQ,P,KT,KTP,KTS,ECUT,ETSQ,Y(),YMAC,KTLAST,` `& ROUND` `PARAMETER (ROUND=0.99999D0)` `COMMON /KTCOMM/ETOT,RSQ,P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX),` `& KT(NMAX),KTLAST(NMAX),HIST(NMAX),NUM` `IF (ETOT.EQ.0) CALL KTWARN('KTJOIN',100,999)` `IF (ECUT.EQ.0) THEN` `ETSQ=1/ETOT2` `ELSE` `ETSQ=1/ECUT2` `ENDIF` `J=1` `DO 100 I=1,NUM` `IF (HIST(I).GT.NMAX.AND.ETSQKTLAST(I).GE.ROUNDYMAC) THEN` `Y(J)=ETSQKT(I)` `J=J+1` `ENDIF` `100 CONTINUE` `DO 200 I=J,NUM` `Y(I)=0` `200 CONTINUE` `RETURN` `999 RETURN 1` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTRECO(RECO,PP,NN,ECUT,YCUT,YMAC,PJET,JET,NJET,NSUB,)` `IMPLICIT NONE` `C---RECONSTRUCT KINEMATICS OF JET SYSTEM, WHICH HAS ALREADY BEEN` `C ANALYSED BY KTCLUS. NOTE THAT NO CONSISTENCY CHECK IS MADE: USER` `C IS TRUSTED TO USE THE SAME PP VALUES AS FOR KTCLUS` `C` `C RECO = INPUT : RECOMBINATION SCHEME (NEED NOT BE SAME AS KTCLUS)` `C PP(I,J) = INPUT : 4-MOMENTUM OF Jth PARTICLE: I=1,4 => PX,PY,PZ,E` `C NN = INPUT : NUMBER OF PARTICLES` `C ECUT = INPUT : DENOMINATOR OF KT MEASURE. IF ZERO, ETOT IS USED` `C YCUT = INPUT : Y VALUE AT WHICH TO RECONSTRUCT JET MOMENTA` `C YMAC = INPUT : Y VALUE USED TO DEFINE MACRO-JETS, TO DETERMINE` `C WHICH JETS ARE SUB-JETS` `C PJET(I,J)=OUTPUT : 4-MOMENTUM OF Jth JET AT SCALE YCUT` `C JET(J) =OUTPUT : THE MACRO-JET WHICH CONTAINS THE Jth JET,` `C SET TO ZERO IF JET IS NOT A SUB-JET` `C NJET =OUTPUT : THE NUMBER OF JETS` `C NSUB =OUTPUT : THE NUMBER OF SUB-JETS (EQUAL TO THE NUMBER OF` `C NON-ZERO ENTRIES IN JET())` `C LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT` `C COULD NOT BE PROCESSED` `C` `C NOTE THAT THE MOMENTA ARE DECLARED DOUBLE PRECISION,` `C AND ALL OTHER FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION` `C` `INTEGER NMAX,RECO,NUM,N,NN,NJET,NSUB,JET(),HIST,IMIN,JMIN,I,J` `PARAMETER (NMAX=512)` `DOUBLE PRECISION PP(4,),PJET(4,)` `DOUBLE PRECISION ECUT,P,KT,KTP,KTS,ETOT,RSQ,ETSQ,YCUT,YMAC,KTLAST,` `& ROUND` `PARAMETER (ROUND=0.99999D0)` `COMMON /KTCOMM/ETOT,RSQ,P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX),` `& KT(NMAX),KTLAST(NMAX),HIST(NMAX),NUM` `C---CHECK INPUT` `IF (RECO.LT.1.OR.RECO.GT.3) THEN` `PRINT ,'RECO=',RECO` `CALL KTWARN('KTRECO',100,999)` `ENDIF` `C---COPY PP TO P` `N=NN` `IF (NUM.NE.NN) CALL KTWARN('KTRECO',101,999)` `CALL KTCOPY(PP,N,P,(RECO.NE.1))` `IF (ECUT.EQ.0) THEN` `ETSQ=1/ETOT2` `ELSE` `ETSQ=1/ECUT2` `ENDIF` `C---KEEP MERGING UNTIL YCUT` `100 IF (ETSQKT(N).LT.ROUNDYCUT) THEN` `IF (HIST(N).LE.NMAX) THEN` `CALL KTMOVE(P,KTP,KTS,NMAX,N,HIST(N),0)` `ELSE` `IMIN=HIST(N)/NMAX` `JMIN=HIST(N)-IMINNMAX` `CALL KTMERG(P,KTP,KTS,NMAX,IMIN,JMIN,N,0,0,0,RECO)` `CALL KTMOVE(P,KTP,KTS,NMAX,N,JMIN,0)` `ENDIF` `N=N-1` `IF (N.GT.0) GOTO 100` `ENDIF` `C---IF YCUT IS TOO LARGE THERE ARE NO JETS` `NJET=N` `NSUB=N` `IF (N.EQ.0) RETURN` `C---SET UP OUTPUT MOMENTA` `DO 210 I=1,NJET` `IF (RECO.EQ.1) THEN` `DO 200 J=1,4` `PJET(J,I)=P(J,I)` `200 CONTINUE` `ELSE` `PJET(1,I)=P(6,I)COS(P(8,I))` `PJET(2,I)=P(6,I)SIN(P(8,I))` `PJET(3,I)=P(6,I)SINH(P(7,I))` `PJET(4,I)=P(6,I)COSH(P(7,I))` `ENDIF` `JET(I)=I` `210 CONTINUE` `C---KEEP MERGING UNTIL YMAC TO FIND THE FATE OF EACH JET` `300 IF (ETSQKT(N).LT.ROUNDYMAC) THEN` `IF (HIST(N).LE.NMAX) THEN` `IMIN=0` `JMIN=HIST(N)` `NSUB=NSUB-1` `ELSE` `IMIN=HIST(N)/NMAX` `JMIN=HIST(N)-IMINNMAX` `IF (ETSQKTLAST(N).LT.ROUNDYMAC) NSUB=NSUB-1` `ENDIF` `DO 310 I=1,NJET` `IF (JET(I).EQ.JMIN) JET(I)=IMIN` `IF (JET(I).EQ.N) JET(I)=JMIN` `310 CONTINUE` `N=N-1` `IF (N.GT.0) GOTO 300` `ENDIF` `RETURN` `999 RETURN 1` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTINCL(RECO,PP,NN,PJET,JET,NJET,)` `IMPLICIT NONE` `C---RECONSTRUCT KINEMATICS OF JET SYSTEM, WHICH HAS ALREADY BEEN` `C ANALYSED BY KTCLUS ACCORDING TO THE INCLUSIVE JET DEFINITION. NOTE` `C THAT NO CONSISTENCY CHECK IS MADE: USER IS TRUSTED TO USE THE SAME` `C PP VALUES AS FOR KTCLUS` `C` `C RECO = INPUT : RECOMBINATION SCHEME (NEED NOT BE SAME AS KTCLUS)` `C PP(I,J) = INPUT : 4-MOMENTUM OF Jth PARTICLE: I=1,4 => PX,PY,PZ,E` `C NN = INPUT : NUMBER OF PARTICLES` `C PJET(I,J)=OUTPUT : 4-MOMENTUM OF Jth JET AT SCALE YCUT` `C JET(J) =OUTPUT : THE JET WHICH CONTAINS THE Jth PARTICLE` `C NJET =OUTPUT : THE NUMBER OF JETS` `C LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT` `C COULD NOT BE PROCESSED` `C` `C NOTE THAT THE MOMENTA ARE DECLARED DOUBLE PRECISION,` `C AND ALL OTHER FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION` `C` `INTEGER NMAX,RECO,NUM,N,NN,NJET,JET(),HIST,IMIN,JMIN,I,J` `PARAMETER (NMAX=512)` `DOUBLE PRECISION PP(4,),PJET(4,)` `DOUBLE PRECISION P,KT,KTP,KTS,ETOT,RSQ,KTLAST` `COMMON /KTCOMM/ETOT,RSQ,P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX),` `& KT(NMAX),KTLAST(NMAX),HIST(NMAX),NUM` `C---CHECK INPUT` `IF (RECO.LT.1.OR.RECO.GT.3) CALL KTWARN('KTINCL',100,999)` `C---COPY PP TO P` `N=NN` `IF (NUM.NE.NN) CALL KTWARN('KTINCL',101,999)` `CALL KTCOPY(PP,N,P,(RECO.NE.1))` `C---INITIALLY EVERY PARTICLE IS IN ITS OWN JET` `DO 100 I=1,NN` `JET(I)=I` `100 CONTINUE` `C---KEEP MERGING TO THE BITTER END` `NJET=0` `200 IF (N.GT.0) THEN` `IF (HIST(N).LE.NMAX) THEN` `IMIN=0` `JMIN=HIST(N)` `NJET=NJET+1` `IF (RECO.EQ.1) THEN` `DO 300 J=1,4` `PJET(J,NJET)=P(J,JMIN)` `300 CONTINUE` `ELSE` `PJET(1,NJET)=P(6,JMIN)COS(P(8,JMIN))` `PJET(2,NJET)=P(6,JMIN)SIN(P(8,JMIN))` `PJET(3,NJET)=P(6,JMIN)SINH(P(7,JMIN))` `PJET(4,NJET)=P(6,JMIN)COSH(P(7,JMIN))` `ENDIF` `CALL KTMOVE(P,KTP,KTS,NMAX,N,JMIN,0)` `ELSE` `IMIN=HIST(N)/NMAX` `JMIN=HIST(N)-IMINNMAX` `CALL KTMERG(P,KTP,KTS,NMAX,IMIN,JMIN,N,0,0,0,RECO)` `CALL KTMOVE(P,KTP,KTS,NMAX,N,JMIN,0)` `ENDIF` `DO 400 I=1,NN` `IF (JET(I).EQ.JMIN) JET(I)=IMIN` `IF (JET(I).EQ.N) JET(I)=JMIN` `IF (JET(I).EQ.0) JET(I)=-NJET` `400 CONTINUE` `N=N-1` `GOTO 200` `ENDIF` `C---FINALLY EVERY PARTICLE MUST BE IN AN INCLUSIVE JET` `DO 500 I=1,NN` `C---IF THERE ARE ANY UNASSIGNED PARTICLES SOMETHING MUST HAVE GONE WRONG` `IF (JET(I).GE.0) CALL KTWARN('KTINCL',102,999)` `JET(I)=-JET(I)` `500 CONTINUE` `RETURN` `999 RETURN 1` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTISUB(N,NY,YCUT,NSUB,)` `IMPLICIT NONE` `C---COUNT THE NUMBER OF SUB-JETS IN THE Nth INCLUSIVE JET OF AN EVENT` `C THAT HAS ALREADY BEEN ANALYSED BY KTCLUS.` `C` `C N = INPUT : WHICH INCLUSIVE JET TO USE` `C NY = INPUT : NUMBER OF YCUT VALUES` `C YCUT(J) = INPUT : Y VALUES AT WHICH NUMBERS OF SUB-JETS ARE COUNTED` `C NSUB(J) =OUTPUT : NUMBER OF SUB-JETS AT YCUT(J)` `C LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT` `C COULD NOT BE PROCESSED` `C` `C NOTE THAT ALL FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION` `C` `INTEGER N,NY,NSUB(NY),NMAX,HIST,I,J,NUM,NM` `PARAMETER (NMAX=512)` `DOUBLE PRECISION YCUT(NY),ETOT,RSQ,P,KT,KTP,KTS,KTLAST,ROUND,EPS` `PARAMETER (ROUND=0.99999D0)` `COMMON /KTCOMM/ETOT,RSQ,P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX),` `& KT(NMAX),KTLAST(NMAX),HIST(NMAX),NUM` `DATA EPS/1D-6/` `DO 100 I=1,NY` `NSUB(I)=0` `100 CONTINUE` `C---FIND WHICH MERGING CORRESPONDS TO THE NTH INCLUSIVE JET` `NM=0` `J=0` `DO 110 I=NUM,1,-1` `IF (HIST(I).LE.NMAX) J=J+1` `IF (J.EQ.N) THEN` `NM=I` `GOTO 120` `ENDIF` `110 CONTINUE` `120 CONTINUE` `C---GIVE UP IF THERE ARE LESS THAN N INCLUSIVE JETS` `IF (NM.EQ.0) CALL KTWARN('KTISUB',100,999)` `DO 210 I=NUM,1,-1` `DO 200 J=1,NY` `IF (NSUB(J).EQ.0.AND.RSQKT(I).GE.ROUNDYCUT(J)KT(NM))` `& NSUB(J)=I` `IF (NSUB(J).NE.0.AND.ABS(KTLAST(I)-KTLAST(NM)).GT.EPS)` `& NSUB(J)=NSUB(J)-1` `200 CONTINUE` `210 CONTINUE` `RETURN` `999 RETURN 1` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTIJOI(N,Y,)` `IMPLICIT NONE` `C---GIVE SAME INFORMATION AS LAST CALL TO KTCLUS EXCEPT THAT ONLY` `C MERGES OF TWO SUB-JETS INSIDE THE Nth INCLUSIVE JET ARE RECORDED` `C` `C N = INPUT : WHICH INCLUSIVE JET TO USE` `C Y(J) =OUTPUT : Y VALUE WHERE JET CHANGED FROM HAVING` `C J+1 SUB-JETS TO HAVING J` `C LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT` `C COULD NOT BE PROCESSED` `C` `C NOTE THAT ALL FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION` `C` `INTEGER NMAX,HIST,NUM,I,J,N,NM` `PARAMETER (NMAX=512)` `DOUBLE PRECISION ETOT,RSQ,P,KT,KTP,KTS,Y(),KTLAST,EPS` `COMMON /KTCOMM/ETOT,RSQ,P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX),` `& KT(NMAX),KTLAST(NMAX),HIST(NMAX),NUM` `DATA EPS/1D-6/` `C---FIND WHICH MERGING CORRESPONDS TO THE NTH INCLUSIVE JET` `NM=0` `J=0` `DO 100 I=NUM,1,-1` `IF (HIST(I).LE.NMAX) J=J+1` `IF (J.EQ.N) THEN` `NM=I` `GOTO 105` `ENDIF` `100 CONTINUE` `105 CONTINUE` `C---GIVE UP IF THERE ARE LESS THAN N INCLUSIVE JETS` `IF (NM.EQ.0) CALL KTWARN('KTIJOI',100,999)` `J=1` `DO 110 I=1,NUM` `IF (HIST(I).GT.NMAX.AND.ABS(KTLAST(I)-KTLAST(NM)).LT.EPS) THEN` `Y(J)=RSQKT(I)/KT(NM)` `J=J+1` `ENDIF` `110 CONTINUE` `DO 200 I=J,NUM` `Y(I)=0` `200 CONTINUE` `RETURN` `999 RETURN 1` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTIREC(RECO,PP,NN,N,YCUT,PSUB,NSUB,)` `IMPLICIT NONE` `C---RECONSTRUCT KINEMATICS OF SUB-JET SYSTEM IN THE Nth INCLUSIVE JET` `C OF AN EVENT THAT HAS ALREADY BEEN ANALYSED BY KTCLUS` `C` `C RECO = INPUT : RECOMBINATION SCHEME (NEED NOT BE SAME AS KTCLUS)` `C PP(I,J) = INPUT : 4-MOMENTUM OF Jth PARTICLE: I=1,4 => PX,PY,PZ,E` `C NN = INPUT : NUMBER OF PARTICLES` `C N = INPUT : WHICH INCLUSIVE JET TO USE` `C YCUT = INPUT : Y VALUE AT WHICH TO RECONSTRUCT JET MOMENTA` `C PSUB(I,J)=OUTPUT : 4-MOMENTUM OF Jth SUB-JET AT SCALE YCUT` `C NSUB =OUTPUT : THE NUMBER OF SUB-JETS` `C LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT` `C COULD NOT BE PROCESSED` `C` `C NOTE THAT THE MOMENTA ARE DECLARED DOUBLE PRECISION,` `C AND ALL OTHER FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION` `C` `INTEGER NMAX,RECO,NUM,NN,NJET,NSUB,JET,HIST,I,J,N,NM` `PARAMETER (NMAX=512)` `DOUBLE PRECISION PP(4,),PSUB(4,)` `DOUBLE PRECISION ECUT,P,KT,KTP,KTS,ETOT,RSQ,YCUT,YMAC,KTLAST` `COMMON /KTCOMM/ETOT,RSQ,P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX),` `& KT(NMAX),KTLAST(NMAX),HIST(NMAX),NUM` `DIMENSION JET(NMAX)` `C---FIND WHICH MERGING CORRESPONDS TO THE NTH INCLUSIVE JET` `NM=0` `J=0` `DO 100 I=NUM,1,-1` `IF (HIST(I).LE.NMAX) J=J+1` `IF (J.EQ.N) THEN` `NM=I` `GOTO 110` `ENDIF` `100 CONTINUE` `110 CONTINUE` `C---GIVE UP IF THERE ARE LESS THAN N INCLUSIVE JETS` `IF (NM.EQ.0) CALL KTWARN('KTIREC',102,999)` `C---RECONSTRUCT THE JETS AT THE APPROPRIATE SCALE` `ECUT=SQRT(KT(NM)/RSQ)` `YMAC=RSQ` `CALL KTRECO(RECO,PP,NN,ECUT,YCUT,YMAC,PSUB,JET,NJET,NSUB,999)` `C---GET RID OF THE ONES THAT DO NOT END UP IN THE JET WE WANT` `NSUB=0` `DO 210 I=1,NJET` `IF (JET(I).EQ.HIST(NM)) THEN` `NSUB=NSUB+1` `DO 200 J=1,4` `PSUB(J,NSUB)=PSUB(J,I)` `200 CONTINUE` `ENDIF` `210 CONTINUE` `RETURN` `999 RETURN 1` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTWICH(ECUT,YCUT,JET,NJET,)` `IMPLICIT NONE` `C---GIVE A LIST OF WHICH JET EACH ORIGINAL PARTICLE ENDED UP IN AT SCALE` `C YCUT, TOGETHER WITH THE NUMBER OF JETS AT THAT SCALE.` `C` `C ECUT = INPUT : DENOMINATOR OF KT MEASURE. IF ZERO, ETOT IS USED` `C YCUT = INPUT : Y VALUE AT WHICH TO DEFINE JETS` `C JET(J) =OUTPUT : THE JET WHICH CONTAINS THE Jth PARTICLE,` `C SET TO ZERO IF IT WAS PUT INTO THE BEAM JETS` `C NJET =OUTPUT : THE NUMBER OF JETS AT SCALE YCUT (SO JET()` `C ENTRIES WILL BE IN THE RANGE 0 -> NJET)` `C LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT` `C COULD NOT BE PROCESSED` `C` `C NOTE THAT ALL FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION` `C` `INTEGER JET(),NJET,NTEMP` `DOUBLE PRECISION ECUT,YCUT` `CALL KTWCHS(ECUT,YCUT,YCUT,JET,NJET,NTEMP,999)` `RETURN` `999 RETURN 1` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTWCHS(ECUT,YCUT,YMAC,JET,NJET,NSUB,)` `IMPLICIT NONE` `C---GIVE A LIST OF WHICH SUB-JET EACH ORIGINAL PARTICLE ENDED UP IN AT` `C SCALE YCUT, WITH MACRO-JET SCALE YMAC, TOGETHER WITH THE NUMBER OF` `C JETS AT SCALE YCUT AND THE NUMBER OF THEM WHICH ARE SUB-JETS.` `C` `C ECUT = INPUT : DENOMINATOR OF KT MEASURE. IF ZERO, ETOT IS USED` `C YCUT = INPUT : Y VALUE AT WHICH TO DEFINE JETS` `C YMAC = INPUT : Y VALUE AT WHICH TO DEFINE MACRO-JETS` `C JET(J) =OUTPUT : THE JET WHICH CONTAINS THE Jth PARTICLE,` `C SET TO ZERO IF IT WAS PUT INTO THE BEAM JETS` `C NJET =OUTPUT : THE NUMBER OF JETS AT SCALE YCUT (SO JET()` `C ENTRIES WILL BE IN THE RANGE 0 -> NJET)` `C NSUB =OUTPUT : THE NUMBER OF SUB-JETS AT SCALE YCUT, WITH` `C MACRO-JETS DEFINED AT SCALE YMAC (SO ONLY NSUB` `C OF THE JETS 1 -> NJET WILL APPEAR IN JET())` `C LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT` `C COULD NOT BE PROCESSED` `C` `C NOTE THAT ALL FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION` `C` `INTEGER NMAX,JET(),NJET,NSUB,HIST,NUM,I,J,JSUB` `PARAMETER (NMAX=512)` `DOUBLE PRECISION P1(4,NMAX),P2(4,NMAX)` `DOUBLE PRECISION ECUT,YCUT,YMAC,ZERO,ETOT,RSQ,P,KTP,KTS,KT,KTLAST` `COMMON /KTCOMM/ETOT,RSQ,P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX),` `& KT(NMAX),KTLAST(NMAX),HIST(NMAX),NUM` `DIMENSION JSUB(NMAX)` `C---THE MOMENTA HAVE TO BEEN GIVEN LEGAL VALUES,` `C EVEN THOUGH THEY WILL NEVER BE USED` `DATA ((P1(J,I),I=1,NMAX),J=1,4),ZERO` `& /NMAX1,NMAX0,NMAX0,NMAX1,0/` `C---FIRST GET A LIST OF WHICH PARTICLE IS IN WHICH JET AT YCUT` `CALL KTRECO(1,P1,NUM,ECUT,ZERO,YCUT,P2,JET,NJET,NSUB,999)` `C---THEN FIND OUT WHICH JETS ARE SUBJETS` `CALL KTRECO(1,P1,NUM,ECUT,YCUT,YMAC,P2,JSUB,NJET,NSUB,999)` `C---AND MODIFY JET() ACCORDINGLY` `DO 10 I=1,NUM` `IF (JET(I).NE.0) THEN` `IF (JSUB(JET(I)).EQ.0) JET(I)=0` `ENDIF` `10 CONTINUE` `RETURN` `999 RETURN 1` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTFRAM(IOPT,CMF,SIGN,Z,XZ,N,P,Q,)` `IMPLICIT NONE` `C---BOOST PARTICLES IN P TO/FROM FRAME GIVEN BY CMF, Z, XZ.` `C---IN THIS FRAME CMZ IS STATIONARY,` `C Z IS ALONG THE (SIGN)Z-AXIS (SIGN=+ OR -)` `C XZ IS IN THE X-Z PLANE (WITH POSITIVE X COMPONENT)` `C---IF Z HAS LENGTH ZERO, OR SIGN=0, NO ROTATION IS PERFORMED` `C---IF XZ HAS ZERO COMPONENT PERPENDICULAR TO Z IN THAT FRAME,` `C NO AZIMUTHAL ROTATION IS PERFORMED` `C` `C IOPT = INPUT : 0=TO FRAME, 1=FROM FRAME` `C CMF(I) = INPUT : 4-MOMENTUM WHICH IS STATIONARY IN THE FRAME` `C SIGN = INPUT : DIRECTION OF Z IN THE FRAME, NOTE THAT` `C ONLY ITS SIGN IS USED, NOT ITS MAGNITUDE` `C Z(I) = INPUT : 4-MOMENTUM WHICH LIES ON THE (SIGN)Z-AXIS` `C XZ(I) = INPUT : 4-MOMENTUM WHICH LIES IN THE X-Z PLANE` `C N = INPUT : NUMBER OF PARTICLES IN P` `C P(I,J) = INPUT : 4-MOMENTUM OF JTH PARTICLE BEFORE` `C Q(I,J) = OUTPUT : 4-MOMENTUM OF JTH PARTICLE AFTER` `C LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT` `C COULD NOT BE PROCESSED` `C` `C NOTE THAT ALL MOMENTA ARE DOUBLE PRECISION` `C` `C NOTE THAT IT IS SAFE TO CALL WITH P=Q` `C` `INTEGER IOPT,I,N` `DOUBLE PRECISION CMF(4),SIGN,Z(4),XZ(4),P(4,N),Q(4,N),` `& R(4,4),NEW(4),OLD(4)` `IF (IOPT.LT.0.OR.IOPT.GT.1) CALL KTWARN('KTFRAM',200,999)` `C---FIND BOOST TO GET THERE FROM LAB` `CALL KTUNIT(R)` `CALL KTLBST(0,R,CMF,999)` `C---FIND ROTATION TO PUT BOOSTED Z ON THE (SIGN)Z AXIS` `IF (SIGN.NE.0) THEN` `CALL KTVMUL(R,Z,OLD)` `IF (OLD(1).NE.0.OR.OLD(2).NE.0.OR.OLD(3).NE.0) THEN` `NEW(1)=0` `NEW(2)=0` `NEW(3)=SIGN` `NEW(4)=ABS(SIGN)` `CALL KTRROT(R,OLD,NEW,999)` `C---FIND ROTATION TO PUT BOOSTED AND ROTATED XZ INTO X-Z PLANE` `CALL KTVMUL(R,XZ,OLD)` `IF (OLD(1).NE.0.OR.OLD(2).NE.0) THEN` `NEW(1)=1` `NEW(2)=0` `NEW(3)=0` `NEW(4)=1` `OLD(3)=0` `C---NOTE THAT A POTENTIALLY AWKWARD SPECIAL CASE IS AVERTED, BECAUSE IF` `C OLD AND NEW ARE EXACTLY BACK-TO-BACK, THE ROTATION AXIS IS UNDEFINED` `C BUT IN THAT CASE KTRROT WILL USE THE Z AXIS, AS REQUIRED` `CALL KTRROT(R,OLD,NEW,999)` `ENDIF` `ENDIF` `ENDIF` `C---INVERT THE TRANSFORMATION IF NECESSARY` `IF (IOPT.EQ.1) CALL KTINVT(R,R)` `C---APPLY THE RESULT TO ALL THE VECTORS` `DO 30 I=1,N` `CALL KTVMUL(R,P(1,I),Q(1,I))` `30 CONTINUE` `RETURN` `999 RETURN 1` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTBREI(IOPT,PLEP,PHAD,POUT,N,P,Q,)` `IMPLICIT NONE` `C---BOOST PARTICLES IN P TO/FROM BREIT FRAME` `C` `C IOPT = INPUT : 0/2=TO BREIT FRAME, 1/3=FROM BREIT FRAME` `C 0/1=NO AZIMUTHAL ROTATION AFTERWARDS` `C 2/3=LEPTON PLANE ROTATED INTO THE X-Z PLANE` `C PLEP = INPUT : MOMENTUM OF INCOMING LEPTON IN +Z DIRECTION` `C PHAD = INPUT : MOMENTUM OF INCOMING HADRON IN +Z DIRECTION` `C POUT(I) = INPUT : 4-MOMENTUM OF OUTGOING LEPTON` `C N = INPUT : NUMBER OF PARTICLES IN P` `C P(I,J) = INPUT : 4-MOMENTUM OF JTH PARTICLE BEFORE` `C Q(I,J) = OUTPUT : 4-MOMENTUM OF JTH PARTICLE AFTER` `C LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT` `C COULD NOT BE PROCESSED (MOST LIKELY DUE TO PARTICLES HAVING SMALLER` `C ENERGY THAN MOMENTUM)` `C` `C NOTE THAT ALL MOMENTA ARE DOUBLE PRECISION` `C` `C NOTE THAT IT IS SAFE TO CALL WITH P=Q` `C` `INTEGER IOPT,N` `DOUBLE PRECISION PLEP,PHAD,POUT(4),P(4,N),Q(4,N),` `& CMF(4),Z(4),XZ(4),DOT,QDQ` `C---CHECK INPUT` `IF (IOPT.LT.0.OR.IOPT.GT.3) CALL KTWARN('KTBREI',200,999)` `C---FIND 4-MOMENTUM OF BREIT FRAME (TIMES AN ARBITRARY FACTOR)` `DOT=ABS(PHAD)(ABS(PLEP)-POUT(4))-PHAD(PLEP-POUT(3))` `QDQ=(ABS(PLEP)-POUT(4))2-(PLEP-POUT(3))2-POUT(2)2-POUT(1)2` `CMF(1)=DOT( -POUT(1))` `CMF(2)=DOT( -POUT(2))` `CMF(3)=DOT( PLEP -POUT(3))-QDQ* PHAD` `CMF(4)=DOT(ABS(PLEP)-POUT(4))-QDQABS(PHAD)` `C---FIND ROTATION TO PUT INCOMING HADRON BACK ON Z-AXIS` `Z(1)=0` `Z(2)=0` `Z(3)=PHAD` `Z(4)=ABS(PHAD)` `XZ(1)=0` `XZ(2)=0` `XZ(3)=0` `XZ(4)=0` `C---DO THE BOOST` `IF (IOPT.LE.1) THEN` `CALL KTFRAM(IOPT,CMF,PHAD,Z,XZ,N,P,Q,999)` `ELSE` `CALL KTFRAM(IOPT-2,CMF,PHAD,Z,POUT,N,P,Q,999)` `ENDIF` `RETURN` `999 RETURN 1` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTHADR(IOPT,PLEP,PHAD,POUT,N,P,Q,)` `IMPLICIT NONE` `C---BOOST PARTICLES IN P TO/FROM HADRONIC CMF` `C` `C ARGUMENTS ARE EXACTLY AS FOR KTBREI` `C` `C NOTE THAT ALL MOMENTA ARE DOUBLE PRECISION` `C` `C NOTE THAT IT IS SAFE TO CALL WITH P=Q` `C` `INTEGER IOPT,N` `DOUBLE PRECISION PLEP,PHAD,POUT(4),P(4,N),Q(4,N),` `& CMF(4),Z(4),XZ(4)` `C---CHECK INPUT` `IF (IOPT.LT.0.OR.IOPT.GT.3) CALL KTWARN('KTHADR',200,999)` `C---FIND 4-MOMENTUM OF HADRONIC CMF` `CMF(1)= -POUT(1)` `CMF(2)= -POUT(2)` `CMF(3)= PLEP -POUT(3)+ PHAD` `CMF(4)=ABS(PLEP)-POUT(4)+ABS(PHAD)` `C---FIND ROTATION TO PUT INCOMING HADRON BACK ON Z-AXIS` `Z(1)=0` `Z(2)=0` `Z(3)=PHAD` `Z(4)=ABS(PHAD)` `XZ(1)=0` `XZ(2)=0` `XZ(3)=0` `XZ(4)=0` `C---DO THE BOOST` `IF (IOPT.LE.1) THEN` `CALL KTFRAM(IOPT,CMF,PHAD,Z,XZ,N,P,Q,999)` `ELSE` `CALL KTFRAM(IOPT-2,CMF,PHAD,Z,POUT,N,P,Q,999)` `ENDIF` `RETURN` `999 RETURN 1` `END` `C-----------------------------------------------------------------------` `FUNCTION KTPAIR(ANGL,P,Q,ANGLE)` `IMPLICIT NONE` `C---CALCULATE LOCAL KT OF PAIR, USING ANGULAR SCHEME:` `C 1=>ANGULAR, 2=>DeltaR, 3=>f(DeltaEta,DeltaPhi)` `C WHERE f(eta,phi)=2(COSH(eta)-COS(phi)) IS THE QCD EMISSION METRIC` `C---IF ANGLE<0, IT IS SET TO THE ANGULAR PART OF THE LOCAL KT ON RETURN` `C IF ANGLE>0, IT IS USED INSTEAD OF THE ANGULAR PART OF THE LOCAL KT` `INTEGER ANGL` `DOUBLE PRECISION P(9),Q(9),KTPAIR,R,KTMDPI,ANGLE,ETA,PHI,ESQ` `C---COMPONENTS OF MOMENTA ARE PX,PY,PZ,E,1/P,PT,ETA,PHI,PT*2` `R=ANGLE` `IF (ANGL.EQ.1) THEN` `IF (R.LE.0) R=2(1-(P(1)Q(1)+P(2)Q(2)+P(3)Q(3))(P(5)Q(5)))` `ESQ=MIN(P(4),Q(4))2` `ELSEIF (ANGL.EQ.2.OR.ANGL.EQ.3) THEN` `IF (R.LE.0) THEN` `ETA=P(7)-Q(7)` `PHI=KTMDPI(P(8)-Q(8))` `IF (ANGL.EQ.2) THEN` `R=ETA2+PHI2` `ELSE` `R=2(COSH(ETA)-COS(PHI))` `ENDIF` `ENDIF` `ESQ=MIN(P(9),Q(9))` `ELSEIF (ANGL.EQ.4) THEN` `ESQ=(1d0/(P(5)Q(5))-P(1)Q(1)-P(2)Q(2)-` `&P(3)Q(3))2D0/(P(5)Q(5))/(0.0001D0+1d0/P(5)+1d0/Q(5))*2` `R=1d0` `ELSE` `ktpair = 0D0` `CALL KTWARN('KTPAIR',200,999)` `STOP` `ENDIF` `KTPAIR=ESQR` `IF (ANGLE.LT.0) ANGLE=R` `999 END` `C-----------------------------------------------------------------------` `FUNCTION KTSING(ANGL,TYPE,P)` `IMPLICIT NONE` `C---CALCULATE KT OF PARTICLE, USING ANGULAR SCHEME:` `C 1=>ANGULAR, 2=>DeltaR, 3=>f(DeltaEta,DeltaPhi)` `C---TYPE=1 FOR E+E-, 2 FOR EP, 3 FOR PE, 4 FOR PP` `C FOR EP, PROTON DIRECTION IS DEFINED AS -Z` `C FOR PE, PROTON DIRECTION IS DEFINED AS +Z` `DOUBLE PRECISION KTSING,P(9)` `DOUBLE PRECISION COSTH,R,SMALL` `INTEGER ANGL,TYPE` `DATA SMALL/1D-4/` `IF (ANGL.EQ.1.OR.ANGL.EQ.4) THEN` `COSTH=P(3)P(5)` `IF (TYPE.EQ.2) THEN` `COSTH=-COSTH` `ELSEIF (TYPE.EQ.4) THEN` `COSTH=ABS(COSTH)` `ELSEIF (TYPE.NE.1.AND.TYPE.NE.3) THEN` `ktsing = 0D0` `CALL KTWARN('KTSING',200,999)` `STOP` `ENDIF` `R=2(1-COSTH)` `C---IF CLOSE TO BEAM, USE APPROX 2(1-COS(THETA))=SIN2(THETA)` `IF (R.LT.SMALL) R=(P(1)2+P(2)2)P(5)2` `KTSING=P(4)2R` `ELSEIF (ANGL.EQ.2.OR.ANGL.EQ.3) THEN` `KTSING=P(9)` `ELSE` `ktsing = 0D0` `CALL KTWARN('KTSING',201,999)` `STOP` `ENDIF` `999 END` `C-----------------------------------------------------------------------` `SUBROUTINE KTPMIN(A,NMAX,N,IMIN,JMIN)` `IMPLICIT NONE` `C---FIND THE MINIMUM MEMBER OF A(NMAX,NMAX) WITH IMIN < JMIN <= N` `INTEGER NMAX,N,IMIN,JMIN,KMIN,I,J,K` `C---REMEMBER THAT A(X+(Y-1)NMAX)=A(X,Y)` `C THESE LOOPING VARIABLES ARE J=Y-2, I=X+(Y-1)NMAX` `DOUBLE PRECISION A(),AMIN` `K=1+NMAX` `KMIN=K` `AMIN=A(KMIN)` `DO 110 J=0,N-2` `DO 100 I=K,K+J` `IF (A(I).LT.AMIN) THEN` `KMIN=I` `AMIN=A(KMIN)` `ENDIF` `100 CONTINUE` `K=K+NMAX` `110 CONTINUE` `JMIN=KMIN/NMAX+1` `IMIN=KMIN-(JMIN-1)NMAX` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTSMIN(A,NMAX,N,IMIN)` `IMPLICIT NONE` `C---FIND THE MINIMUM MEMBER OF A` `INTEGER N,NMAX,IMIN,I` `DOUBLE PRECISION A(NMAX)` `IMIN=1` `DO 100 I=1,N` `IF (A(I).LT.A(IMIN)) IMIN=I` `100 CONTINUE` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTCOPY(A,N,B,ONSHLL)` `IMPLICIT NONE` `C---COPY FROM A TO B. 5TH=1/(3-MTM), 6TH=PT, 7TH=ETA, 8TH=PHI, 9TH=PT2` `C IF ONSHLL IS .TRUE. PARTICLE ENTRIES ARE PUT ON-SHELL BY SETTING E=P` `INTEGER I,N` `DOUBLE PRECISION A(4,N)` `LOGICAL ONSHLL` `DOUBLE PRECISION B(9,N),ETAMAX,SINMIN,EPS` `DATA ETAMAX,SINMIN,EPS/10,0,1D-6/` `C---SINMIN GETS CALCULATED ON FIRST CALL` `IF (SINMIN.EQ.0) SINMIN=1/COSH(ETAMAX)` `DO 100 I=1,N` `B(1,I)=A(1,I)` `B(2,I)=A(2,I)` `B(3,I)=A(3,I)` `B(4,I)=A(4,I)` `B(5,I)=SQRT(A(1,I)2+A(2,I)2+A(3,I)2)` `IF (ONSHLL) B(4,I)=B(5,I)` `IF (B(5,I).EQ.0) B(5,I)=1D-10` `B(5,I)=1/B(5,I)` `B(9,I)=A(1,I)2+A(2,I)2` `B(6,I)=SQRT(B(9,I))` `B(7,I)=B(6,I)B(5,I)` `IF (B(7,I).GT.SINMIN) THEN` `B(7,I)=A(4,I)2-A(3,I)2` `IF (B(7,I).LE.EPSB(4,I)2.OR.ONSHLL) B(7,I)=B(9,I)` `B(7,I)=LOG((B(4,I)+ABS(B(3,I)))2/B(7,I))/2` `ELSE` `B(7,I)=ETAMAX+2` `ENDIF` `B(7,I)=SIGN(B(7,I),B(3,I))` `IF (A(1,I).EQ.0 .AND. A(2,I).EQ.0) THEN` `B(8,I)=0` `ELSE` `B(8,I)=ATAN2(A(2,I),A(1,I))` `ENDIF` `100 CONTINUE` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTMERG(P,KTP,KTS,NMAX,I,J,N,TYPE,ANGL,MONO,RECO)` `IMPLICIT NONE` `C---MERGE THE Jth PARTICLE IN P INTO THE Ith PARTICLE` `C J IS ASSUMED GREATER THAN I. P CONTAINS N PARTICLES BEFORE MERGING.` `C---ALSO RECALCULATING THE CORRESPONDING KTP AND KTS VALUES IF MONO.GT.0` `C FROM THE RECOMBINED ANGULAR MEASURES IF MONO.GT.1` `C---NOTE THAT IF MONO.LE.0, TYPE AND ANGL ARE NOT USED` `INTEGER ANGL,RECO,TYPE,I,J,K,N,NMAX,MONO` `DOUBLE PRECISION P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX),PT,PTT,` `& KTMDPI,KTUP,PI,PJ,ANG,KTPAIR,KTSING,ETAMAX,EPS` `KTUP(I,J)=KTP(MAX(I,J),MIN(I,J))` `DATA ETAMAX,EPS/10,1D-6/` `IF (J.LE.I) CALL KTWARN('KTMERG',200,999)` `C---COMBINE ANGULAR MEASURES IF NECESSARY` `IF (MONO.GT.1) THEN` `DO 100 K=1,N` `IF (K.NE.I.AND.K.NE.J) THEN` `IF (RECO.EQ.1) THEN` `PI=P(4,I)` `PJ=P(4,J)` `ELSEIF (RECO.EQ.2) THEN` `PI=P(6,I)` `PJ=P(6,J)` `ELSEIF (RECO.EQ.3) THEN` `PI=P(9,I)` `PJ=P(9,J)` `ELSE` `CALL KTWARN('KTMERG',201,999)` `STOP` `ENDIF` `IF (PI.EQ.0.AND.PJ.EQ.0) THEN` `PI=1` `PJ=1` `ENDIF` `KTP(MAX(I,K),MIN(I,K))=` `& (PIKTUP(I,K)+PJKTUP(J,K))/(PI+PJ)` `ENDIF` `100 CONTINUE` `ENDIF` `IF (RECO.EQ.1) THEN` `C---VECTOR ADDITION` `P(1,I)=P(1,I)+P(1,J)` `P(2,I)=P(2,I)+P(2,J)` `P(3,I)=P(3,I)+P(3,J)` `c P(4,I)=P(4,I)+P(4,J) ! JA` `P(5,I)=SQRT(P(1,I)2+P(2,I)2+P(3,I)*2)` `P(4,I)=P(5,I) ! JA (Massless scheme)` `IF (P(5,I).EQ.0) THEN` `P(5,I)=1` `ELSE` `P(5,I)=1/P(5,I)` `ENDIF` `ELSEIF (RECO.EQ.2) THEN` `C---PT WEIGHTED ETA-PHI ADDITION` `PT=P(6,I)+P(6,J)` `IF (PT.EQ.0) THEN` `PTT=1` `ELSE` `PTT=1/PT` `ENDIF` `P(7,I)=(P(6,I)P(7,I)+P(6,J)P(7,J))PTT` `P(8,I)=KTMDPI(P(8,I)+P(6,J)PTTKTMDPI(P(8,J)-P(8,I)))` `P(6,I)=PT` `P(9,I)=PT2` `ELSEIF (RECO.EQ.3) THEN` `C---PT2 WEIGHTED ETA-PHI ADDITION` `PT=P(9,I)+P(9,J)` `IF (PT.EQ.0) THEN` `PTT=1` `ELSE` `PTT=1/PT` `ENDIF` `P(7,I)=(P(9,I)P(7,I)+P(9,J)P(7,J))PTT` `P(8,I)=KTMDPI(P(8,I)+P(9,J)PTTKTMDPI(P(8,J)-P(8,I)))` `P(6,I)=P(6,I)+P(6,J)` `P(9,I)=P(6,I)2` `ELSE` `CALL KTWARN('KTMERG',202,999)` `STOP` `ENDIF` `C---IF MONO.GT.0 CALCULATE NEW KT MEASURES. IF MONO.GT.1 USE ANGULAR ONES.` `IF (MONO.LE.0) RETURN` `C---CONVERTING BETWEEN 4-MTM AND PT,ETA,PHI IF NECESSARY` `IF (ANGL.NE.1.AND.RECO.EQ.1) THEN` `P(9,I)=P(1,I)2+P(2,I)2` `P(7,I)=P(4,I)2-P(3,I)2` `IF (P(7,I).LE.EPSP(4,I)2) P(7,I)=P(9,I)` `IF (P(7,I).GT.0) THEN` `P(7,I)=LOG((P(4,I)+ABS(P(3,I)))2/P(7,I))/2` `IF (P(7,I).GT.ETAMAX) P(7,I)=ETAMAX+2` `ELSE` `P(7,I)=ETAMAX+2` `ENDIF` `P(7,I)=SIGN(P(7,I),P(3,I))` `IF (P(1,I).NE.0.AND.P(2,I).NE.0) THEN` `P(8,I)=ATAN2(P(2,I),P(1,I))` `ELSE` `P(8,I)=0` `ENDIF` `ELSEIF (ANGL.EQ.1.AND.RECO.NE.1) THEN` `P(1,I)=P(6,I)COS(P(8,I))` `P(2,I)=P(6,I)SIN(P(8,I))` `P(3,I)=P(6,I)SINH(P(7,I))` `P(4,I)=P(6,I)COSH(P(7,I))` `IF (P(4,I).NE.0) THEN` `P(5,I)=1/P(4,I)` `ELSE` `P(5,I)=1` `ENDIF` `ENDIF` `ANG=0` `DO 200 K=1,N` `IF (K.NE.I.AND.K.NE.J) THEN` `IF (MONO.GT.1) ANG=KTUP(I,K)` `KTP(MIN(I,K),MAX(I,K))=` `& KTPAIR(ANGL,P(1,I),P(1,K),ANG)` `ENDIF` `200 CONTINUE` `KTS(I)=KTSING(ANGL,TYPE,P(1,I))` `999 END` `C-----------------------------------------------------------------------` `SUBROUTINE KTMOVE(P,KTP,KTS,NMAX,N,J,IOPT)` `IMPLICIT NONE` `C---MOVE THE Nth PARTICLE IN P TO THE Jth POSITION` `C---ALSO MOVING KTP AND KTS IF IOPT.GT.0` `INTEGER I,J,N,NMAX,IOPT` `DOUBLE PRECISION P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX)` `DO 100 I=1,9` `P(I,J)=P(I,N)` `100 CONTINUE` `IF (IOPT.LE.0) RETURN` `DO 110 I=1,J-1` `KTP(I,J)=KTP(I,N)` `KTP(J,I)=KTP(N,I)` `110 CONTINUE` `DO 120 I=J+1,N-1` `KTP(J,I)=KTP(I,N)` `KTP(I,J)=KTP(N,I)` `120 CONTINUE` `KTS(J)=KTS(N)` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTUNIT(R)` `IMPLICIT NONE` `C SET R EQUAL TO THE 4 BY 4 IDENTITY MATRIX` `DOUBLE PRECISION R(4,4)` `INTEGER I,J` `DO 20 I=1,4` `DO 10 J=1,4` `R(I,J)=0` `IF (I.EQ.J) R(I,J)=1` `10 CONTINUE` `20 CONTINUE` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTLBST(IOPT,R,A,)` `IMPLICIT NONE` `C PREMULTIPLY R BY THE 4 BY 4 MATRIX TO` `C LORENTZ BOOST TO/FROM THE CM FRAME OF A` `C IOPT=0 => TO` `C IOPT=1 => FROM` `C` `C LAST ARGUMENT IS LABEL TO JUMP TO IF A IS NOT TIME-LIKE` `C` `INTEGER IOPT,I,J` `DOUBLE PRECISION R(4,4),A(4),B(4),C(4,4),M` `DO 10 I=1,4` `B(I)=A(I)` `10 CONTINUE` `M=B(4)2-B(1)2-B(2)2-B(3)2` `IF (M.LE.0) CALL KTWARN('KTLBST',100,999)` `M=SQRT(M)` `B(4)=B(4)+M` `M=1/(MB(4))` `IF (IOPT.EQ.0) THEN` `B(4)=-B(4)` `ELSEIF (IOPT.NE.1) THEN` `CALL KTWARN('KTLBST',200,999)` `STOP` `ENDIF` `DO 30 I=1,4` `DO 20 J=1,4` `C(I,J)=B(I)B(J)M` `IF (I.EQ.J) C(I,J)=C(I,J)+1` `20 CONTINUE` `30 CONTINUE` `C(4,4)=C(4,4)-2` `CALL KTMMUL(C,R,R)` `RETURN` `999 RETURN 1` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTRROT(R,A,B,)` `IMPLICIT NONE` `C PREMULTIPLY R BY THE 4 BY 4 MATRIX TO` `C ROTATE FROM VECTOR A TO VECTOR B BY THE SHORTEST ROUTE` `C IF THEY ARE EXACTLY BACK-TO-BACK, THE ROTATION AXIS IS THE VECTOR` `C WHICH IS PERPENDICULAR TO THEM AND THE X AXIS, UNLESS THEY ARE` `C PERPENDICULAR TO THE Y AXIS, WHEN IT IS THE VECTOR WHICH IS` `C PERPENDICULAR TO THEM AND THE Y AXIS.` `C NOTE THAT THESE CONDITIONS GUARANTEE THAT IF BOTH ARE PERPENDICULAR` `C TO THE Z AXIS, IT WILL BE USED AS THE ROTATION AXIS.` `C` `C LAST ARGUMENT IS LABEL TO JUMP TO IF EITHER HAS LENGTH ZERO` `C` `DOUBLE PRECISION R(4,4),M(4,4),A(4),B(4),C(4),D(4),AL,BL,CL,DL,EPS` `C---SQRT(2EPS) IS THE ANGLE IN RADIANS OF THE SMALLEST ALLOWED ROTATION` `C NOTE THAT IF YOU CONVERT THIS PROGRAM TO SINGLE PRECISION, YOU WILL` `C NEED TO INCREASE EPS TO AROUND 0.5E-4` `PARAMETER (EPS=0.5D-6)` `AL=A(1)2+A(2)2+A(3)2` `BL=B(1)2+B(2)2+B(3)2` `IF (AL.LE.0.OR.BL.LE.0) CALL KTWARN('KTRROT',100,999)` `AL=1/SQRT(AL)` `BL=1/SQRT(BL)` `CL=(A(1)B(1)+A(2)B(2)+A(3)B(3))ALBL` `C---IF THEY ARE COLLINEAR, DON'T NEED TO DO ANYTHING` `IF (CL.GE.1-EPS) THEN` `RETURN` `C---IF THEY ARE BACK-TO-BACK, USE THE AXIS PERP TO THEM AND X AXIS` `ELSEIF (CL.LE.-1+EPS) THEN` `IF (ABS(B(2)).GT.EPS) THEN` `C(1)= 0` `C(2)=-B(3)` `C(3)= B(2)` `C---UNLESS THEY ARE PERPENDICULAR TO THE Y AXIS,` `ELSE` `C(1)= B(3)` `C(2)= 0` `C(3)=-B(1)` `ENDIF` `C---OTHERWISE FIND ROTATION AXIS` `ELSE` `C(1)=A(2)B(3)-A(3)B(2)` `C(2)=A(3)B(1)-A(1)B(3)` `C(3)=A(1)B(2)-A(2)B(1)` `ENDIF` `CL=C(1)2+C(2)2+C(3)2` `IF (CL.LE.0) CALL KTWARN('KTRROT',101,999)` `CL=1/SQRT(CL)` `C---FIND ROTATION TO INTERMEDIATE AXES FROM A` `D(1)=A(2)C(3)-A(3)C(2)` `D(2)=A(3)C(1)-A(1)C(3)` `D(3)=A(1)C(2)-A(2)C(1)` `DL=ALCL` `M(1,1)=A(1)AL` `M(1,2)=A(2)AL` `M(1,3)=A(3)AL` `M(1,4)=0` `M(2,1)=C(1)CL` `M(2,2)=C(2)CL` `M(2,3)=C(3)CL` `M(2,4)=0` `M(3,1)=D(1)DL` `M(3,2)=D(2)DL` `M(3,3)=D(3)DL` `M(3,4)=0` `M(4,1)=0` `M(4,2)=0` `M(4,3)=0` `M(4,4)=1` `CALL KTMMUL(M,R,R)` `C---AND ROTATION FROM INTERMEDIATE AXES TO B` `D(1)=B(2)C(3)-B(3)C(2)` `D(2)=B(3)C(1)-B(1)C(3)` `D(3)=B(1)C(2)-B(2)C(1)` `DL=BLCL` `M(1,1)=B(1)BL` `M(2,1)=B(2)BL` `M(3,1)=B(3)BL` `M(1,2)=C(1)CL` `M(2,2)=C(2)CL` `M(3,2)=C(3)CL` `M(1,3)=D(1)DL` `M(2,3)=D(2)DL` `M(3,3)=D(3)DL` `CALL KTMMUL(M,R,R)` `RETURN` `999 RETURN 1` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTVMUL(M,A,B)` `IMPLICIT NONE` `C 4 BY 4 MATRIX TIMES 4 VECTOR: B=MA.` `C ALL ARE DOUBLE PRECISION` `C IT IS SAFE TO CALL WITH B=A` `C FIRST SUBSCRIPT=ROWS, SECOND=COLUMNS` `DOUBLE PRECISION M(4,4),A(4),B(4),C(4)` `INTEGER I,J` `DO 20 I=1,4` `C(I)=0` `DO 10 J=1,4` `C(I)=C(I)+M(I,J)A(J)` `10 CONTINUE` `20 CONTINUE` `DO 30 I=1,4` `B(I)=C(I)` `30 CONTINUE` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTMMUL(A,B,C)` `IMPLICIT NONE` `C 4 BY 4 MATRIX MULTIPLICATION: C=AB.` `C ALL ARE DOUBLE PRECISION` `C IT IS SAFE TO CALL WITH C=A OR B.` `C FIRST SUBSCRIPT=ROWS, SECOND=COLUMNS` `DOUBLE PRECISION A(4,4),B(4,4),C(4,4),D(4,4)` `INTEGER I,J,K` `DO 30 I=1,4` `DO 20 J=1,4` `D(I,J)=0` `DO 10 K=1,4` `D(I,J)=D(I,J)+A(I,K)B(K,J)` `10 CONTINUE` `20 CONTINUE` `30 CONTINUE` `DO 50 I=1,4` `DO 40 J=1,4` `C(I,J)=D(I,J)` `40 CONTINUE` `50 CONTINUE` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTINVT(A,B)` `IMPLICIT NONE` `C---INVERT TRANSFORMATION MATRIX A` `C` `C A = INPUT : 4 BY 4 TRANSFORMATION MATRIX` `C B = OUTPUT : INVERTED TRANSFORMATION MATRIX` `C` `C IF A IS NOT A TRANSFORMATION MATRIX YOU WILL GET STRANGE RESULTS` `C` `C NOTE THAT IT IS SAFE TO CALL WITH A=B` `C` `DOUBLE PRECISION A(4,4),B(4,4),C(4,4)` `INTEGER I,J` `C---TRANSPOSE` `DO 20 I=1,4` `DO 10 J=1,4` `C(I,J)=A(J,I)` `10 CONTINUE` `20 CONTINUE` `C---NEGATE ENERGY-MOMENTUM MIXING TERMS` `DO 30 I=1,3` `C(4,I)=-C(4,I)` `C(I,4)=-C(I,4)` `30 CONTINUE` `C---OUTPUT` `DO 50 I=1,4` `DO 40 J=1,4` `B(I,J)=C(I,J)` `40 CONTINUE` `50 CONTINUE` `END` `C-----------------------------------------------------------------------` `FUNCTION KTMDPI(PHI)` `IMPLICIT NONE` `C---RETURNS PHI, MOVED ONTO THE RANGE [-PI,PI)` `DOUBLE PRECISION KTMDPI,PHI,PI,TWOPI,THRPI,EPS` `PARAMETER (PI=3.14159265358979324D0,TWOPI=6.28318530717958648D0,` `& THRPI=9.42477796076937972D0)` `PARAMETER (EPS=1D-15)` `KTMDPI=PHI` `IF (KTMDPI.LE.PI) THEN` `IF (KTMDPI.GT.-PI) THEN` `GOTO 100` `ELSEIF (KTMDPI.GT.-THRPI) THEN` `KTMDPI=KTMDPI+TWOPI` `ELSE` `KTMDPI=-MOD(PI-KTMDPI,TWOPI)+PI` `ENDIF` `ELSEIF (KTMDPI.LE.THRPI) THEN` `KTMDPI=KTMDPI-TWOPI` `ELSE` `KTMDPI=MOD(PI+KTMDPI,TWOPI)-PI` `ENDIF` `100 IF (ABS(KTMDPI).LT.EPS) KTMDPI=0` `END` `C-----------------------------------------------------------------------` `SUBROUTINE KTWARN(SUBRTN,ICODE,)` `C DEALS WITH ERRORS DURING EXECUTION` `C SUBRTN = NAME OF CALLING SUBROUTINE` `C ICODE = ERROR CODE: - 99 PRINT WARNING & CONTINUE` `C 100-199 PRINT WARNING & JUMP` `C 200- PRINT WARNING & STOP DEAD` `C-----------------------------------------------------------------------` `INTEGER ICODE` `CHARACTER6 SUBRTN` `WRITE (6,10) SUBRTN,ICODE` `10 FORMAT(/' KTWARN CALLED FROM SUBPROGRAM ',A6,': CODE =',I4/)` `IF (ICODE.LT.100) RETURN` `IF (ICODE.LT.200) RETURN 1` `STOP` `END` `C-----------------------------------------------------------------------` `C-----------------------------------------------------------------------` `C-----------------------------------------------------------------------`

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C-----------------------------------------------------------------------
C-----------------------------------------------------------------------
C-----------------------------------------------------------------------
C     KTCLUS: written by Mike Seymour, July 1992.
C     Last modified November 2000.
C     Please send comments or suggestions to Mike.Seymour@rl.ac.uk
C
C     This is a general-purpose kt clustering package.
C     It can handle ee, ep and pp collisions.
C     It is loosely based on the program of Siggi Bethke.
C
C     The time taken (on a 10MIP machine) is (0.2microsec)*N**3
C     where N is the number of particles.
C     Over 90 percent of this time is used in subroutine KTPMIN, which
C     simply finds the minimum member of a one-dimensional array.
C     It is well worth thinking about optimization: on the SPARCstation
C     a factor of two increase was obtained simply by increasing the
C     optimization level from its default value.
C
C     The approach is to separate the different stages of analysis.
C     KTCLUS does all the clustering and records a merging history.
C     It returns a simple list of the y values at which each merging
C     occured. Then the following routines can be called to give extra
C     information on the most recently analysed event.
C     KTCLUR is identical but includes an R parameter, see below.
C     KTYCUT gives the number of jets at each given YCUT value.
C     KTYSUB gives the number of sub-jets at each given YCUT value.
C     KTBEAM gives same info as KTCLUS but only for merges with the beam
C     KTJOIN gives same info as KTCLUS but for merges of sub-jets.
C     KTRECO reconstructs the jet momenta at a given value of YCUT.
C     It also gives information on which jets at scale YCUT belong to
C     which macro-jets at scale YMAC, for studying sub-jet properties.
C     KTINCL reconstructs the jet momenta according to the inclusive jet
C     definition of Ellis and Soper.
C     KTISUB, KTIJOI and KTIREC are like KTYSUB, KTJOIN and KTRECO,
C     except that they only apply to one inclusive jet at a time,
C     with the pt of that jet automatically used for ECUT.
C     KTWICH gives a list of which particles ended up in which jets.
C     KTWCHS gives the same thing, but only for subjets.
C     Note that the numbering of jets used by these two routines is
C     guaranteed to be the same as that used by KTRECO.
C
C     The collision type and analysis type are indicated by the first
C     argument of KTCLUS. IMODE=<TYPE><ANGLE><MONO><RECOM> where
C     TYPE:  1=>ee, 2=>ep with p in -z direction, 3=>pe, 4=>pp
C     ANGLE: 1=>angular kt def., 2=>DeltaR, 3=>f(DeltaEta,DeltaPhi)
C            where f()=2(cosh(eta)-cos(phi)) is the QCD emission metric
C     MONO:  1=>derive relative pseudoparticle angles from jets
C            2=>monotonic definitions of relative angles
C     RECOM: 1=>E recombination scheme, 2=>pt scheme, 3=>pt**2 scheme
C
C     There are also abbreviated forms for the most common combinations:
C     IMODE=1 => E scheme in e+e-                              (=1111)
C           2 => E scheme in ep                                (=2111)
C           3 => E scheme in pe                                (=3111)
C           4 => E scheme in pp                                (=4111)
C           5 => covariant E scheme in pp                      (=4211)
C           6 => covariant pt-scheme in pp                     (=4212)
C           7 => covariant monotonic pt**2-scheme in pp        (=4223)
C
C     KTRECO no longer needs to reconstruct the momenta according to the
C     same recombination scheme in which they were clustered. Its first
C     argument gives the scheme, taking the same values as RECOM above.
C
C     Note that unlike previous versions, all variables which hold y
C     values have been named in a consistent way:
C     Y()  is the output scale at which jets were merged,
C     YCUT is the input scale at which jets should be counted, and
C          jet-momenta reconstructed etc,
C     YMAC is the input macro-jet scale, used in determining whether
C          or not each jet is a sub-jet.
C     The original scheme defined in our papers is equivalent to always
C     setting YMAC=1.
C     Whenever a YCUT or YMAC variable is used, it is rounded down
C     infinitesimally, so that for example, setting YCUT=Y(2) refers
C     to the scale where the event is 2-jet, even if rounding errors
C     have shifted its value slightly.
C
C     An R parameter can be used in hadron-hadron collisions by
C     calling KTCLUR instead of KTCLUS.  This is as suggested by
C     Ellis and Soper, but implemented slightly differently,
C     as in M.H. Seymour, LU TP 94/2 (submitted to Nucl. Phys. B.).
C     R**2 multiplies the single Kt everywhere it is used.
C     Calling KTCLUR with R=1 is identical to calling KTCLUS.
C     R plays a similar role to the jet radius in a cone-type algorithm,
C     but is scaled up by about 40% (ie R=0.7 in a cone algorithm is
C     similar to this algorithm with R=1).
C     Note that R.EQ.1 must be used for the e+e- and ep versions,
C     and is strongly recommended for the hadron-hadron version.
C     However, R values smaller than 1 have been found to be useful for
C     certain applications, particularly the mass reconstruction of
C     highly-boosted colour-singlets such as high-pt hadronic Ws,
C     as in M.H. Seymour, LU TP 93/8 (to appear in Z. Phys. C.).
C     Situations in which R<1 is useful are likely to also be those in
C     which the inclusive reconstruction method is more useful.
C
C     Also included is a set of routines for doing Lorentz boosts:
C     KTLBST finds the boost matrix to/from the cm frame of a 4-vector
C     KTRROT finds the rotation matrix from one vector to another
C     KTMMUL multiplies together two matrices
C     KTVMUL multiplies a vector by a matrix
C     KTINVT inverts a transformation matrix (nb NOT a general 4 by 4)
C     KTFRAM boosts a list of vectors between two arbitrary frames
C     KTBREI boosts a list of vectors between the lab and Breit frames
C     KTHADR boosts a list of vectors between the lab and hadronic cmf
C       The last two need the momenta in the +z direction of the lepton
C       and hadron beams, and the 4-momentum of the outgoing lepton.
C
C     The main reference is:
C       S. Catani, Yu.L. Dokshitzer, M.H. Seymour and B.R. Webber,
C         Nucl.Phys.B406(1993)187.
C     The ep version was proposed in:
C       S. Catani, Yu.L. Dokshitzer and B.R. Webber,
C         Phys.Lett.285B(1992)291.
C     The inclusive reconstruction method was proposed in:
C       S.D. Ellis and D.E. Soper,
C         Phys.Rev.D48(1993)3160.
C
C-----------------------------------------------------------------------
C-----------------------------------------------------------------------
C-----------------------------------------------------------------------
      SUBROUTINE KTCLUS(IMODE,PP,NN,ECUT,Y,*)
      IMPLICIT NONE
C---DO CLUSTER ANALYSIS OF PARTICLES IN PP
C
C   IMODE   = INPUT  : DESCRIBED ABOVE
C   PP(I,J) = INPUT  : 4-MOMENTUM OF Jth PARTICLE: I=1,4 => PX,PY,PZ,E
C   NN      = INPUT  : NUMBER OF PARTICLES
C   ECUT    = INPUT  : DENOMINATOR OF KT MEASURE. IF ZERO, ETOT IS USED
C   Y(J)    = OUTPUT : VALUE OF Y FOR WHICH EVENT CHANGES FROM BEING
C                        J JET TO J-1 JET
C   LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT
C   COULD NOT BE PROCESSED (MOST LIKELY DUE TO TOO MANY PARTICLES)
C
C   NOTE THAT THE MOMENTA ARE DECLARED DOUBLE PRECISION,
C   AND ALL OTHER FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION
C
      INTEGER IMODE,NN
      DOUBLE PRECISION PP(4,*)
      DOUBLE PRECISION ECUT,Y(*),ONE
      ONE=1
      CALL KTCLUR(IMODE,PP,NN,ONE,ECUT,Y,*999)
      RETURN
 999  RETURN 1
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTCLUR(IMODE,PP,NN,R,ECUT,Y,*)
      IMPLICIT NONE
C---DO CLUSTER ANALYSIS OF PARTICLES IN PP
C
C   IMODE   = INPUT  : DESCRIBED ABOVE
C   PP(I,J) = INPUT  : 4-MOMENTUM OF Jth PARTICLE: I=1,4 => PX,PY,PZ,E
C   NN      = INPUT  : NUMBER OF PARTICLES
C   R       = INPUT  : ELLIS AND SOPER'S R PARAMETER, SEE ABOVE.
C   ECUT    = INPUT  : DENOMINATOR OF KT MEASURE. IF ZERO, ETOT IS USED
C   Y(J)    = OUTPUT : VALUE OF Y FOR WHICH EVENT CHANGES FROM BEING
C                        J JET TO J-1 JET
C   LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT
C   COULD NOT BE PROCESSED (MOST LIKELY DUE TO TOO MANY PARTICLES)
C
C   NOTE THAT THE MOMENTA ARE DECLARED DOUBLE PRECISION,
C   AND ALL OTHER FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION
C
      INTEGER NMAX,IM,IMODE,TYPE,ANGL,MONO,RECO,N,I,J,NN,
     &     IMIN,JMIN,KMIN,NUM,HIST,INJET,IABBR,NABBR
      PARAMETER (NMAX=512,NABBR=7)
      DOUBLE PRECISION PP(4,*)
      DOUBLE PRECISION R,ECUT,Y(*),P,KT,ETOT,RSQ,KTP,KTS,KTPAIR,KTSING,
     &     KTMIN,ETSQ,KTLAST,KTMAX,KTTMP
      LOGICAL FIRST
      CHARACTER TITLE(4,4)*10
C---KT RECORDS THE KT**2 OF EACH MERGING.
C---KTLAST RECORDS FOR EACH MERGING, THE HIGHEST ECUT**2 FOR WHICH THE
C   RESULT IS NOT MERGED WITH THE BEAM (COULD BE LARGER THAN THE
C   KT**2 AT WHICH IT WAS MERGED IF THE KT VALUES ARE NOT MONOTONIC).
C   THIS MAY SOUND POINTLESS, BUT ITS USEFUL FOR DETERMINING WHETHER
C   SUB-JETS SURVIVED TO SCALE Y=YMAC OR NOT.
C---HIST RECORDS MERGING HISTORY:
C   N=>DELETED TRACK N, M*NMAX+N=>MERGED TRACKS M AND N (M<N).
      COMMON /KTCOMM/ETOT,RSQ,P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX),
     &  KT(NMAX),KTLAST(NMAX),HIST(NMAX),NUM
      DIMENSION INJET(NMAX),IABBR(NABBR)
      DATA FIRST,TITLE,IABBR/.TRUE.,
     &     'e+e-      ','ep        ','pe        ','pp        ',
     &     'angle     ','DeltaR    ','f(DeltaR) ','**********',
     &     'no        ','yes       ','**********','**********',
     &     'E         ','Pt        ','Pt**2     ','**********',
     &     1111,2111,3111,4111,4211,4212,4223/
C---CHECK INPUT
      IM=IMODE
      IF (IM.GE.1.AND.IM.LE.NABBR) IM=IABBR(IM)
      TYPE=MOD(IM/1000,10)
      ANGL=MOD(IM/100 ,10)
      MONO=MOD(IM/10  ,10)
      RECO=MOD(IM     ,10)
      IF (NN.GT.NMAX.OR.NN.LT.1.OR.(NN.LT.2.AND.TYPE.EQ.1))
     &     CALL KTWARN('KTCLUS',100,*999)
      IF (TYPE.LT.1.OR.TYPE.GT.4.OR.ANGL.LT.1.OR.ANGL.GT.4.OR.
     &    MONO.LT.1.OR.MONO.GT.2.OR.RECO.LT.1.OR.RECO.GT.3)
     &     CALL KTWARN('KTCLUS',101,*999)
      IF (FIRST) THEN
         WRITE (6,'(/,1X,54(''*'')/A)')
     &   ' KTCLUS: written by Mike Seymour, July 1992.'
         WRITE (6,'(A)')
     &   ' Last modified November 2000.'
         WRITE (6,'(A)')
     &   ' Please send comments or suggestions to Mike.Seymour@rl.ac.uk'
         WRITE (6,'(/A,I2,2A)')
     &   '       Collision type =',TYPE,' = ',TITLE(TYPE,1)
         WRITE (6,'(A,I2,2A)')
     &   '     Angular variable =',ANGL,' = ',TITLE(ANGL,2)
         WRITE (6,'(A,I2,2A)')
     &   ' Monotonic definition =',MONO,' = ',TITLE(MONO,3)
         WRITE (6,'(A,I2,2A)')
     &   ' Recombination scheme =',RECO,' = ',TITLE(RECO,4)
         IF (R.NE.1) THEN
         WRITE (6,'(A,F5.2)')
     &   '     Radius parameter =',R
         IF (TYPE.NE.4) WRITE (6,'(A)')
     &   ' R.NE.1 is strongly discouraged for this collision type!'
         ENDIF
         WRITE (6,'(1X,54(''*'')/)')
         FIRST=.FALSE.
      ENDIF
C---COPY PP TO P
      N=NN
      NUM=NN
      CALL KTCOPY(PP,N,P,(RECO.NE.1))
      ETOT=0
      DO 100 I=1,N
         ETOT=ETOT+P(4,I)
 100  CONTINUE
      IF (ETOT.EQ.0) CALL KTWARN('KTCLUS',102,*999)
      IF (ECUT.EQ.0) THEN
         ETSQ=1/ETOT**2
      ELSE
         ETSQ=1/ECUT**2
      ENDIF
      RSQ=R**2
C---CALCULATE ALL PAIR KT's
      DO 210 I=1,N-1
         DO 200 J=I+1,N
            KTP(J,I)=-1
            KTP(I,J)=KTPAIR(ANGL,P(1,I),P(1,J),KTP(J,I))
 200     CONTINUE
 210  CONTINUE
C---CALCULATE ALL SINGLE KT's
      DO 230 I=1,N
         KTS(I)=KTSING(ANGL,TYPE,P(1,I))
 230  CONTINUE
      KTMAX=0
C---MAIN LOOP
 300  CONTINUE
C---FIND MINIMUM MEMBER OF KTP
      CALL KTPMIN(KTP,NMAX,N,IMIN,JMIN)
C---FIND MINIMUM MEMBER OF KTS
      CALL KTSMIN(KTS,NMAX,N,KMIN)
C---STORE Y VALUE OF TRANSITION FROM N TO N-1 JETS
      KTMIN=KTP(IMIN,JMIN)
      KTTMP=RSQ*KTS(KMIN)
      IF ((TYPE.GE.2.AND.TYPE.LE.4).AND.
     &     (KTTMP.LE.KTMIN.OR.N.EQ.1))
     &     KTMIN=KTTMP
      KT(N)=KTMIN
      Y(N)=KT(N)*ETSQ
C---IF MONO.GT.1, SEQUENCE IS SUPPOSED TO BE MONOTONIC, IF NOT, WARN
      IF (KTMIN.LT.KTMAX.AND.MONO.GT.1) CALL KTWARN('KTCLUS',1,*999)
      IF (KTMIN.GE.KTMAX) KTMAX=KTMIN
C---IF LOWEST KT IS TO A BEAM, THROW IT AWAY AND MOVE LAST ENTRY UP
      IF (KTMIN.EQ.KTTMP) THEN
         CALL KTMOVE(P,KTP,KTS,NMAX,N,KMIN,1)
C---UPDATE HISTORY AND CROSS-REFERENCES
         HIST(N)=KMIN
         INJET(N)=KMIN
         DO 400 I=N,NN
            IF (INJET(I).EQ.KMIN) THEN
               KTLAST(I)=KTMAX
               INJET(I)=0
            ELSEIF (INJET(I).EQ.N) THEN
               INJET(I)=KMIN
            ENDIF
 400     CONTINUE
C---OTHERWISE MERGE JETS IMIN AND JMIN AND MOVE LAST ENTRY UP
      ELSE
         CALL KTMERG(P,KTP,KTS,NMAX,IMIN,JMIN,N,TYPE,ANGL,MONO,RECO)
         CALL KTMOVE(P,KTP,KTS,NMAX,N,JMIN,1)
C---UPDATE HISTORY AND CROSS-REFERENCES
         HIST(N)=IMIN*NMAX+JMIN
         INJET(N)=IMIN
         DO 600 I=N,NN
            IF (INJET(I).EQ.JMIN) THEN
               INJET(I)=IMIN
            ELSEIF (INJET(I).EQ.N) THEN
               INJET(I)=JMIN
            ENDIF
 600     CONTINUE
      ENDIF
C---THATS ALL THERE IS TO IT
      N=N-1
      IF (N.GT.1 .OR. N.GT.0.AND.(TYPE.GE.2.AND.TYPE.LE.4)) GOTO 300
      IF (N.EQ.1) THEN
         KT(N)=1D20
         Y(N)=KT(N)*ETSQ
      ENDIF
      RETURN
 999  RETURN 1
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTYCUT(ECUT,NY,YCUT,NJET,*)
      IMPLICIT NONE
C---COUNT THE NUMBER OF JETS AT EACH VALUE OF YCUT, FOR EVENT WHICH HAS
C   ALREADY BEEN ANALYSED BY KTCLUS.
C
C   ECUT    = INPUT : DENOMINATOR OF KT MEASURE. IF ZERO, ETOT IS USED
C   NY      = INPUT : NUMBER OF YCUT VALUES
C   YCUT(J) = INPUT : Y VALUES AT WHICH NUMBERS OF JETS ARE COUNTED
C   NJET(J) =OUTPUT : NUMBER OF JETS AT YCUT(J)
C   LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT
C   COULD NOT BE PROCESSED
C
C   NOTE THAT ALL FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION
C
      INTEGER NY,NJET(NY),NMAX,HIST,I,J,NUM
      PARAMETER (NMAX=512)
      DOUBLE PRECISION YCUT(NY),ETOT,RSQ,P,KT,KTP,KTS,ETSQ,ECUT,KTLAST,
     &     ROUND
      PARAMETER (ROUND=0.99999D0)
      COMMON /KTCOMM/ETOT,RSQ,P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX),
     &  KT(NMAX),KTLAST(NMAX),HIST(NMAX),NUM
      IF (ETOT.EQ.0) CALL KTWARN('KTYCUT',100,*999)
      IF (ECUT.EQ.0) THEN
         ETSQ=1/ETOT**2
      ELSE
         ETSQ=1/ECUT**2
      ENDIF
      DO 100 I=1,NY
         NJET(I)=0
 100  CONTINUE
      DO 210 I=NUM,1,-1
         DO 200 J=1,NY
            IF (NJET(J).EQ.0.AND.KT(I)*ETSQ.GE.ROUND*YCUT(J)) NJET(J)=I
 200     CONTINUE
 210  CONTINUE
      RETURN
 999  RETURN 1
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTYSUB(ECUT,NY,YCUT,YMAC,NSUB,*)
      IMPLICIT NONE
C---COUNT THE NUMBER OF SUB-JETS AT EACH VALUE OF YCUT, FOR EVENT WHICH
C   HAS ALREADY BEEN ANALYSED BY KTCLUS.
C   REMEMBER THAT A SUB-JET IS DEFINED AS A JET AT Y=YCUT WHICH HAS NOT
C   YET BEEN MERGED WITH THE BEAM AT Y=YMAC.
C
C   ECUT    = INPUT : DENOMINATOR OF KT MEASURE. IF ZERO, ETOT IS USED
C   NY      = INPUT : NUMBER OF YCUT VALUES
C   YCUT(J) = INPUT : Y VALUES AT WHICH NUMBERS OF SUB-JETS ARE COUNTED
C   YMAC    = INPUT : Y VALUE USED TO DEFINE MACRO-JETS, TO DETERMINE
C                       WHICH JETS ARE SUB-JETS
C   NSUB(J) =OUTPUT : NUMBER OF SUB-JETS AT YCUT(J)
C   LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT
C   COULD NOT BE PROCESSED
C
C   NOTE THAT ALL FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION
C
      INTEGER NY,NSUB(NY),NMAX,HIST,I,J,NUM
      PARAMETER (NMAX=512)
      DOUBLE PRECISION YCUT(NY),YMAC,ETOT,RSQ,P,KT,KTP,KTS,ETSQ,ECUT,
     &     KTLAST,ROUND
      PARAMETER (ROUND=0.99999D0)
      COMMON /KTCOMM/ETOT,RSQ,P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX),
     &  KT(NMAX),KTLAST(NMAX),HIST(NMAX),NUM
      IF (ETOT.EQ.0) CALL KTWARN('KTYSUB',100,*999)
      IF (ECUT.EQ.0) THEN
         ETSQ=1/ETOT**2
      ELSE
         ETSQ=1/ECUT**2
      ENDIF
      DO 100 I=1,NY
         NSUB(I)=0
 100  CONTINUE
      DO 210 I=NUM,1,-1
         DO 200 J=1,NY
            IF (NSUB(J).EQ.0.AND.KT(I)*ETSQ.GE.ROUND*YCUT(J)) NSUB(J)=I
            IF (NSUB(J).NE.0.AND.KTLAST(I)*ETSQ.LT.ROUND*YMAC)
     &          NSUB(J)=NSUB(J)-1
 200     CONTINUE
 210  CONTINUE
      RETURN
 999  RETURN 1
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTBEAM(ECUT,Y,*)
      IMPLICIT NONE
C---GIVE SAME INFORMATION AS LAST CALL TO KTCLUS EXCEPT THAT ONLY
C   TRANSITIONS WHERE A JET WAS MERGED WITH THE BEAM JET ARE RECORDED
C
C   ECUT    = INPUT : DENOMINATOR OF KT MEASURE. IF ZERO, ETOT IS USED
C   Y(J)    =OUTPUT : Y VALUE WHERE Jth HARDEST JET WAS MERGED WITH BEAM
C   LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT
C   COULD NOT BE PROCESSED
C
C   NOTE THAT ALL FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION
C
      INTEGER NMAX,HIST,NUM,I,J
      PARAMETER (NMAX=512)
      DOUBLE PRECISION ETOT,RSQ,P,KT,KTP,KTS,ECUT,ETSQ,Y(*),KTLAST
      COMMON /KTCOMM/ETOT,RSQ,P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX),
     &  KT(NMAX),KTLAST(NMAX),HIST(NMAX),NUM
      IF (ETOT.EQ.0) CALL KTWARN('KTBEAM',100,*999)
      IF (ECUT.EQ.0) THEN
         ETSQ=1/ETOT**2
      ELSE
         ETSQ=1/ECUT**2
      ENDIF
      J=1
      DO 100 I=1,NUM
         IF (HIST(I).LE.NMAX) THEN
            Y(J)=ETSQ*KT(I)
            J=J+1
         ENDIF
 100  CONTINUE
      DO 200 I=J,NUM
         Y(I)=0
 200  CONTINUE
      RETURN
 999  RETURN 1
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTJOIN(ECUT,YMAC,Y,*)
      IMPLICIT NONE
C---GIVE SAME INFORMATION AS LAST CALL TO KTCLUS EXCEPT THAT ONLY
C   TRANSITIONS WHERE TWO SUB-JETS WERE JOINED ARE RECORDED
C   REMEMBER THAT A SUB-JET IS DEFINED AS A JET AT Y=YCUT WHICH HAS NOT
C   YET BEEN MERGED WITH THE BEAM AT Y=YMAC.
C
C   ECUT    = INPUT : DENOMINATOR OF KT MEASURE. IF ZERO, ETOT IS USED
C   YMAC    = INPUT : VALUE OF Y USED TO DEFINE MACRO-JETS
C   Y(J)    =OUTPUT : Y VALUE WHERE EVENT CHANGED FROM HAVING
C                         N+J SUB-JETS TO HAVING N+J-1, WHERE N IS
C                         THE NUMBER OF MACRO-JETS AT SCALE YMAC
C   LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT
C   COULD NOT BE PROCESSED
C
C   NOTE THAT ALL FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION
C
      INTEGER NMAX,HIST,NUM,I,J
      PARAMETER (NMAX=512)
      DOUBLE PRECISION ETOT,RSQ,P,KT,KTP,KTS,ECUT,ETSQ,Y(*),YMAC,KTLAST,
     &     ROUND
      PARAMETER (ROUND=0.99999D0)
      COMMON /KTCOMM/ETOT,RSQ,P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX),
     &  KT(NMAX),KTLAST(NMAX),HIST(NMAX),NUM
      IF (ETOT.EQ.0) CALL KTWARN('KTJOIN',100,*999)
      IF (ECUT.EQ.0) THEN
         ETSQ=1/ETOT**2
      ELSE
         ETSQ=1/ECUT**2
      ENDIF
      J=1
      DO 100 I=1,NUM
         IF (HIST(I).GT.NMAX.AND.ETSQ*KTLAST(I).GE.ROUND*YMAC) THEN
            Y(J)=ETSQ*KT(I)
            J=J+1
         ENDIF
 100  CONTINUE
      DO 200 I=J,NUM
         Y(I)=0
 200  CONTINUE
      RETURN
 999  RETURN 1
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTRECO(RECO,PP,NN,ECUT,YCUT,YMAC,PJET,JET,NJET,NSUB,*)
      IMPLICIT NONE
C---RECONSTRUCT KINEMATICS OF JET SYSTEM, WHICH HAS ALREADY BEEN
C   ANALYSED BY KTCLUS. NOTE THAT NO CONSISTENCY CHECK IS MADE: USER
C   IS TRUSTED TO USE THE SAME PP VALUES AS FOR KTCLUS
C
C   RECO     = INPUT : RECOMBINATION SCHEME (NEED NOT BE SAME AS KTCLUS)
C   PP(I,J)  = INPUT : 4-MOMENTUM OF Jth PARTICLE: I=1,4 => PX,PY,PZ,E
C   NN       = INPUT : NUMBER OF PARTICLES
C   ECUT     = INPUT : DENOMINATOR OF KT MEASURE. IF ZERO, ETOT IS USED
C   YCUT     = INPUT : Y VALUE AT WHICH TO RECONSTRUCT JET MOMENTA
C   YMAC     = INPUT : Y VALUE USED TO DEFINE MACRO-JETS, TO DETERMINE
C                        WHICH JETS ARE SUB-JETS
C   PJET(I,J)=OUTPUT : 4-MOMENTUM OF Jth JET AT SCALE YCUT
C   JET(J)   =OUTPUT : THE MACRO-JET WHICH CONTAINS THE Jth JET,
C                        SET TO ZERO IF JET IS NOT A SUB-JET
C   NJET     =OUTPUT : THE NUMBER OF JETS
C   NSUB     =OUTPUT : THE NUMBER OF SUB-JETS (EQUAL TO THE NUMBER OF
C                        NON-ZERO ENTRIES IN JET())
C   LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT
C   COULD NOT BE PROCESSED
C
C   NOTE THAT THE MOMENTA ARE DECLARED DOUBLE PRECISION,
C   AND ALL OTHER FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION
C
      INTEGER NMAX,RECO,NUM,N,NN,NJET,NSUB,JET(*),HIST,IMIN,JMIN,I,J
      PARAMETER (NMAX=512)
      DOUBLE PRECISION PP(4,*),PJET(4,*)
      DOUBLE PRECISION ECUT,P,KT,KTP,KTS,ETOT,RSQ,ETSQ,YCUT,YMAC,KTLAST,
     &     ROUND
      PARAMETER (ROUND=0.99999D0)
      COMMON /KTCOMM/ETOT,RSQ,P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX),
     &  KT(NMAX),KTLAST(NMAX),HIST(NMAX),NUM
C---CHECK INPUT
      IF (RECO.LT.1.OR.RECO.GT.3) THEN
        PRINT *,'RECO=',RECO
        CALL KTWARN('KTRECO',100,*999)
      ENDIF
C---COPY PP TO P
      N=NN
      IF (NUM.NE.NN) CALL KTWARN('KTRECO',101,*999)
      CALL KTCOPY(PP,N,P,(RECO.NE.1))
      IF (ECUT.EQ.0) THEN
         ETSQ=1/ETOT**2
      ELSE
         ETSQ=1/ECUT**2
      ENDIF
C---KEEP MERGING UNTIL YCUT
 100  IF (ETSQ*KT(N).LT.ROUND*YCUT) THEN
         IF (HIST(N).LE.NMAX) THEN
            CALL KTMOVE(P,KTP,KTS,NMAX,N,HIST(N),0)
         ELSE
            IMIN=HIST(N)/NMAX
            JMIN=HIST(N)-IMIN*NMAX
            CALL KTMERG(P,KTP,KTS,NMAX,IMIN,JMIN,N,0,0,0,RECO)
            CALL KTMOVE(P,KTP,KTS,NMAX,N,JMIN,0)
         ENDIF
         N=N-1
         IF (N.GT.0) GOTO 100
      ENDIF
C---IF YCUT IS TOO LARGE THERE ARE NO JETS
      NJET=N
      NSUB=N
      IF (N.EQ.0) RETURN
C---SET UP OUTPUT MOMENTA
      DO 210 I=1,NJET
         IF (RECO.EQ.1) THEN
            DO 200 J=1,4
               PJET(J,I)=P(J,I)
 200        CONTINUE
         ELSE
            PJET(1,I)=P(6,I)*COS(P(8,I))
            PJET(2,I)=P(6,I)*SIN(P(8,I))
            PJET(3,I)=P(6,I)*SINH(P(7,I))
            PJET(4,I)=P(6,I)*COSH(P(7,I))
         ENDIF
         JET(I)=I
 210  CONTINUE
C---KEEP MERGING UNTIL YMAC TO FIND THE FATE OF EACH JET
 300  IF (ETSQ*KT(N).LT.ROUND*YMAC) THEN
         IF (HIST(N).LE.NMAX) THEN
            IMIN=0
            JMIN=HIST(N)
            NSUB=NSUB-1
         ELSE
            IMIN=HIST(N)/NMAX
            JMIN=HIST(N)-IMIN*NMAX
            IF (ETSQ*KTLAST(N).LT.ROUND*YMAC) NSUB=NSUB-1
         ENDIF
         DO 310 I=1,NJET
            IF (JET(I).EQ.JMIN) JET(I)=IMIN
            IF (JET(I).EQ.N) JET(I)=JMIN
 310     CONTINUE
         N=N-1
         IF (N.GT.0) GOTO 300
      ENDIF
      RETURN
 999  RETURN 1
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTINCL(RECO,PP,NN,PJET,JET,NJET,*)
      IMPLICIT NONE
C---RECONSTRUCT KINEMATICS OF JET SYSTEM, WHICH HAS ALREADY BEEN
C   ANALYSED BY KTCLUS ACCORDING TO THE INCLUSIVE JET DEFINITION. NOTE
C   THAT NO CONSISTENCY CHECK IS MADE: USER IS TRUSTED TO USE THE SAME
C   PP VALUES AS FOR KTCLUS
C
C   RECO     = INPUT : RECOMBINATION SCHEME (NEED NOT BE SAME AS KTCLUS)
C   PP(I,J)  = INPUT : 4-MOMENTUM OF Jth PARTICLE: I=1,4 => PX,PY,PZ,E
C   NN       = INPUT : NUMBER OF PARTICLES
C   PJET(I,J)=OUTPUT : 4-MOMENTUM OF Jth JET AT SCALE YCUT
C   JET(J)   =OUTPUT : THE JET WHICH CONTAINS THE Jth PARTICLE
C   NJET     =OUTPUT : THE NUMBER OF JETS
C   LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT
C   COULD NOT BE PROCESSED
C
C   NOTE THAT THE MOMENTA ARE DECLARED DOUBLE PRECISION,
C   AND ALL OTHER FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION
C
      INTEGER NMAX,RECO,NUM,N,NN,NJET,JET(*),HIST,IMIN,JMIN,I,J
      PARAMETER (NMAX=512)
      DOUBLE PRECISION PP(4,*),PJET(4,*)
      DOUBLE PRECISION P,KT,KTP,KTS,ETOT,RSQ,KTLAST
      COMMON /KTCOMM/ETOT,RSQ,P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX),
     &  KT(NMAX),KTLAST(NMAX),HIST(NMAX),NUM
C---CHECK INPUT
      IF (RECO.LT.1.OR.RECO.GT.3) CALL KTWARN('KTINCL',100,*999)
C---COPY PP TO P
      N=NN
      IF (NUM.NE.NN) CALL KTWARN('KTINCL',101,*999)
      CALL KTCOPY(PP,N,P,(RECO.NE.1))
C---INITIALLY EVERY PARTICLE IS IN ITS OWN JET
      DO 100 I=1,NN
         JET(I)=I
 100  CONTINUE
C---KEEP MERGING TO THE BITTER END
      NJET=0
 200  IF (N.GT.0) THEN
         IF (HIST(N).LE.NMAX) THEN
            IMIN=0
            JMIN=HIST(N)
            NJET=NJET+1
            IF (RECO.EQ.1) THEN
               DO 300 J=1,4
                  PJET(J,NJET)=P(J,JMIN)
 300           CONTINUE
            ELSE
               PJET(1,NJET)=P(6,JMIN)*COS(P(8,JMIN))
               PJET(2,NJET)=P(6,JMIN)*SIN(P(8,JMIN))
               PJET(3,NJET)=P(6,JMIN)*SINH(P(7,JMIN))
               PJET(4,NJET)=P(6,JMIN)*COSH(P(7,JMIN))
            ENDIF
            CALL KTMOVE(P,KTP,KTS,NMAX,N,JMIN,0)
         ELSE
            IMIN=HIST(N)/NMAX
            JMIN=HIST(N)-IMIN*NMAX
            CALL KTMERG(P,KTP,KTS,NMAX,IMIN,JMIN,N,0,0,0,RECO)
            CALL KTMOVE(P,KTP,KTS,NMAX,N,JMIN,0)
         ENDIF
         DO 400 I=1,NN
            IF (JET(I).EQ.JMIN) JET(I)=IMIN
            IF (JET(I).EQ.N) JET(I)=JMIN
            IF (JET(I).EQ.0) JET(I)=-NJET
 400     CONTINUE
         N=N-1
         GOTO 200
      ENDIF
C---FINALLY EVERY PARTICLE MUST BE IN AN INCLUSIVE JET
      DO 500 I=1,NN
C---IF THERE ARE ANY UNASSIGNED PARTICLES SOMETHING MUST HAVE GONE WRONG
         IF (JET(I).GE.0) CALL KTWARN('KTINCL',102,*999)
         JET(I)=-JET(I)
 500  CONTINUE
      RETURN
 999  RETURN 1
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTISUB(N,NY,YCUT,NSUB,*)
      IMPLICIT NONE
C---COUNT THE NUMBER OF SUB-JETS IN THE Nth INCLUSIVE JET OF AN EVENT
C   THAT HAS ALREADY BEEN ANALYSED BY KTCLUS.
C
C   N       = INPUT : WHICH INCLUSIVE JET TO USE
C   NY      = INPUT : NUMBER OF YCUT VALUES
C   YCUT(J) = INPUT : Y VALUES AT WHICH NUMBERS OF SUB-JETS ARE COUNTED
C   NSUB(J) =OUTPUT : NUMBER OF SUB-JETS AT YCUT(J)
C   LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT
C   COULD NOT BE PROCESSED
C
C   NOTE THAT ALL FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION
C
      INTEGER N,NY,NSUB(NY),NMAX,HIST,I,J,NUM,NM
      PARAMETER (NMAX=512)
      DOUBLE PRECISION YCUT(NY),ETOT,RSQ,P,KT,KTP,KTS,KTLAST,ROUND,EPS
      PARAMETER (ROUND=0.99999D0)
      COMMON /KTCOMM/ETOT,RSQ,P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX),
     &  KT(NMAX),KTLAST(NMAX),HIST(NMAX),NUM
      DATA EPS/1D-6/
      DO 100 I=1,NY
         NSUB(I)=0
 100  CONTINUE
C---FIND WHICH MERGING CORRESPONDS TO THE NTH INCLUSIVE JET
      NM=0
      J=0
      DO 110 I=NUM,1,-1
        IF (HIST(I).LE.NMAX) J=J+1
        IF (J.EQ.N) THEN
          NM=I
          GOTO 120
        ENDIF
 110  CONTINUE
 120  CONTINUE
C---GIVE UP IF THERE ARE LESS THAN N INCLUSIVE JETS
      IF (NM.EQ.0) CALL KTWARN('KTISUB',100,*999)
      DO 210 I=NUM,1,-1
         DO 200 J=1,NY
            IF (NSUB(J).EQ.0.AND.RSQ*KT(I).GE.ROUND*YCUT(J)*KT(NM))
     &          NSUB(J)=I
            IF (NSUB(J).NE.0.AND.ABS(KTLAST(I)-KTLAST(NM)).GT.EPS)
     &          NSUB(J)=NSUB(J)-1
 200     CONTINUE
 210  CONTINUE
      RETURN
 999  RETURN 1
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTIJOI(N,Y,*)
      IMPLICIT NONE
C---GIVE SAME INFORMATION AS LAST CALL TO KTCLUS EXCEPT THAT ONLY
C   MERGES OF TWO SUB-JETS INSIDE THE Nth INCLUSIVE JET ARE RECORDED
C
C   N       = INPUT : WHICH INCLUSIVE JET TO USE
C   Y(J)    =OUTPUT : Y VALUE WHERE JET CHANGED FROM HAVING
C                         J+1 SUB-JETS TO HAVING J
C   LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT
C   COULD NOT BE PROCESSED
C
C   NOTE THAT ALL FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION
C
      INTEGER NMAX,HIST,NUM,I,J,N,NM
      PARAMETER (NMAX=512)
      DOUBLE PRECISION ETOT,RSQ,P,KT,KTP,KTS,Y(*),KTLAST,EPS
      COMMON /KTCOMM/ETOT,RSQ,P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX),
     &  KT(NMAX),KTLAST(NMAX),HIST(NMAX),NUM
      DATA EPS/1D-6/
C---FIND WHICH MERGING CORRESPONDS TO THE NTH INCLUSIVE JET
      NM=0
      J=0
      DO 100 I=NUM,1,-1
        IF (HIST(I).LE.NMAX) J=J+1
        IF (J.EQ.N) THEN
          NM=I
          GOTO 105
        ENDIF
 100  CONTINUE
 105  CONTINUE
C---GIVE UP IF THERE ARE LESS THAN N INCLUSIVE JETS
      IF (NM.EQ.0) CALL KTWARN('KTIJOI',100,*999)
      J=1
      DO 110 I=1,NUM
         IF (HIST(I).GT.NMAX.AND.ABS(KTLAST(I)-KTLAST(NM)).LT.EPS) THEN
            Y(J)=RSQ*KT(I)/KT(NM)
            J=J+1
         ENDIF
 110  CONTINUE
      DO 200 I=J,NUM
         Y(I)=0
 200  CONTINUE
      RETURN
 999  RETURN 1
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTIREC(RECO,PP,NN,N,YCUT,PSUB,NSUB,*)
      IMPLICIT NONE
C---RECONSTRUCT KINEMATICS OF SUB-JET SYSTEM IN THE Nth INCLUSIVE JET
C   OF AN EVENT THAT HAS ALREADY BEEN ANALYSED BY KTCLUS
C
C   RECO     = INPUT : RECOMBINATION SCHEME (NEED NOT BE SAME AS KTCLUS)
C   PP(I,J)  = INPUT : 4-MOMENTUM OF Jth PARTICLE: I=1,4 => PX,PY,PZ,E
C   NN       = INPUT : NUMBER OF PARTICLES
C   N        = INPUT : WHICH INCLUSIVE JET TO USE
C   YCUT     = INPUT : Y VALUE AT WHICH TO RECONSTRUCT JET MOMENTA
C   PSUB(I,J)=OUTPUT : 4-MOMENTUM OF Jth SUB-JET AT SCALE YCUT
C   NSUB     =OUTPUT : THE NUMBER OF SUB-JETS
C   LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT
C   COULD NOT BE PROCESSED
C
C   NOTE THAT THE MOMENTA ARE DECLARED DOUBLE PRECISION,
C   AND ALL OTHER FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION
C
      INTEGER NMAX,RECO,NUM,NN,NJET,NSUB,JET,HIST,I,J,N,NM
      PARAMETER (NMAX=512)
      DOUBLE PRECISION PP(4,*),PSUB(4,*)
      DOUBLE PRECISION ECUT,P,KT,KTP,KTS,ETOT,RSQ,YCUT,YMAC,KTLAST
      COMMON /KTCOMM/ETOT,RSQ,P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX),
     &  KT(NMAX),KTLAST(NMAX),HIST(NMAX),NUM
      DIMENSION JET(NMAX)
C---FIND WHICH MERGING CORRESPONDS TO THE NTH INCLUSIVE JET
      NM=0
      J=0
      DO 100 I=NUM,1,-1
         IF (HIST(I).LE.NMAX) J=J+1
         IF (J.EQ.N) THEN
            NM=I
            GOTO 110
         ENDIF
 100  CONTINUE
 110  CONTINUE
C---GIVE UP IF THERE ARE LESS THAN N INCLUSIVE JETS
      IF (NM.EQ.0) CALL KTWARN('KTIREC',102,*999)
C---RECONSTRUCT THE JETS AT THE APPROPRIATE SCALE
      ECUT=SQRT(KT(NM)/RSQ)
      YMAC=RSQ
      CALL KTRECO(RECO,PP,NN,ECUT,YCUT,YMAC,PSUB,JET,NJET,NSUB,*999)
C---GET RID OF THE ONES THAT DO NOT END UP IN THE JET WE WANT
      NSUB=0
      DO 210 I=1,NJET
         IF (JET(I).EQ.HIST(NM)) THEN
            NSUB=NSUB+1
            DO 200 J=1,4
               PSUB(J,NSUB)=PSUB(J,I)
 200        CONTINUE
         ENDIF
 210  CONTINUE
      RETURN
 999  RETURN 1
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTWICH(ECUT,YCUT,JET,NJET,*)
      IMPLICIT NONE
C---GIVE A LIST OF WHICH JET EACH ORIGINAL PARTICLE ENDED UP IN AT SCALE
C   YCUT, TOGETHER WITH THE NUMBER OF JETS AT THAT SCALE.
C
C   ECUT     = INPUT : DENOMINATOR OF KT MEASURE. IF ZERO, ETOT IS USED
C   YCUT     = INPUT : Y VALUE AT WHICH TO DEFINE JETS
C   JET(J)   =OUTPUT : THE JET WHICH CONTAINS THE Jth PARTICLE,
C                        SET TO ZERO IF IT WAS PUT INTO THE BEAM JETS
C   NJET     =OUTPUT : THE NUMBER OF JETS AT SCALE YCUT (SO JET()
C                        ENTRIES WILL BE IN THE RANGE 0 -> NJET)
C   LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT
C   COULD NOT BE PROCESSED
C
C   NOTE THAT ALL FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION
C
      INTEGER JET(*),NJET,NTEMP
      DOUBLE PRECISION ECUT,YCUT
      CALL KTWCHS(ECUT,YCUT,YCUT,JET,NJET,NTEMP,*999)
      RETURN
 999  RETURN 1
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTWCHS(ECUT,YCUT,YMAC,JET,NJET,NSUB,*)
      IMPLICIT NONE
C---GIVE A LIST OF WHICH SUB-JET EACH ORIGINAL PARTICLE ENDED UP IN AT
C   SCALE YCUT, WITH MACRO-JET SCALE YMAC, TOGETHER WITH THE NUMBER OF
C   JETS AT SCALE YCUT AND THE NUMBER OF THEM WHICH ARE SUB-JETS.
C
C   ECUT     = INPUT : DENOMINATOR OF KT MEASURE. IF ZERO, ETOT IS USED
C   YCUT     = INPUT : Y VALUE AT WHICH TO DEFINE JETS
C   YMAC     = INPUT : Y VALUE AT WHICH TO DEFINE MACRO-JETS
C   JET(J)   =OUTPUT : THE JET WHICH CONTAINS THE Jth PARTICLE,
C                        SET TO ZERO IF IT WAS PUT INTO THE BEAM JETS
C   NJET     =OUTPUT : THE NUMBER OF JETS AT SCALE YCUT (SO JET()
C                        ENTRIES WILL BE IN THE RANGE 0 -> NJET)
C   NSUB     =OUTPUT : THE NUMBER OF SUB-JETS AT SCALE YCUT, WITH
C                        MACRO-JETS DEFINED AT SCALE YMAC (SO ONLY NSUB
C                        OF THE JETS 1 -> NJET WILL APPEAR IN JET())
C   LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT
C   COULD NOT BE PROCESSED
C
C   NOTE THAT ALL FLOATING POINT VARIABLES ARE DECLARED DOUBLE PRECISION
C
      INTEGER NMAX,JET(*),NJET,NSUB,HIST,NUM,I,J,JSUB
      PARAMETER (NMAX=512)
      DOUBLE PRECISION P1(4,NMAX),P2(4,NMAX)
      DOUBLE PRECISION ECUT,YCUT,YMAC,ZERO,ETOT,RSQ,P,KTP,KTS,KT,KTLAST
      COMMON /KTCOMM/ETOT,RSQ,P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX),
     &  KT(NMAX),KTLAST(NMAX),HIST(NMAX),NUM
      DIMENSION JSUB(NMAX)
C---THE MOMENTA HAVE TO BEEN GIVEN LEGAL VALUES,
C   EVEN THOUGH THEY WILL NEVER BE USED
      DATA ((P1(J,I),I=1,NMAX),J=1,4),ZERO
     &  /NMAX*1,NMAX*0,NMAX*0,NMAX*1,0/
C---FIRST GET A LIST OF WHICH PARTICLE IS IN WHICH JET AT YCUT
      CALL KTRECO(1,P1,NUM,ECUT,ZERO,YCUT,P2,JET,NJET,NSUB,*999)
C---THEN FIND OUT WHICH JETS ARE SUBJETS
      CALL KTRECO(1,P1,NUM,ECUT,YCUT,YMAC,P2,JSUB,NJET,NSUB,*999)
C---AND MODIFY JET() ACCORDINGLY
      DO 10 I=1,NUM
        IF (JET(I).NE.0) THEN
          IF (JSUB(JET(I)).EQ.0) JET(I)=0
        ENDIF
 10   CONTINUE
      RETURN
 999  RETURN 1
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTFRAM(IOPT,CMF,SIGN,Z,XZ,N,P,Q,*)
      IMPLICIT NONE
C---BOOST PARTICLES IN P TO/FROM FRAME GIVEN BY CMF, Z, XZ.
C---IN THIS FRAME CMZ IS STATIONARY,
C                   Z IS ALONG THE (SIGN)Z-AXIS (SIGN=+ OR -)
C                  XZ IS IN THE X-Z PLANE (WITH POSITIVE X COMPONENT)
C---IF Z HAS LENGTH ZERO, OR SIGN=0, NO ROTATION IS PERFORMED
C---IF XZ HAS ZERO COMPONENT PERPENDICULAR TO Z IN THAT FRAME,
C   NO AZIMUTHAL ROTATION IS PERFORMED
C
C   IOPT    = INPUT  : 0=TO FRAME, 1=FROM FRAME
C   CMF(I)  = INPUT  : 4-MOMENTUM WHICH IS STATIONARY IN THE FRAME
C   SIGN    = INPUT  : DIRECTION OF Z IN THE FRAME, NOTE THAT
C                        ONLY ITS SIGN IS USED, NOT ITS MAGNITUDE
C   Z(I)    = INPUT  : 4-MOMENTUM WHICH LIES ON THE (SIGN)Z-AXIS
C   XZ(I)   = INPUT  : 4-MOMENTUM WHICH LIES IN THE X-Z PLANE
C   N       = INPUT  : NUMBER OF PARTICLES IN P
C   P(I,J)  = INPUT  : 4-MOMENTUM OF JTH PARTICLE BEFORE
C   Q(I,J)  = OUTPUT : 4-MOMENTUM OF JTH PARTICLE AFTER
C   LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT
C   COULD NOT BE PROCESSED
C
C   NOTE THAT ALL MOMENTA ARE DOUBLE PRECISION
C
C   NOTE THAT IT IS SAFE TO CALL WITH P=Q
C   
      INTEGER IOPT,I,N
      DOUBLE PRECISION CMF(4),SIGN,Z(4),XZ(4),P(4,N),Q(4,N),
     &  R(4,4),NEW(4),OLD(4)
      IF (IOPT.LT.0.OR.IOPT.GT.1) CALL KTWARN('KTFRAM',200,*999)
C---FIND BOOST TO GET THERE FROM LAB
      CALL KTUNIT(R)
      CALL KTLBST(0,R,CMF,*999)
C---FIND ROTATION TO PUT BOOSTED Z ON THE (SIGN)Z AXIS
      IF (SIGN.NE.0) THEN
        CALL KTVMUL(R,Z,OLD)
        IF (OLD(1).NE.0.OR.OLD(2).NE.0.OR.OLD(3).NE.0) THEN
          NEW(1)=0
          NEW(2)=0
          NEW(3)=SIGN
          NEW(4)=ABS(SIGN)
          CALL KTRROT(R,OLD,NEW,*999)
C---FIND ROTATION TO PUT BOOSTED AND ROTATED XZ INTO X-Z PLANE
          CALL KTVMUL(R,XZ,OLD)
          IF (OLD(1).NE.0.OR.OLD(2).NE.0) THEN
            NEW(1)=1
            NEW(2)=0
            NEW(3)=0
            NEW(4)=1
            OLD(3)=0
C---NOTE THAT A POTENTIALLY AWKWARD SPECIAL CASE IS AVERTED, BECAUSE IF
C   OLD AND NEW ARE EXACTLY BACK-TO-BACK, THE ROTATION AXIS IS UNDEFINED
C   BUT IN THAT CASE KTRROT WILL USE THE Z AXIS, AS REQUIRED
            CALL KTRROT(R,OLD,NEW,*999)
          ENDIF
        ENDIF
      ENDIF
C---INVERT THE TRANSFORMATION IF NECESSARY
      IF (IOPT.EQ.1) CALL KTINVT(R,R)
C---APPLY THE RESULT TO ALL THE VECTORS
      DO 30 I=1,N
        CALL KTVMUL(R,P(1,I),Q(1,I))
 30   CONTINUE
      RETURN
 999  RETURN 1
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTBREI(IOPT,PLEP,PHAD,POUT,N,P,Q,*)
      IMPLICIT NONE
C---BOOST PARTICLES IN P TO/FROM BREIT FRAME
C
C   IOPT    = INPUT  : 0/2=TO BREIT FRAME, 1/3=FROM BREIT FRAME
C                      0/1=NO AZIMUTHAL ROTATION AFTERWARDS
C                      2/3=LEPTON PLANE ROTATED INTO THE X-Z PLANE
C   PLEP    = INPUT  : MOMENTUM OF INCOMING LEPTON IN +Z DIRECTION
C   PHAD    = INPUT  : MOMENTUM OF INCOMING HADRON IN +Z DIRECTION
C   POUT(I) = INPUT  : 4-MOMENTUM OF OUTGOING LEPTON
C   N       = INPUT  : NUMBER OF PARTICLES IN P
C   P(I,J)  = INPUT  : 4-MOMENTUM OF JTH PARTICLE BEFORE
C   Q(I,J)  = OUTPUT : 4-MOMENTUM OF JTH PARTICLE AFTER
C   LAST ARGUMENT IS LABEL TO JUMP TO IF FOR ANY REASON THE EVENT
C   COULD NOT BE PROCESSED (MOST LIKELY DUE TO PARTICLES HAVING SMALLER
C   ENERGY THAN MOMENTUM)
C
C   NOTE THAT ALL MOMENTA ARE DOUBLE PRECISION
C
C   NOTE THAT IT IS SAFE TO CALL WITH P=Q
C   
      INTEGER IOPT,N
      DOUBLE PRECISION PLEP,PHAD,POUT(4),P(4,N),Q(4,N),
     &  CMF(4),Z(4),XZ(4),DOT,QDQ
C---CHECK INPUT
      IF (IOPT.LT.0.OR.IOPT.GT.3) CALL KTWARN('KTBREI',200,*999)
C---FIND 4-MOMENTUM OF BREIT FRAME (TIMES AN ARBITRARY FACTOR)
      DOT=ABS(PHAD)*(ABS(PLEP)-POUT(4))-PHAD*(PLEP-POUT(3))
      QDQ=(ABS(PLEP)-POUT(4))**2-(PLEP-POUT(3))**2-POUT(2)**2-POUT(1)**2
      CMF(1)=DOT*(         -POUT(1))
      CMF(2)=DOT*(         -POUT(2))
      CMF(3)=DOT*(    PLEP -POUT(3))-QDQ*    PHAD
      CMF(4)=DOT*(ABS(PLEP)-POUT(4))-QDQ*ABS(PHAD)
C---FIND ROTATION TO PUT INCOMING HADRON BACK ON Z-AXIS
      Z(1)=0
      Z(2)=0
      Z(3)=PHAD
      Z(4)=ABS(PHAD)
      XZ(1)=0
      XZ(2)=0
      XZ(3)=0
      XZ(4)=0
C---DO THE BOOST
      IF (IOPT.LE.1) THEN
        CALL KTFRAM(IOPT,CMF,PHAD,Z,XZ,N,P,Q,*999)
      ELSE
        CALL KTFRAM(IOPT-2,CMF,PHAD,Z,POUT,N,P,Q,*999)
      ENDIF
      RETURN
 999  RETURN 1
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTHADR(IOPT,PLEP,PHAD,POUT,N,P,Q,*)
      IMPLICIT NONE
C---BOOST PARTICLES IN P TO/FROM HADRONIC CMF
C
C   ARGUMENTS ARE EXACTLY AS FOR KTBREI
C
C   NOTE THAT ALL MOMENTA ARE DOUBLE PRECISION
C
C   NOTE THAT IT IS SAFE TO CALL WITH P=Q
C   
      INTEGER IOPT,N
      DOUBLE PRECISION PLEP,PHAD,POUT(4),P(4,N),Q(4,N),
     &  CMF(4),Z(4),XZ(4)
C---CHECK INPUT
      IF (IOPT.LT.0.OR.IOPT.GT.3) CALL KTWARN('KTHADR',200,*999)
C---FIND 4-MOMENTUM OF HADRONIC CMF
      CMF(1)=         -POUT(1)
      CMF(2)=         -POUT(2)
      CMF(3)=    PLEP -POUT(3)+    PHAD
      CMF(4)=ABS(PLEP)-POUT(4)+ABS(PHAD)
C---FIND ROTATION TO PUT INCOMING HADRON BACK ON Z-AXIS
      Z(1)=0
      Z(2)=0
      Z(3)=PHAD
      Z(4)=ABS(PHAD)
      XZ(1)=0
      XZ(2)=0
      XZ(3)=0
      XZ(4)=0
C---DO THE BOOST
      IF (IOPT.LE.1) THEN
        CALL KTFRAM(IOPT,CMF,PHAD,Z,XZ,N,P,Q,*999)
      ELSE
        CALL KTFRAM(IOPT-2,CMF,PHAD,Z,POUT,N,P,Q,*999)
      ENDIF
      RETURN
 999  RETURN 1
      END
C-----------------------------------------------------------------------
      FUNCTION KTPAIR(ANGL,P,Q,ANGLE)
      IMPLICIT NONE
C---CALCULATE LOCAL KT OF PAIR, USING ANGULAR SCHEME:
C   1=>ANGULAR, 2=>DeltaR, 3=>f(DeltaEta,DeltaPhi)
C   WHERE f(eta,phi)=2(COSH(eta)-COS(phi)) IS THE QCD EMISSION METRIC
C---IF ANGLE<0, IT IS SET TO THE ANGULAR PART OF THE LOCAL KT ON RETURN
C   IF ANGLE>0, IT IS USED INSTEAD OF THE ANGULAR PART OF THE LOCAL KT
      INTEGER ANGL
      DOUBLE PRECISION P(9),Q(9),KTPAIR,R,KTMDPI,ANGLE,ETA,PHI,ESQ
C---COMPONENTS OF MOMENTA ARE PX,PY,PZ,E,1/P,PT,ETA,PHI,PT**2
      R=ANGLE
      IF (ANGL.EQ.1) THEN
         IF (R.LE.0) R=2*(1-(P(1)*Q(1)+P(2)*Q(2)+P(3)*Q(3))*(P(5)*Q(5)))
         ESQ=MIN(P(4),Q(4))**2
      ELSEIF (ANGL.EQ.2.OR.ANGL.EQ.3) THEN
         IF (R.LE.0) THEN
            ETA=P(7)-Q(7)
            PHI=KTMDPI(P(8)-Q(8))
            IF (ANGL.EQ.2) THEN
               R=ETA**2+PHI**2
            ELSE
               R=2*(COSH(ETA)-COS(PHI))
            ENDIF
         ENDIF
         ESQ=MIN(P(9),Q(9))
      ELSEIF (ANGL.EQ.4) THEN
        ESQ=(1d0/(P(5)*Q(5))-P(1)*Q(1)-P(2)*Q(2)-
     &P(3)*Q(3))*2D0/(P(5)*Q(5))/(0.0001D0+1d0/P(5)+1d0/Q(5))**2        
        R=1d0
      ELSE
         ktpair = 0D0
	 CALL KTWARN('KTPAIR',200,*999)
         STOP
      ENDIF
      KTPAIR=ESQ*R
      IF (ANGLE.LT.0) ANGLE=R
 999  END
C-----------------------------------------------------------------------
      FUNCTION KTSING(ANGL,TYPE,P)
      IMPLICIT NONE
C---CALCULATE KT OF PARTICLE, USING ANGULAR SCHEME:
C   1=>ANGULAR, 2=>DeltaR, 3=>f(DeltaEta,DeltaPhi)
C---TYPE=1 FOR E+E-, 2 FOR EP, 3 FOR PE, 4 FOR PP
C   FOR EP, PROTON DIRECTION IS DEFINED AS -Z
C   FOR PE, PROTON DIRECTION IS DEFINED AS +Z
      DOUBLE PRECISION KTSING,P(9)
      DOUBLE PRECISION COSTH,R,SMALL
      INTEGER ANGL,TYPE
      DATA SMALL/1D-4/
      IF (ANGL.EQ.1.OR.ANGL.EQ.4) THEN
         COSTH=P(3)*P(5)
         IF (TYPE.EQ.2) THEN
            COSTH=-COSTH
         ELSEIF (TYPE.EQ.4) THEN
            COSTH=ABS(COSTH)
         ELSEIF (TYPE.NE.1.AND.TYPE.NE.3) THEN
	    ktsing = 0D0
            CALL KTWARN('KTSING',200,*999)
            STOP
         ENDIF
         R=2*(1-COSTH)
C---IF CLOSE TO BEAM, USE APPROX 2*(1-COS(THETA))=SIN**2(THETA)
         IF (R.LT.SMALL) R=(P(1)**2+P(2)**2)*P(5)**2
         KTSING=P(4)**2*R
      ELSEIF (ANGL.EQ.2.OR.ANGL.EQ.3) THEN
         KTSING=P(9)
      ELSE
	 ktsing = 0D0
         CALL KTWARN('KTSING',201,*999)
         STOP
      ENDIF
 999  END
C-----------------------------------------------------------------------
      SUBROUTINE KTPMIN(A,NMAX,N,IMIN,JMIN)
      IMPLICIT NONE
C---FIND THE MINIMUM MEMBER OF A(NMAX,NMAX) WITH IMIN < JMIN <= N
      INTEGER NMAX,N,IMIN,JMIN,KMIN,I,J,K
C---REMEMBER THAT A(X+(Y-1)*NMAX)=A(X,Y)
C   THESE LOOPING VARIABLES ARE J=Y-2, I=X+(Y-1)*NMAX
      DOUBLE PRECISION A(*),AMIN
      K=1+NMAX
      KMIN=K
      AMIN=A(KMIN)
      DO 110 J=0,N-2
         DO 100 I=K,K+J
            IF (A(I).LT.AMIN) THEN
               KMIN=I
               AMIN=A(KMIN)
            ENDIF
 100     CONTINUE
         K=K+NMAX
 110  CONTINUE
      JMIN=KMIN/NMAX+1
      IMIN=KMIN-(JMIN-1)*NMAX
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTSMIN(A,NMAX,N,IMIN)
      IMPLICIT NONE
C---FIND THE MINIMUM MEMBER OF A
      INTEGER N,NMAX,IMIN,I
      DOUBLE PRECISION A(NMAX)
      IMIN=1
      DO 100 I=1,N
         IF (A(I).LT.A(IMIN)) IMIN=I
 100  CONTINUE
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTCOPY(A,N,B,ONSHLL)
      IMPLICIT NONE
C---COPY FROM A TO B. 5TH=1/(3-MTM), 6TH=PT, 7TH=ETA, 8TH=PHI, 9TH=PT**2
C   IF ONSHLL IS .TRUE. PARTICLE ENTRIES ARE PUT ON-SHELL BY SETTING E=P
      INTEGER I,N
      DOUBLE PRECISION A(4,N)
      LOGICAL ONSHLL
      DOUBLE PRECISION B(9,N),ETAMAX,SINMIN,EPS
      DATA ETAMAX,SINMIN,EPS/10,0,1D-6/
C---SINMIN GETS CALCULATED ON FIRST CALL
      IF (SINMIN.EQ.0) SINMIN=1/COSH(ETAMAX)
      DO 100 I=1,N
         B(1,I)=A(1,I)
         B(2,I)=A(2,I)
         B(3,I)=A(3,I)
         B(4,I)=A(4,I)
         B(5,I)=SQRT(A(1,I)**2+A(2,I)**2+A(3,I)**2)
         IF (ONSHLL) B(4,I)=B(5,I)
         IF (B(5,I).EQ.0) B(5,I)=1D-10
         B(5,I)=1/B(5,I)
         B(9,I)=A(1,I)**2+A(2,I)**2
         B(6,I)=SQRT(B(9,I))
         B(7,I)=B(6,I)*B(5,I)
         IF (B(7,I).GT.SINMIN) THEN
            B(7,I)=A(4,I)**2-A(3,I)**2
            IF (B(7,I).LE.EPS*B(4,I)**2.OR.ONSHLL) B(7,I)=B(9,I)
            B(7,I)=LOG((B(4,I)+ABS(B(3,I)))**2/B(7,I))/2
         ELSE
            B(7,I)=ETAMAX+2
         ENDIF
         B(7,I)=SIGN(B(7,I),B(3,I))
         IF (A(1,I).EQ.0 .AND. A(2,I).EQ.0) THEN
            B(8,I)=0
         ELSE
            B(8,I)=ATAN2(A(2,I),A(1,I))
         ENDIF
 100  CONTINUE
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTMERG(P,KTP,KTS,NMAX,I,J,N,TYPE,ANGL,MONO,RECO)
      IMPLICIT NONE
C---MERGE THE Jth PARTICLE IN P INTO THE Ith PARTICLE
C   J IS ASSUMED GREATER THAN I. P CONTAINS N PARTICLES BEFORE MERGING.
C---ALSO RECALCULATING THE CORRESPONDING KTP AND KTS VALUES IF MONO.GT.0
C   FROM THE RECOMBINED ANGULAR MEASURES IF MONO.GT.1
C---NOTE THAT IF MONO.LE.0, TYPE AND ANGL ARE NOT USED
      INTEGER ANGL,RECO,TYPE,I,J,K,N,NMAX,MONO
      DOUBLE PRECISION P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX),PT,PTT,
     &     KTMDPI,KTUP,PI,PJ,ANG,KTPAIR,KTSING,ETAMAX,EPS
      KTUP(I,J)=KTP(MAX(I,J),MIN(I,J))
      DATA ETAMAX,EPS/10,1D-6/
      IF (J.LE.I) CALL KTWARN('KTMERG',200,*999)
C---COMBINE ANGULAR MEASURES IF NECESSARY
      IF (MONO.GT.1) THEN
         DO 100 K=1,N
            IF (K.NE.I.AND.K.NE.J) THEN
               IF (RECO.EQ.1) THEN
                  PI=P(4,I)
                  PJ=P(4,J)
               ELSEIF (RECO.EQ.2) THEN
                  PI=P(6,I)
                  PJ=P(6,J)
               ELSEIF (RECO.EQ.3) THEN
                  PI=P(9,I)
                  PJ=P(9,J)
               ELSE
                  CALL KTWARN('KTMERG',201,*999)
                  STOP
               ENDIF
               IF (PI.EQ.0.AND.PJ.EQ.0) THEN
                  PI=1
                  PJ=1
               ENDIF
               KTP(MAX(I,K),MIN(I,K))=
     &              (PI*KTUP(I,K)+PJ*KTUP(J,K))/(PI+PJ)
            ENDIF
 100     CONTINUE
      ENDIF
      IF (RECO.EQ.1) THEN
C---VECTOR ADDITION
         P(1,I)=P(1,I)+P(1,J)
         P(2,I)=P(2,I)+P(2,J)
         P(3,I)=P(3,I)+P(3,J)
c         P(4,I)=P(4,I)+P(4,J) ! JA
         P(5,I)=SQRT(P(1,I)**2+P(2,I)**2+P(3,I)**2)
         P(4,I)=P(5,I) ! JA (Massless scheme)
         IF (P(5,I).EQ.0) THEN
            P(5,I)=1
         ELSE
            P(5,I)=1/P(5,I)
         ENDIF
      ELSEIF (RECO.EQ.2) THEN
C---PT WEIGHTED ETA-PHI ADDITION
         PT=P(6,I)+P(6,J)
         IF (PT.EQ.0) THEN
            PTT=1
         ELSE
            PTT=1/PT
         ENDIF
         P(7,I)=(P(6,I)*P(7,I)+P(6,J)*P(7,J))*PTT
         P(8,I)=KTMDPI(P(8,I)+P(6,J)*PTT*KTMDPI(P(8,J)-P(8,I)))
         P(6,I)=PT
         P(9,I)=PT**2
      ELSEIF (RECO.EQ.3) THEN
C---PT**2 WEIGHTED ETA-PHI ADDITION
         PT=P(9,I)+P(9,J)
         IF (PT.EQ.0) THEN
            PTT=1
         ELSE
            PTT=1/PT
         ENDIF
         P(7,I)=(P(9,I)*P(7,I)+P(9,J)*P(7,J))*PTT
         P(8,I)=KTMDPI(P(8,I)+P(9,J)*PTT*KTMDPI(P(8,J)-P(8,I)))
         P(6,I)=P(6,I)+P(6,J)
         P(9,I)=P(6,I)**2
      ELSE
         CALL KTWARN('KTMERG',202,*999)
         STOP
      ENDIF
C---IF MONO.GT.0 CALCULATE NEW KT MEASURES. IF MONO.GT.1 USE ANGULAR ONES.
      IF (MONO.LE.0) RETURN
C---CONVERTING BETWEEN 4-MTM AND PT,ETA,PHI IF NECESSARY
      IF (ANGL.NE.1.AND.RECO.EQ.1) THEN
         P(9,I)=P(1,I)**2+P(2,I)**2
         P(7,I)=P(4,I)**2-P(3,I)**2
         IF (P(7,I).LE.EPS*P(4,I)**2) P(7,I)=P(9,I)
         IF (P(7,I).GT.0) THEN
            P(7,I)=LOG((P(4,I)+ABS(P(3,I)))**2/P(7,I))/2
            IF (P(7,I).GT.ETAMAX) P(7,I)=ETAMAX+2
         ELSE
            P(7,I)=ETAMAX+2
         ENDIF
         P(7,I)=SIGN(P(7,I),P(3,I))
         IF (P(1,I).NE.0.AND.P(2,I).NE.0) THEN
            P(8,I)=ATAN2(P(2,I),P(1,I))
         ELSE
            P(8,I)=0
         ENDIF
      ELSEIF (ANGL.EQ.1.AND.RECO.NE.1) THEN
         P(1,I)=P(6,I)*COS(P(8,I))
         P(2,I)=P(6,I)*SIN(P(8,I))
         P(3,I)=P(6,I)*SINH(P(7,I))
         P(4,I)=P(6,I)*COSH(P(7,I))
         IF (P(4,I).NE.0) THEN
            P(5,I)=1/P(4,I)
         ELSE
            P(5,I)=1
         ENDIF
      ENDIF
      ANG=0
      DO 200 K=1,N
         IF (K.NE.I.AND.K.NE.J) THEN
            IF (MONO.GT.1) ANG=KTUP(I,K)
            KTP(MIN(I,K),MAX(I,K))=
     &           KTPAIR(ANGL,P(1,I),P(1,K),ANG)
         ENDIF
 200  CONTINUE
      KTS(I)=KTSING(ANGL,TYPE,P(1,I))
 999  END
C-----------------------------------------------------------------------
      SUBROUTINE KTMOVE(P,KTP,KTS,NMAX,N,J,IOPT)
      IMPLICIT NONE
C---MOVE THE Nth PARTICLE IN P TO THE Jth POSITION
C---ALSO MOVING KTP AND KTS IF IOPT.GT.0
      INTEGER I,J,N,NMAX,IOPT
      DOUBLE PRECISION P(9,NMAX),KTP(NMAX,NMAX),KTS(NMAX)
      DO 100 I=1,9
         P(I,J)=P(I,N)
 100  CONTINUE
      IF (IOPT.LE.0) RETURN
      DO 110 I=1,J-1
         KTP(I,J)=KTP(I,N)
         KTP(J,I)=KTP(N,I)
 110  CONTINUE
      DO 120 I=J+1,N-1
         KTP(J,I)=KTP(I,N)
         KTP(I,J)=KTP(N,I)
 120  CONTINUE
      KTS(J)=KTS(N)
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTUNIT(R)
      IMPLICIT NONE
C   SET R EQUAL TO THE 4 BY 4 IDENTITY MATRIX
      DOUBLE PRECISION R(4,4)
      INTEGER I,J
      DO 20 I=1,4
        DO 10 J=1,4
          R(I,J)=0
          IF (I.EQ.J) R(I,J)=1
 10     CONTINUE
 20   CONTINUE
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTLBST(IOPT,R,A,*)
      IMPLICIT NONE
C   PREMULTIPLY R BY THE 4 BY 4 MATRIX TO
C   LORENTZ BOOST TO/FROM THE CM FRAME OF A
C   IOPT=0 => TO
C   IOPT=1 => FROM
C
C   LAST ARGUMENT IS LABEL TO JUMP TO IF A IS NOT TIME-LIKE
C
      INTEGER IOPT,I,J
      DOUBLE PRECISION R(4,4),A(4),B(4),C(4,4),M
      DO 10 I=1,4
        B(I)=A(I)
 10   CONTINUE
      M=B(4)**2-B(1)**2-B(2)**2-B(3)**2
      IF (M.LE.0) CALL KTWARN('KTLBST',100,*999)
      M=SQRT(M)
      B(4)=B(4)+M
      M=1/(M*B(4))
      IF (IOPT.EQ.0) THEN
        B(4)=-B(4)
      ELSEIF (IOPT.NE.1) THEN
        CALL KTWARN('KTLBST',200,*999)
        STOP
      ENDIF
      DO 30 I=1,4
        DO 20 J=1,4
          C(I,J)=B(I)*B(J)*M
          IF (I.EQ.J) C(I,J)=C(I,J)+1
 20     CONTINUE
 30   CONTINUE
      C(4,4)=C(4,4)-2
      CALL KTMMUL(C,R,R)
      RETURN
 999  RETURN 1
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTRROT(R,A,B,*)
      IMPLICIT NONE
C   PREMULTIPLY R BY THE 4 BY 4 MATRIX TO
C   ROTATE FROM VECTOR A TO VECTOR B BY THE SHORTEST ROUTE
C   IF THEY ARE EXACTLY BACK-TO-BACK, THE ROTATION AXIS IS THE VECTOR
C   WHICH IS PERPENDICULAR TO THEM AND THE X AXIS, UNLESS THEY ARE
C   PERPENDICULAR TO THE Y AXIS, WHEN IT IS THE VECTOR WHICH IS
C   PERPENDICULAR TO THEM AND THE Y AXIS.
C   NOTE THAT THESE CONDITIONS GUARANTEE THAT IF BOTH ARE PERPENDICULAR
C   TO THE Z AXIS, IT WILL BE USED AS THE ROTATION AXIS.
C
C   LAST ARGUMENT IS LABEL TO JUMP TO IF EITHER HAS LENGTH ZERO
C
      DOUBLE PRECISION R(4,4),M(4,4),A(4),B(4),C(4),D(4),AL,BL,CL,DL,EPS
C---SQRT(2*EPS) IS THE ANGLE IN RADIANS OF THE SMALLEST ALLOWED ROTATION
C   NOTE THAT IF YOU CONVERT THIS PROGRAM TO SINGLE PRECISION, YOU WILL
C   NEED TO INCREASE EPS TO AROUND 0.5E-4
      PARAMETER (EPS=0.5D-6)
      AL=A(1)**2+A(2)**2+A(3)**2
      BL=B(1)**2+B(2)**2+B(3)**2
      IF (AL.LE.0.OR.BL.LE.0) CALL KTWARN('KTRROT',100,*999)
      AL=1/SQRT(AL)
      BL=1/SQRT(BL)
      CL=(A(1)*B(1)+A(2)*B(2)+A(3)*B(3))*AL*BL
C---IF THEY ARE COLLINEAR, DON'T NEED TO DO ANYTHING
      IF (CL.GE.1-EPS) THEN
        RETURN
C---IF THEY ARE BACK-TO-BACK, USE THE AXIS PERP TO THEM AND X AXIS
      ELSEIF (CL.LE.-1+EPS) THEN
        IF (ABS(B(2)).GT.EPS) THEN
          C(1)= 0
          C(2)=-B(3)
          C(3)= B(2)
C---UNLESS THEY ARE PERPENDICULAR TO THE Y AXIS,
        ELSE
          C(1)= B(3)
          C(2)= 0
          C(3)=-B(1)
        ENDIF
C---OTHERWISE FIND ROTATION AXIS
      ELSE
        C(1)=A(2)*B(3)-A(3)*B(2)
        C(2)=A(3)*B(1)-A(1)*B(3)
        C(3)=A(1)*B(2)-A(2)*B(1)
      ENDIF
      CL=C(1)**2+C(2)**2+C(3)**2
      IF (CL.LE.0) CALL KTWARN('KTRROT',101,*999)
      CL=1/SQRT(CL)
C---FIND ROTATION TO INTERMEDIATE AXES FROM A
      D(1)=A(2)*C(3)-A(3)*C(2)
      D(2)=A(3)*C(1)-A(1)*C(3)
      D(3)=A(1)*C(2)-A(2)*C(1)
      DL=AL*CL
      M(1,1)=A(1)*AL
      M(1,2)=A(2)*AL
      M(1,3)=A(3)*AL
      M(1,4)=0
      M(2,1)=C(1)*CL
      M(2,2)=C(2)*CL
      M(2,3)=C(3)*CL
      M(2,4)=0
      M(3,1)=D(1)*DL
      M(3,2)=D(2)*DL
      M(3,3)=D(3)*DL
      M(3,4)=0
      M(4,1)=0
      M(4,2)=0
      M(4,3)=0
      M(4,4)=1
      CALL KTMMUL(M,R,R)
C---AND ROTATION FROM INTERMEDIATE AXES TO B
      D(1)=B(2)*C(3)-B(3)*C(2)
      D(2)=B(3)*C(1)-B(1)*C(3)
      D(3)=B(1)*C(2)-B(2)*C(1)
      DL=BL*CL
      M(1,1)=B(1)*BL
      M(2,1)=B(2)*BL
      M(3,1)=B(3)*BL
      M(1,2)=C(1)*CL
      M(2,2)=C(2)*CL
      M(3,2)=C(3)*CL
      M(1,3)=D(1)*DL
      M(2,3)=D(2)*DL
      M(3,3)=D(3)*DL
      CALL KTMMUL(M,R,R)
      RETURN
 999  RETURN 1
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTVMUL(M,A,B)
      IMPLICIT NONE
C   4 BY 4 MATRIX TIMES 4 VECTOR: B=M*A.
C   ALL ARE DOUBLE PRECISION
C   IT IS SAFE TO CALL WITH B=A
C   FIRST SUBSCRIPT=ROWS, SECOND=COLUMNS
      DOUBLE PRECISION M(4,4),A(4),B(4),C(4)
      INTEGER I,J
      DO 20 I=1,4
        C(I)=0
        DO 10 J=1,4
          C(I)=C(I)+M(I,J)*A(J)
 10     CONTINUE
 20   CONTINUE
      DO 30 I=1,4
        B(I)=C(I)
 30   CONTINUE
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTMMUL(A,B,C)
      IMPLICIT NONE
C   4 BY 4 MATRIX MULTIPLICATION: C=A*B.
C   ALL ARE DOUBLE PRECISION
C   IT IS SAFE TO CALL WITH C=A OR B.
C   FIRST SUBSCRIPT=ROWS, SECOND=COLUMNS
      DOUBLE PRECISION A(4,4),B(4,4),C(4,4),D(4,4)
      INTEGER I,J,K
      DO 30 I=1,4
        DO 20 J=1,4
          D(I,J)=0
          DO 10 K=1,4
            D(I,J)=D(I,J)+A(I,K)*B(K,J)
 10       CONTINUE
 20     CONTINUE
 30   CONTINUE
      DO 50 I=1,4
        DO 40 J=1,4
          C(I,J)=D(I,J)
 40     CONTINUE
 50   CONTINUE
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTINVT(A,B)
      IMPLICIT NONE
C---INVERT TRANSFORMATION MATRIX A
C
C   A = INPUT  : 4 BY 4 TRANSFORMATION MATRIX
C   B = OUTPUT : INVERTED TRANSFORMATION MATRIX
C
C   IF A IS NOT A TRANSFORMATION MATRIX YOU WILL GET STRANGE RESULTS
C
C   NOTE THAT IT IS SAFE TO CALL WITH A=B
C
      DOUBLE PRECISION A(4,4),B(4,4),C(4,4)
      INTEGER I,J
C---TRANSPOSE
      DO 20 I=1,4
        DO 10 J=1,4
          C(I,J)=A(J,I)
 10     CONTINUE
 20   CONTINUE
C---NEGATE ENERGY-MOMENTUM MIXING TERMS
      DO 30 I=1,3
        C(4,I)=-C(4,I)
        C(I,4)=-C(I,4)
 30   CONTINUE
C---OUTPUT
      DO 50 I=1,4
        DO 40 J=1,4
          B(I,J)=C(I,J)
 40     CONTINUE
 50   CONTINUE
      END
C-----------------------------------------------------------------------
      FUNCTION KTMDPI(PHI)
      IMPLICIT NONE
C---RETURNS PHI, MOVED ONTO THE RANGE [-PI,PI)
      DOUBLE PRECISION KTMDPI,PHI,PI,TWOPI,THRPI,EPS
      PARAMETER (PI=3.14159265358979324D0,TWOPI=6.28318530717958648D0,
     &     THRPI=9.42477796076937972D0)
      PARAMETER (EPS=1D-15)
      KTMDPI=PHI
      IF (KTMDPI.LE.PI) THEN
        IF (KTMDPI.GT.-PI) THEN
          GOTO 100
        ELSEIF (KTMDPI.GT.-THRPI) THEN
          KTMDPI=KTMDPI+TWOPI
        ELSE
          KTMDPI=-MOD(PI-KTMDPI,TWOPI)+PI
        ENDIF
      ELSEIF (KTMDPI.LE.THRPI) THEN
        KTMDPI=KTMDPI-TWOPI
      ELSE
        KTMDPI=MOD(PI+KTMDPI,TWOPI)-PI
      ENDIF
 100  IF (ABS(KTMDPI).LT.EPS) KTMDPI=0
      END
C-----------------------------------------------------------------------
      SUBROUTINE KTWARN(SUBRTN,ICODE,*)
C     DEALS WITH ERRORS DURING EXECUTION
C     SUBRTN = NAME OF CALLING SUBROUTINE
C     ICODE  = ERROR CODE:    - 99 PRINT WARNING & CONTINUE
C                          100-199 PRINT WARNING & JUMP
C                          200-    PRINT WARNING & STOP DEAD
C-----------------------------------------------------------------------
      INTEGER ICODE
      CHARACTER*6 SUBRTN
      WRITE (6,10) SUBRTN,ICODE
   10 FORMAT(/' KTWARN CALLED FROM SUBPROGRAM ',A6,': CODE =',I4/)
      IF (ICODE.LT.100) RETURN
      IF (ICODE.LT.200) RETURN 1
      STOP
      END
C-----------------------------------------------------------------------
C-----------------------------------------------------------------------
C-----------------------------------------------------------------------