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Statistical Analysis and Histogramming Reference

1. N tuple Id 10 N tuple Title CERN Population Creation 12 06 92 11 46 34 lt sk ok oR oK k 5k ok oR Pk 9k 5k oF OR FOR KROROROR kkk kkk k kkk k INTEGER CATEGORY FLAG AGE SERVICE CHILDREN GRADE STEP HRWEEK COST CHARACTER DIVISION 4 NATION 4 COMMON CERN CATEGORY FLAG SERVICE CHILDREN GRADE STEP HRWEEK COST COMMON CERN1 DIVISION NATION CALL HBNAME 10 0 CLEAR CALL HBNAME 10 CERN CATEGORY SET CALL HBNAMC 10 CERN DIVISION SET Enter user code here END This skeleton is used in the example below to prepare a Job for analysing the Ntuple data sample Example of Fortran code based on skeleton PROGRAM NEWNTUP PARAMETER NWPAWC 30000 PARAMETER LRECL 1024 COMMON PAWC IPAW NWPAWC CALL HLIMIT NWPAWC CALL HROPEN 1 MYFILE cern hbook LRECL ISTAT CALL HRIN 10 9999 0 CALL STAFF CALL HREND MYFILE END SUBROUTINE STAFF gt k k 2k k k 2k R R ok ok 2k 2K ak K K ok 2k OR OR OROR This file was generated HUWFUN lt sk sk oR oK sk sk ok oR EE RR AK kkk k N tuple Id 10 50 Chapter 3 Ntuples
2. IIa AI a AI ACI k OVE 975 925 9 875 85 825 775 725 675 65 625 575 55 525 475 45 425 375 35 325 3 275 25 225 175 125 075 05 025 UND 0 LOW EDGE 2222222222 2223333333333222 2233444444444433222 2233445566666655443322 2222333333332222 E 2233445566666655443322 22233444455444433222 2223333333333222 22223333332222 22233333333222 223334444444433322 PY te a AS a te a EE t 2222222222222222 a wees Vu 222222233333333332222222 223345567778877765543322 2222233333333443333333322222 2334567788999998776544322 22223333344444444444444333332222 2234567889 98876543322 2222333344445555555555444433332222 233456789ABBBBBBA98765443222 222233344445555555555555544443332222 23445789 AABCCCCBBA987 6543222 222233334445
3. 64 60 56 52 I 48 32 28 I 1 24 I I I I 20 I II I I 16 I I 12 I 8 4 CHANNELS 100 0 10 0 1 2 3 4 5 6 7 8 PET I 1 9 0 1 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 CONTENTS 100 1111111111111 10 112224658012445755432099687543222121221233455666557776678686676664543343222221111 1 21124626818147606828212710478511552225771649871850922032539736953183588893942434650812591167574 LOW EDGE 1 111111111122222222223333333333444444444455555555556666666666777777777788888888889999999999 10 1 O 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789 ENTRIES BIN WID CHISQUAR 200 ALL CHANNELS 0 5000E 04 UNDERFLOW 0 1000E 01 MEAN VALUE 0 4834E 00 R M S 0 8156E 02 0 0000 00 OVERFLOW 0 2184 00 0 0000 00 151 152 Function minimization by SUBROUTINE HFITV Variable metric method ID 0 CHOPT V K OR OK OR k OR RK R K R K K Chapter 7 Fitting parameterization and smoothing Convergence when estimated distance to minimum EDM
4. 1 CALL FCN 1 000 SIZE LIMITS 0 10000E 01 0 00000E 00 1 0000 0 10000E 01 0 00000E 00 1 0000 0 56E 16 144 Chapter 7 Fitting parameterization and smoothing 2 SET ERR 0 5000 3 MIGRAD FIRST CALL TO USER FUNCTION NEW START POINT WITH IFLAG 4 START MIGRAD MINIMIZATION STRATEGY 1 CONVERGENCE WHEN EDM LT 0 50 04 FCN 8317 393 FROM MIGRAD STATUS INITIATE 8 CALLS 10 TOTAL EDM unknown STRATEGY 1 NO ERROR MATRIX EXT PARAMETER CURRENT GUESS STEP FIRST NO NAME VALUE ERROR SIZE DERIVATIVE 1 P1 0 50000 0 10000E 01 0 20001E 01 8 1370 2 P2 0 50000 0 10000 01 0 20001 01 8 7598 ERR DEF 0 50 MIGRAD MINIMIZATION HAS CONVERGED MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX COVARIANCE MATRIX CALCULATED SUCCESSFULLY FCN 8319 763 FROM MIGRAD STATUS CONVERGED 45 CALLS 47 TOTAL EDM 0 66 08 STRATEGY 1 ERROR MATRIX ACCURATE EXT PARAMETER STEP FIRST NO NAME VALUE ERROR SIZE DERIVATIVE 1 P1 0 64665 0 75183E 01 0 25797E 02 0 77581E 03 2 P2 0 35335 0 70935E 01 0 24335E 02 0 10448 02 ERR DEF 0 50 EXTERNAL ERROR MATRIX NDIM 50 NPAR 2 ERR DEF 0 50 0 570E 02 0 460E 02 0 460E 02 0 507E 02 PARAMETER CORRELATION COEFFICIENTS NO GLOBAL 1 2 1 0 85488 1 000 0 855 2 0 85488 0 855 1 000 4 SET ERR 1 200 M
5. 100 0 10 0 1 2 3 4 5 6 NO 70 CONTENTS 10 1 LOW EDGE 10 1 ENTRIES BIN WID m 0 Chapter 4 Advanced features for booking and editing operations 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 11223345678899999988765443221111111111122223333444444444444444433332222111111 0000000001234681505297653183799848145791483964333346791469146813567899998765318641964197531087654322 0000123583003267539488304339899027929647999998500671879261615911069969969960119505050742236063223694 1247315797649110704725408821516203649039012333618823383230115137101215512101720499659126352424226173 4557197143534774472257850306737109143583172717457650550628417019558717717855896970455185631419095996 111111111122222222223333333333444444444455555555556666666666777777777788888888889999999999 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567 890123456789 100 ALL CHANNELS 0 3249E 02 UNDERFLOW 0 0000E 00 OVERFLOW 0 0000E 00 0 1000 01 VALUE 0 4830 00 5 0 2198E 00 4 2 Filling Operations THIS HISTOGRAM IS FILLED ACCORDING 0 THE FUNCTION HTFUN1 HBDDK ID 172 168 164 160 156 152 148 144 140 136 132 128 124 120 116 112 108 104 100 96 92 88 84 80 76 72 68 64 60 56 52 48 44 40 36 32 28 24 20 16 12 8 4 CHANNELS 100 10 1 CONTENTS 100 10
6. 87 4 3 8 Changing Logical unit numbers for output and message files 87 5 Accessing Information 93 5 1 Testing ifa histogram exists in memory 93 52 TesingifantupleisaRWNoraCwN uot us Rok ea 4a ee ee d 93 52 2 4 6a cbe uec Q q Box Ow SOR op RUE woe 93 544 JINumberofeHtHes earn Dedede d ede dk Rer x we eg dem uw dos 94 5 3 Histrogram attributes Contents cc ye ee e e RO RR EOS EUR Q 94 CONES 95 SU oco e ETT 96 38 Associated NCHOD o uoo Rod Rx ee EOS pesce 98 59 Abscissatoechannpel mumber 2 20223 0 9 W RU 98 5 10 Maximum and Minimi hm ex Rx eo 99 SAI Iu UO mun ss He A ed 99 22 Ht egrated cu suce se odo woe dex So Pos 4004 440 Q 100 512 Histocram 255 05 RO ee Dec e 100 5 14 BEES CS 2222 eaux dde deu erede d xe Ue dS ares ey veg 101 6 Operations on Histograms 6 1 JAnthimetic Operations 2222222 Ro eR AUR SUR ES 6 2 Statistical differences between histograms 6 2 1 Weishis and Saturation oa 46 0088 ue xe mom komo om 6 2 2 Statistical Considerations a 6 3 Bin by bin histogram comparisons
7. S NEM IC MU MCCC ETT Fitting parameterization and smoothing ADI LOL cun x O kue Ba Pre Lese UE pM x red Cog 7 1 1 One and two dimensional distributions 7 1 2 Fitting one dimensional histograms with special functions 7 1 3 Fitting one or multi demensional arrays u uu uos sce cao red rts te eee 7 1 9 The user parametric function 2 T2 Basie concepts of MINUIT s ox mom ee a ak w ee 7 2 1 Basic concepts The transformation for parameters with limits 7 2 2 How to get the right answer from MINUIT 7 2 3 Interpretation of Parameter 5 Ton4 MINUIT mteracive mode o lt s cyl s u a om T3 Deprecated DOSE e oo xU Ee TA ParametHzdldD uuo Q as has T SMODE hee ee RUN IR ee ee ee ee 76 Random Number Generation os toas awale uaaa a cm RR Ro 77 Fitting with finite Monte Carlo statistics Tl 2 2 2 pz c 39 Sores Beck 4 Memory Management and input output Routines Memory Usage ahd ZEBRA oom a a ee Sl WHGUse GRAZE Rec itis ce
8. 2 23 22 3 334452 22442 22 2 2 2 2 2 2 2 2 2223422 242 53 22 22 23 33 23 3 23 22 2 2 222 2 2 4 2 4 t 3 22 00000000001111111111222222222233333333334444444444555555555566666666667 77777777 788888888889999999999 0123456789012345678901234567890123456789012345678901234567 890123456789012345678901234567890123456789 2000 SATURATION AT 2 2 3 STEP 1 00 31 MINIMUM O 000 FILLED WITH HFILL HRNDM2 HBDDK 76 74 72 70 68 66 64 62 60 58 56 54 52 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 D 210 II II II 00 I II I II 01 5 5 5 PLO T PROJECTION X I I II II IOI OIII IIII IIOI LEG II II I I I Ir II 01 101 III III IO I OHHHH II II II II 01 LT EL 10 I 10 OII III IFI TUBE OIII IIII IIOI IOIO III III II Top III III 010 IOI III III IO II I DATE 17 12 91 11 II III IIIIIII IIIIO O IOOII I I IOIIOI I OII O IIIII II II II 00 II II II HHHOHHH IIIII II IOIII 10 IIIIIIIII OIO OIIOI III IIIII I I001 I II II w TI II II IIII 00 I IOOI
9. 2000 NPCO CALL 2000 NPLO CALL 2000 4 3 Editing operations END 89 Output Generated THIS HISTOGRAM IS FILLED ACCORDING TO THE FUNCTION HTFUN1 HBOOK ID 110 DATE 17 12 91 NO 8 172 7 168 X 164 X 160 2X 156 XX 5 152 XX5X 148 XXXX7 144 25 140 XXXXXXX5 136 XXXXXXXX 132 XXXXXXXX 128 XXXXXXXX2 124 120 116 XXXXXXXXXXX 112 XXXXXXXXXXX 108 XXXXXXXXXXX 104 5XXXXXXXXXXX2 100 XXXXXXXXXXXXX 96 XXXXXXXXXXXXX 7 92 XXXXXXXXXXXXX7X 88 XXXXXXXXXXXXXXXX 84 XXXXXXXXXXXXXXXX 5 2r 80 XXXXXXXXXXXXXXXX X 2 X 5 76 XXXXXXXXXXXXXXXX X 2X X X 72 XXXXXXXXXXXXXXXX XX XXX2 XX X X 2 68 XXXXXXXXXXXXXXXX2XX 2 XXXX2XXXX2XXXX 64 XXXXXXXXXXXXXXXXXXX 75 XXXXXXXXXXXXXX7 60 X XXXXXXXXXXXXXXXXXXX XXX 7XXXXXXXXXXXXXXX 56 XXXXXXXXXXXXXXXXXXXXX XXX2XXXXXXXXXXXXXXXX 5 52 XXXXXXXXXXXXXXXXXXXXXX XOXXXXXXXXXXXXXXXXXXXX2K 48 SXXXXXXXXXXXXXXXXXXXXXX2 XXXXXXXXXXXXXXXXXXXXXXXX 44 XXXXXXXXXXXXXXXXXXXXXXXX SXXXXXXXXXXXXXXXXXXXXXXXX5 X 40 XXXXXXXXXXXXXXXXXXXXXXXX2 TXXXXXXXXXXXXXXXXXXXXXXXXXX X 36 XXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXX52XX 32 XXXXXXXXXXXXXXXXXXXXXXXXX 2 SXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 28 TXXXXXXXXXXXXXXXXXXXXXXXXX7 5 X 7 2XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX2 X 24 2XXXXXXXXXXXXXXXXXXXXXXXXXXXX2X X X2 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX X25 20 BXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XSXXSXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 7 16
10. 2 2 18 4 2 435263522594 4 324 3 3 332 4422522 5 2 17 375 4 3 4 2 4578359944 84B53 463 2 2222 2423 4 2345 65 2 2 244232 2 3 16 35 2 24223763662898869673 234 2 3 2 242324 5353935752246553345 52 5232 2 15 325 224244796897BAGA8B96944546 32 2 34224422 569642273485454575 3525 3 42 2 14 3 3 6244456768EGABBGBB79A 46245 32 4 4622344424 676772 359 355286244243332 5 13 275 32 3463568EACACCBFB7587557 7532 3 54 4533423262597856637 73533A37 432 2 12 25 2 2433654EE686EA863DA57667 2 2 22 2 22552 25376356364453476246355535233 2 2 11 225 52425363599874645A66836 2 23 322 3 22 5262 63643382436242 32 233 232 2 10 2 44625892363A484243 32 2 342 32 54 444 76254 332 9 175 2 2 23332334432352 5 22 2 2 2 5 424 3 t t 8 15 2 22 22 2 22 2 2 23 2 2 2 2 7 125 t 2 6 21 5 075 4 05 3 025 2 1 UND UND Sk ok ok ok ok ok ok ok ok ok ok ok ok GO ek IIA A a a AI K RK AK LOW EDGE 0 0000000000111111111122222222223333333333444444444455555555556666666666777777777788888888889999999999 0 0123456789012345678901234567890123456789012345678901234567890123456789012345678901
11. CALL RZSTAT 999 CALL 2 END 12 2 wo 1 HBOOK CHANNELS HBOOK ID 10 DATE 0 OVE RRPREENNNNN ODAN OON BOBBY NOO Chapter 1 Introduction ID 20 DATE 02 09 89 ND 10 0 1 2 30 1 N 123456789012345678901234567890 V JESS A A IK 232 2 2 2 2 22 34 2 3322343 3 2 247236663524 23 2 23769597 75 6 2 2 5598576EBCDAA53357_ 2 3278CC9JFO8F98C86643 2 344686AAGJ JMEMIDFG964232 44BB JGMQOPWNICCGI97322 2 545BGOMTSX VYTJMCFA755 2 2 4799DHSRUX VXRQJC57635 25CBEKLZ MXGGCI4322 4 779BN U YOIFB862 266CCLR DIHA464 2 3238ECX T YKPC772 423D6LDS X ZUMGC543 2347CAHSSX UMK75D2 2334AAKML V IIH9773 22565CLJL X Z TL9H948 lt I N 1 XX X X EH KEKE KKK HK EX KKH KEE 0 0 1 2 2 32666EMLN Q ULLQMABB342 1 cina 1 22377BDIUS P TTUNBDA545 2 1 i 2 689ETKKNWUNRIHJCEA472 1 2 3 74BCMJIGOIKEIAAD6643 2 courents 1 2222856AASHGJACB6786 2 2 2 2 273598 0 5977634 gt 24 2 274977548883 2 tou gpoe zt 3367558445 442 2 2 2224 6 7234
12. di NP X a ji N2 v i but this still suffers from the incorrect Gaussian approximation The problem is to find the equivalent treatment for the binned maximum likelihood method Methodology The correct way to view the problem is as follows For each source in each bin there is some unknown expected number of events A The prediction for the number of data events in a bin is not Equation 7 3 but pjAji 7 8 j l From each the corresponding aj is generated by a distribution which is in fact binomial but be taken as Poisson if lt lt which is indeed the case as our problem is just that a large number of total events gives a small number in each bin The total likelihood which is to be maximised is now the combined probability of the observed d and the observed a we want to maximise In Y diln fi fit Aji Aji 7 9 i 1 1 The estimates for the p which we want to know and the A which we re not really interested are found by maximising this likelihood This is the correct methodology to incorporate the MC statistics unfortunately it consists of a maximisation problem in m x n 4 1 unknowns However the problem can be made much more amenable The Solution To find the maximum we differentiate Equation 7 9 including Equation 7 8 for and set the derivatives to zero This gives two sets of equations those for the differentials
13. Block Unpacked Bytes Packed Bytes Packing Factor CERN 44 19 2 316 Total 44 19 2 316 Blocks 1 Variables 11 Columns 11 GEE AEA A IA Staff Age HBOOK ID 8 4 CHANNELS 10 0 1 2 1 12345678901234567890123456789 CONTENTS 100 11 10 1113344344344667019 1 11765888395925376449043 LOW EDGE 10 22222222223333333333444444 1 01234567890123456789012345 ENTRIES 3354 ALL CHANNELS 3354E 04 UND BIN WID 1000 01 MEAN VALUE 4765E 02 R 3 101 DATE 09 03 93 Lr I I HHHHHHHH 864 01 NO 1 II I I I I I I I I I I I I I I I I I T cx I II I II I I I I OVERFLOW 4 0123456789012345 0000 00 Chapter 3 Ntuples 3 7 Ntuple examples Number of years at CERN HBDDK ID 102 DATE 09 03 93 NO 2 a i H 1 HHHHHHHHHHH A m HHHHHHHHHHHHHHHHH CHANNELS 10 0 1 2 3 12345678901234567890123456789012345 CONTENTS 100 1 1111111111111111 10 464450248245 3173629799643522155471 1 35214910935572886595782467209022724 LOW EDGE 10 1 f X df f44 12 2 2 2 2 2 2 2 2 2 3 3 8 3 3 1 1234567890123456789012345678901234 ENTRIES 3354 ALL CHANNELS 3349E 04 UNDERFLOW 0000 00 OVERFLOW 5000
14. 0 5000 00 88 x 84 II 80 II 76 II 72 i T 68 64 E 60 S 56 I 52 48 E I 44 I I ars 40 Ic zin 36 I I qup 32 I zl I II 28 I I I I 24 eT I 20 I I I I 16 E dr seat 3 Te 12 I 8 I I 4 L CHANNELS 10 0 1 2 3 4 1234567890123456789012345678901234567890 CONTENTS 10 1123678875431 11111344443233221 1 3234280076140895066690028139343257552 LOW EDGE 1 111122223333444455556666777788889999 10 1 0 0257025702570257025702570257025702570257 0 0505050505050505050505050505050505050505 ENTRIES 1108 ALL CHANNELS 0 1108E 04 UNDERFLOW 0 0000 00 OVERFLOW 0 0000 00 BIN WID 0 2500E 01 MEAN VALUE 0 4800E 00 5 0 2231E 00 HIST FILLED WITH HFILL AND HRNDM2 HBDDK ID 210 SLICE X DATE 17 12 91 NO 5 SLICE X NO YMIN 0 0000 00 0 3333E 00 34 33 32 31 30 29 I I 28 I IO I 27 L 26 I IT III 25 OI II III 24 II II IOI I 23 II OIIIIII I 22 II I IOIIIII 21 II I IIIOIII 20 IOII IIIIIII I I 19 I III II IIIO I I 18 II II OI TOTT I TD 17 II III I IIOI I I I T 16 IIII 10 I III II I OII IO 15 IIOII I I ITI II I I III III I 14 IOIII I I It II OII I 13 I ITIO I IIO II OIIIII III I 12 I IIOI I IOI II IIIIIOO IIII IIII I 11 O0 III III 10 IIII III IO I IOII I I 10 III II III II 01 1100 III II IIIIIII II 9 I I OI II II III II II OII IIII I OIOIOOIOI II 8 I III I IIII II IIIIII III III
15. 2 240 F 2C ird n 20 1 ao 2 1 1 2 25 1 0 1 2 TEST TEST2 Figure 1 5 Output generated by HPLOT on printer with graphics capabilities Chapter 2 One and two dimensional histograms Basics 2 1 Booking 2 1 1 One dimensional case CALL HBOOK1 ID CHTITL NX XMI XMA VMX Action Books a one dimensional histogram Input parameter description ID histogram identifier integer non zero CHTITL histogram title character variable or constant up to 80 characters NX number of channels XMI lower edge of first channel XMA upper edge of last channel VMX upper limit of single channel content see below VMX 0 means 1 word per channel no packing Special values lt origin and binwidth are calculated automatically and one word is reserved per chan nel Zero 0 is an illegal histogram identifier If the histogram ID already exists it will be deleted and recreated with the new specifications warning message is printed VMX is used to compute the number of bits to be allocated per histogram channel If VMX 1 then one full word is reserved per channel When filling a histogram with weights the latter are truncated to the nearest integer unless one full word is reserved per channel i e VMX 0 Filling with negative weights will give meaningless results unless one word per channel has been allocated Automatic calculation of limits
16. 4 2 4 4 2 3 3 2 2 2 24 43 2 2 2 2 4 2 2 2 4 2 4 2 2 3 2223223 2 3 2 2 42 2 2 3 2 2 2 53 528044 2 2 42 3 2 3 3 243243 4 24 42 2 23 3 2 43 325 3 29 t 24522 384 t 2 552 2 2 22 2 32 2 342223526 24 2 2 3 2 3 2 3 2 2223 233 342 2 22 2 2 6 2 2 2 2 2 22 44342 2 2 3842433242 2 2 2 2 22 42 22 22 3 2 2 2 2 2 22 2 2 2 2 24 2 3 2 22 3 2 2 2 2 22 2 2 p c 2 2 2 3 242 23 306 E 2 3 2 243 3 2 2232 42 322 2 3 2 2 22 2 4 2 2 3 3232 424263344 432 432 28 2 3 2 2 3 45 42 2 22 322234 443 555 4252 3 2 33 2 2 42222 2 4 532 33 2 42243 46334 475443334 2 2 2 2 2 44 2332 2 2 22 2 3 6 255325823646443 2 3 2 3 22 2 2 95 446335 422 22 235347344 45 2 222 2 4 2 3 22 3 3 2 2 2 2 Je 4
17. CATEGORY 2 U 4 4 FLAG 3 4 8 1 100 CERN AGE 4 4 7 0 601 CERN SERVICE 4 0 101 CERN CHILDREN 6 4 3 141 CERN GRADE 7 4 0 15 CERN STEP 8 4 7 20 441 CERN 9 4 05 10 4 DIVISIDN 11 4 NATION II HK I K Block Unpacked Bytes Packed Bytes Packing Factor GIGI ICI 3K K IOI HI IK K CERN 44 19 2 316 Total 44 19 2 316 kkk k ak ak ak ak ak ak ak 3k ak ak ak 3k 3k ak ak 3k 3k 3k ak ak ak 3k 3k k k ak 2K 3k CI ak ak 2k 3k I I A I IKK aK a A A A 2k k 21 21 k a K Ak kak ak Number of blocks 1 Number of columns 11 YK k sk ok oR oR sk sk oF OR K 9k 5k oR I oo oook kk 24 6 2k 2k 2k kkk 2k 2k Note the HFNT error messages which report that out of range data were read in the input file This is an example of the error checking performed by the CWN routines 3 7 Ntuple examples Analysis skeleton generated for above example SUBROUTINE STAFF K sk sk ok oK sk sk 5k oR K 9k 5k 9R OR PK This file was generated by HUWFUN
18. editing operations CALL HINDEX Action Prints the index Remark Routine HISTDO generates the index automatically CALL HTITLE CHGTIT Action Defines a general title to be printed as the header line of each histogram Input parameter CHGTIT general title character variable of up to 80 characters Remark See about passing the title A call to this routine does not destroy any given individual histogram titles 43 2 What to Print 1 dimensional histogram Each 1 dimensional histogram output consists of several parts some compulsory and some optional general title compulsory if defined identifier date and title compulsory the histogram itself default yes channel numbers default yes channel contents default yes error values default 2 no value of the superimposed function if any default no integrated contents default no low edge of channels default yes statistical information default yes Routine HIDOPT can be used to change the above defaults CALL HIDOPT ID CHOPT Action Select an option for a given histogram Input parameters ID Histogram identifier If ID 0 the option is set for all histograms CHOPT Character variable specifying the option chosen see table 4 1 4 3 Editing operations 81 Option Action SETD Set all options to the default values SHOW Print all the options currently set BLAC 1 Dim histogram printed with X ch
19. 48 369 2468 2345 9IR 8GO TELS 6CIOU 5AFKPU 48CGKOS 369CFILORU 2468ACEGIKMOQS 23456789ABCDEFGHIJK 9IR 8G0 TELS 6CIOU 5AFKP 48CGKD 369CFILD 2468ACEGIK 23456789ABCDEF 9I 8G0 TEL 6 48CG 369CF 2468ACE 23456789A 9 8G TE 6c 5A 48 369 2468 2345 0000000000111111111122222222223333333333444444444455555555556666666666777777777788888888889999999999 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789 4000 PLOT OVE El e p S p p ILIO N N N IO Q G w w w G G w w gt gt gt 0 0 8 Chapter 1 Introduction SATURATION AT 31 104881 SCALE 2 3 STATISTICS I I STEP 1 00 MINIMUM 0 000 I I 15 batch as the first step of the analysis MAINFRAME WORKSTATION Batch Job Interactive Data Analysis with PAW HBOOK ZEBRA KUIP Tapes HPLOT Raw Data HBOOK DST HIGZ ZEBRA SIGMA COMIS MINUIT Interactive access High quality via RLOGIN graphics output or file transfer using ZFTP Figure 1 1 Schematic presentation of the various steps in the data analysis
20. i e 40 NCHANX 2 NCHANY 2 PACK space for projections slices and bands which are 1 D histograms NT Number of Ntuples 52 1 Space occupied by headers and buffers of Ntuple i see routines HBOOKN and HBNT 8 3 Directories hbook histogram data are kept in a zebra tree structure similar to the directory structure of the Unix file system Note that the zebra RZ package uses the same conventions In fact hbook uses the zebra RZ package to manage files With this convention all references to histograms are still made using an integer identifier but this identifier is relative to a directory hbook initially sets the current directory to be PAWC This directory remains the current directory until changed either explicitly or implicitly by one of the calls described below As with the Unix file system the current directory can be a subdirectory e g PAWC L1 PAWC L1 L21 and PAWC L1 L22 These hbook directories can reside in the local memory of the computer i e the PAWC common or they be stored on a local LUN1 or remote disk file system VXCRNA They can even be dynamically created by a producer in the memory of a remote computer and shared by that machine with the user s machine via global section VMS or shared memory Unix HMDIR HCDIR HLDIR HDDIR HPDIR PAWC local memory X X X X X LUN1 local disk X X X X X USER VXCRNA telnet rsh remote disk X X X GLOSEC
21. A simple example of the two kinds of skeletons generated with routine HUWFUN is given below An other more complex example can be found on page 49 where the code of a fully worked out subroutine based on such a sketeton can also be studied In paw the command UWFUNC generates a skeleton for the RWN or CWN analysis function automatically Example of Ntuple definition HUWFUN usage COMMON CVECT V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 Vii V12 V13 V14 V15 V16 V17 V18 V19 V20 book N tuple 20 CALL HBNT 20 1 block 20 variable N tuple CALL HBNAME 20 VECT V1 V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15 V16 V17 V18 V19 V20 OPEN 11 FILE nt20 f STATUS UNKNOWN OPEN 12 FILE nt20p f STATUS UNKNOWN CALL HUWFUN 11 20 NT20 0 B CALL HUWFUN 12 20 NT20 0 40 Chapter 3 Ntuples The HUWFUN output files nt20 f and nt20p f look like File nt20 f SUBROUTINE NT20 FEO OR OO RR I kkk kkk kk This file was generated by HUWFUN FEO OO OR KK N tuple Id 20 N tuple Title 1 block 20 variable N tuple Creation 11 06 92 18 46 10 OR ook kk kkk kkk OR OR REAL V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15 V16 V17 V18 V19 V20 COMMON VECT V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15 V16 V17 V18 V19 V2
22. ELO0SS 10 ABS Y CALL HFN 10 EVENT CONTINUE Obtain the definitions of the Ntuple NVAR MTUPLE CALL HGIVEN 10 CHTITL NVAR CHTAGZ RLOW RHIGH PRINT Definitions of Ntuple 10 PRINT Title CHTITL 1 LENOCC CHTITL PRINT Number of variables NVAR DO 20 I 1 NVAR PRINT 9001 I RLOW I RHIGH I Min Max values for column 13 1X F10 5 1X F10 5 CONTINUE Get the contents of event 333 CALL HGNPAR 10 TEST CALL HGNF 10 333 EVENT IERR PRINT IERR EVENT 3 5 Get information about an Ntuple 37 Get the number of events in this Ntuple CALL HNOENT 10 NEVENT PRINT 99 CONTINUE END 3 5 2 Retrieve the contents of a CWN into a common block CALL HGNT ID IDNEVT IERR Action Retrieve information about a CWN row Input parameters ID Identifier of the Ntuple IDNEVT Number of the event about which information is required Output parameter IERR Error return code 0 if event was found The information is restored at the addresses specified by HBNAME or HBNAMC for CHARACTER data If the information is being retrieved by a program other than the one that wrote the Ntuple then HBNAME or HBNAMC must be called as appropriate see below CALL HBNAME ID 0 CLEAR CALL HBNAME ID CHBLOK VARIABLE SET These calls are required as HBOOK must obtain the location at which the requested information is to be returned which is obvio
23. Go to parent directory PAW CDET CALL HCDIR TPC Goto TPC subdirectory again CALL HCDIR VERTEX 9 Goto directory PAW CDET VERTEX i e one level up then one down again This concept of directories also applies to the direct access files when using HRFILE HRIN and HROUT CALL HLDIR CHPATH CHOPT Action List the contents identifiers type of histograms and titles of a hbook directory This command works with all five different kinds of directories described in figure 8 3 Input parameters CHPATH Character variable or constant containing the name of the directory to be listed CHPATH stands for the current directory CHOPT Character variable specifying the chosen option 162 gi T Chapter 8 Memory Management and input output Routines List only the top directory List all Ntuple extentions HINDEX option selected instead of simple list List only the Ntuples List using RZ format Sort the directory entries List the complete subdirectory tree starting from the specified directory 8 3 Directories 163 List all existing directories in PAWC CALL HLDIR PAWC T CALL HDDIR CHPATH Action Delete a sub directory from memory or local disk Input parameter CHPATH Character variable or constant specifying the pathname of the sub directory to delete CHPATH gt stands for the current directory CALL
24. do 10 1 100000000 call rannor a b call hfi 1 a 1 oak call hf1 2 b 1 call hf1 3 a 2 b 2 1 if mod i 100000 eq 0 2585 X print hserver in loop index i 10 continue 12500 end 10009 77 L 1 ohserver hserver f gon hserver 2 GLOBAL MEMORY CREATED E offset from LQ 1037452510 hserver in loop index 100000 7 7 hserver in loop index 200000 i hserver in loop index 300000 hserver in loop index 00000 Figure 9 2 Visualise histograms in Unix shared hserver in loop index 500000 memory hserver in loop index 600000 hserver in loop index 1700000 On Unix PAW can be used as an online presenter using the shared memory facility at present on Sun and DecStation only and the routines described in section 9 3 Figure 9 2 shows on the left hand side the program which fills the histograms It is compiled and linked with the 77 command and then started It writes the lines shown while going through the event loop Then PAW is started communication is established via the command global sect TEST which declares that the area called MAP is to be shared for data communication and the execution of the KUMAC program shared kumac shown at the top right of the figure is initiated The output shown on the screen then allows to follow interactively using the Update option U of the plot command how the event generator the hserver program fills histogram number one The fi
25. 500 529 Supervisory administrative staff 530 559 Intermediate level administrative staff 560 599 Lower level administrative staff Code for each division Character variable AG DG EF EP FI LEP PS SORS IH TES A flag where the first four bits have the following significance Bit 1 0 means female otherwise male Bit 2 0 means resident otherwise non resident Bit 3 0 means single otherwise head of family Bit 4 0 means fixed term contract otherwise indefinite duration contract Age in years of staff member Number of years of service that the staff member has at CERN Number of dependent children Staff member s position in Grade scale integer between 3 and 14 Staff member s position step inside given grade integer between 0 and 15 Code for staff member s nationality character variable PRO GB GRAM SITO 5 7222 Number of contractual hours worked week between 20 44 Cost of the staff member to CERN in CHF Table 3 1 CERN personnel Ntuple On the next pages we show first the creation run together with its output and the automatically generated analysis skeleton and then the analysis program created based on the skeleton PROGRAM CERN Creating the Ntuple PARAMETER NWPAWC 30000 PARAMETER LRECL 1024
26. CERN Program Library Long Writeups 250 gt IELb O OK Statistical Analysis and Histogramming Reference Manual Information Technology Division CERN Geneva Switzerland Copyright Notice HBOOK Statistical Analysis and Histogramming CERN Library entry 250 Copyright CERN Geneva 1995 1998 Copyright and any other appropriate legal protection of these computer programs and associated documentation reserved in all countries of the world These programs or documentation may not be reproduced by any method without prior written con sent of the Director General of CERN or his delegate Permission for the usage of any programs described herein is granted apriori to those scientific institutes associated with the CERN experimental program or with whom CERN has concluded a scientific collaboration agreement Requests for information should be addressed to CERN Program Library Office CERN IT Division CH 1211 Geneva 23 Switzerland Tel 41 22 767 4951 Fax 41 22 767 8630 Email cernlib cern ch Trademark notice All trademarks appearing in this guide are acknowledged as such Contact Person Olivier Couet IT couet cern ch Technical Realization Michel Goossens goossens cern ch Edition August 1998 Foreword History HBOOK is a Fortran callable package for histogramming and fitting It was originally developed in the 1970s and has since undergone continuous evolu
27. Input parameters ID Histogram identifier FUN Parametric function to be declared EXTERNAL see 7 1 5 Can be defined interactively in the interactive version see paw manual CHOPT Character variable specifying the desired options B Some or all parameters are bounded The arrays STEP PMIN and PMAX must be speci fied By default all parameters vary freely D user specifies the derivatives of the function analytically by providing the user routine HDERIV By default derivatives are computed numerically E Perform a detailed error analysis using the MINUIT routines HESSE and MINOS F Force storing of the result of the fit bin by bin with the histogram for an any dimensional histogram means do to reset the parameters of Application HMINUIT CIL the logaritmic Likelihood fitting method By default the chisquared method is used M Invoke interactive MINUIT W Theresults of the fit are not stored bin by bin with the histogram By default the function is calculated at the centre of each bin in the specified range 902 Quiet mode No printing R a Restricted area of a 1 D or 2 D histogram The limits for the fit are given using in the vector IQUEST is in the communication common QUEST IQUEST 100 as fol lows IFXLOW IQUEST 11 specifies the lower limit in X IFXUP IQUEST 12 specifies the upper limit in X IFYLOW IQUEST 13 specifies the lower limit in Y 2 D IFYUP IQUE
28. NATS INT RDATA 9 HRWEEK RDATA 10 COST RDATA 11 CALL HFNT 10 GOTO 10 read data of person 100 20 I 100 CALL HGNT 10 I IER IF IER NE 0 THEN PRINT Error reading row I ENDIF 48 PRINT Person 100 CATEGORY DIVISION AGE NATION print Ntuple definition CALL HPRNT 10 write batch version of analysis routine to file staff f OPEN 3 FILE staff f STATUS UNKNOWN CALL HUWFUN 3 10 STAFF 0 Chapter 3 Ntuples write Ntuple buffer to disk and close RZ file CALL HROUT 10 ICYCLE CALL HREND MYFILE END Output generated by running above program ERROR in HFNT HRWEEK Value out of range event 2668 ID 10 ERROR HFNT HRWEEK Value out of range event 2673 ID 10 ERROR HFNT HRWEEK Value out of range event 2710 ID 10 ERROR in HFNT HRWEEK Value out of range event 2711 ID 10 ERROR in HFNT HRWEEK Value out of range event 2833 ID 10 Person 100 415 PS 55 FR 9k 5k oR Ntuple ID 10 Entries 3354 CERN Population IOI CII I I IOI HK I K Var numb Packing Range Block Name SG OG OR RK aK kkk 1 4 11 100 600
29. RETURN END 155 156 Chapter 7 THIS HISTOGRAM IS FILLED ACCORDING TO THE FUNCTION HTFUN1 HBOOK 172 168 164 160 156 152 148 144 140 136 132 128 124 120 116 112 108 104 100 96 92 88 84 80 76 72 68 64 60 56 52 48 44 40 36 32 28 24 20 16 12 8 4 CHANNELS 100 10 CONTENTS 100 10 ID 1 LOW EDGE 1 10 1 ENTRIES BIN WID CHISQUAR 0 THIS HISTOGRAM IS FILLED ACCORDING TO THE FUNCTION HTFUN1 ID 2 HBOOK 185 180 175 170 165 160 155 150 145 140 135 130 125 120 115 110 105 100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 CHANNELS 100 10 1 CONTENTS 100 10 1 0 LOW EDGE 1 10 1 0 ENTRIES BIN WID CHISQUAR 0 1 DATE I II I I 17 12 91 NO 18 Fitting parameterization and smoothing HHHHHHHX H HH HH HH I I II I I I I II I I I I I I I cs I I I I I I I I I 0 1 0 1 2 3 4 5 6 7 8 9 0 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 1111111111111 112224658012445755432099687543222121221233455666557776678686676664543343222221111 211246268181476068282127104785115522257716498718509
30. f s 2 i 7 4 This 2 assumes that the distribution for d is Gaussian it is of course Poisson but the Gaussian is good approximation to the Poisson at large numbers Unfortunately it often happens that many of the d are small in this case one can go back to the original Poisson distribution and write down the probability for observing a particular d as di fi f 1 e hz 7 5 7 5 and the estimates of the proportions p are found by maximising total likelihood or for convenience its logarithm remembering eblna and omitting the constant factorials In 2 M dil fi fi 7 6 121 This accounts correctly for the small numbers of data events the bins is technique general use It is often referred to as a binned maximum likelihood fit 7 7 Fitting with finite Monte Carlo statistics 137 But this does not account for the fact that the Monte Carlo samples used may also be of finite size leading to statistical fluctuations in the a In Equation 7 1 it can be seen that these are damped by a factor Np N but we cannot hope that this is small So disagreements between a particular d and f arise from incorrect p from fluctuations in d and from fluctations in the a Binned maximum likelihood reckons with the first two sources but not the third In the x formalism of Equation 7 4 this can be dealt with by adjusting the error used in the denominator 2 d
31. 0 1100E 02 BIN WID 0 6000E 01 MEAN VALUE 0 1499E 01 R M 5 0 9921E 00 3 7 Ntuple examples TEST2 HBOOK ID 20 DATE 17 12 91 CHANNELS 10 U O 1 20 1 12345678901234567890 V gt 5k ok sk sk ok ok Pk 5k k kk RIC OR OR K OVE 22 3 OVE 2 7 233 3 6 20 2 4 396353325 3 19 2 1 2288EBCB89852 2 18 1 8 23 5B7HJIIKC8552 17 1425 525CTIY WQWUF864 2 16 1 2 78BRX WMF8532 15 9 2 328DS KC72 14 6 9 61Y RGA22 2 13 378LU VI563 2 12 43ARX TPC63 2 11 3IQZ UFB53 10 6 298PY SIB83 9 9 65JS QKE55 8 p 132 4358MT NN863 yd 1 5 3 3A1IS QFF7 4 6 1 8 44 ADKQZYX YPG942 5 2 1 4334BELLKCNE7F66 4 E 2 4 327598 7943672 3 3 2 7 23467382 2 2 3 2 332 42 1 UND 2 2 UND sk k ok sk sk ok ok Pk k kkk ke ok ke kk kk kkk k R LOW EDGE 1 3222111 111222 0 07418529630369258147 ENTRIES 10000 PLOT SATURATION 255 10 SCALE 2 3 STATISTICS STEP 1 00 MINIMUM 0 000 kk kk kk kk ok ok ok ok ok ok ok ok ok ok ok ok ok ok ok ok ok ok ok ok IOI I I II I ke K A A a A 21 1 21 21 2k 21 gt K K 2k K K 1 24 2K K NTUPLE ID 30 ENTRIES 10000 N TUPLE kk kk kk ok ok ok ok ok ok ok ok ok ok ok ok ok ok ke ok ok ok ok
32. 11 12 ESSOR STANDARD DEVIATION 1 0 70650 39 144 2 1 0509 33 904 3 0 85147 28 044 4 0 90853 21 530 5 0 82336 6 4213 6 1 0259 20 189 7 0 78401 8 3514 8 1 0731 10 854 9 0 68036 3 3355 0 0 83660 5 0463 1 0 85716 5 4135 2 1 1372 1 2267 DOUBLE PRECISION FUNCTION X gt gt gt 40 320 32 156 29 461 20 018 7 7912 18 482 7 0469 9 0691 4 4675 6 4382 3 9874 3 1189 CONFIDENCE INTERVAL 41 495 30 407 30 877 18 506 9 1611 16 775 TD 7425 2836 5995 8301 5612 0110 DOUBLE PRECISION COEFF P PO P1 P2 HELEFT HBASFT DIMENSION X 1 COEFF 12 IBASFT 1 12 LL L2 C3 C3 C c3 L3 L L3 uuu 20 80 100 50 110 10 130 90 140 30 DATA COEFF 0 40319615E 02 0 32155589E 02 0 29460772E 02 0 20017895E 02 0 77912196 01 0 18481896 02 0 70469122E 01 0 90690550E 01 0 44674803E 01 0 64381900E 01 0 39873663E 01 0 31188760 01 DATA IBASFT 0 20 60 80 100 50 110 10 130 90 140 30 FPARAM 0 DO 25 K 1 12 P 1 DO 15 I 1 1 NUM IBASFT I K 10 ITYP IBASFT I K NUM 10 IF 0 THEN IF ITYP EQ 0 THEN PO 1 P1 2 X 10 1 DO 10 J 2 NUM P2 2 2 X I 1 P1 PO 1 1 2 1 IF IF 0 1 P P HELEFT NUM X I IF ITYP EQ 2 THEN P HBASFT NUM X GOTO 20 END IF END IF CONTINUE FPARAM FPARAM COEFF P CONTINUE
33. 2 4 13 52 54 70 82 HBOOKB 48 HBOOKN 17 19 20 21 27 31 32 142 HBOOKNC 27 HBPRO 49 50 HBPROF 48 HBPROX 50 HBPROY 50 HBSET 18 22 23 HBSLIX 50 50 HBSLIY 50 HBSTAT 82 HCDIR 23 143 148 151 153 HCFITD fit parameters common 99 101 103 HCOMPA 73 HCONVOL 37 HCOPY 15 HCOPYM 153 HCOPYR 15 hcreateg 154 HDDIR 144 HDELET 16 HDERIV 99 101 103 104 HDIFF i 90 90 91 92 94 149 HDIFFB i 92 94 97 HDUMP 87 189 HELEFT 114 HERMES 76 76 HERROR 82 HESSE 99 101 105 125 HEXIST 81 81 HF1 54 55 55 HF1E 55 HF2 51 54 55 56 HFC1 53 57 57 58 HFC2 53 54 57 58 58 HFCNH 103 HFCNV 103 HFF1 55 55 56 HFF2 56 HFILL 4 14 48 51 54 55 HFINAM 102 103 HFIT1 110 HFITEX 110 HFITGA 110 HFITH 98 99 102 103 106 110 HFITHN 98 100 102 103 110 HFITL 110 HFITN 103 110 HFITPO 110 HFITS 110 HFITV 98 101 103 106 110 HFN 17 19 20 21 HFNOV 20 20 HFNT 17 23 27 27 29 43 HFNTB 17 22 27 HFPAK1 56 56 hfree 154 HFUNC 52 53 72 82 142 HGFIT 102 HGIVE 87 HGIVEN 31 HGN 17 31 31 HGNF 17 31 32 32 HGNPAR 31 31 32 HGNT 17 24 33 34 HGNTB 17 24 33 34 36 149 HGNTF 17 24 34 HGNTV 17 24 33 34 36 HI 83 83 HID1 81 81 HID2 81 190 HIDALL 81 HIDOPToption BLAC 72 ERRO 51 NPST 69 PERR 51 PFUN 52 ROTA 75 76 STAR 72 STAT 51 55 70
34. 472 03 0 1387E 02 548E 05 0 9488E 06 0 6145E 05 520E 04 0 2581E 04 0 1647E 05 0 2681E 04 97 03 0 7556E 04 0 2361E 06 0 2208 05 100 03 0 3230 04 0 1566 05 0 1904 05 R k OR OR k k k k K 3K 2 R K k k k k K K Function minimization by SUBROUTINE HFITH Variable metric method ID CHOPT FO HE DR gt lt gt lt gt lt gt lt gt lt gt lt gt lt gt lt oko gt gt K gt K K OR OR OR OR OK OK R R 2k 2k ok oko k 2K 3K K K k K k k K k OK 0 2292E 04 0 2129E 04 0 5683E 04 7 7 Fitting with finite Monte Carlo statistics Convergence when estimated distance to minimum EDM LT 0 10E 03 FCN 69 87250 FROM MIGRAD STATUS CONVERGED 64 CALLS 65 TOTAL EDM 0 38 05 STRATEGY 1 ERROR MATRIX ACCURATE EXT PARAMETER STEP FIRST NO NAME VALUE ERROR SIZE DERIVATIVE 1 2 199 30 3 5192 0 84934 0 13509E 03 0 39761 0 14150E 02 0 10059E 02 1 6362 0 98783E 01 0 10313E 02 0 24990E 03 1 7442 CHISQUARE 0 1075E 01 NPFIT 68 EXAMPLE ND HBDDK ID CHANNELS 100 10 CONTENTS 100 10 T LOW EDGE 1 10 1 0 ENTRIES BIN WID CHISQUAR 0 1000E 01 MEAN VALUE 5 DATE 18 05 92 NO 17 0 1 0 1 2 4 5 8 9 0 123456789012345678901234567890123456789012
35. 5 5 0 CALL HFILL 10 UX 0 1 Go back to the parent directory CALL HCDIR 9 END 8 4 Input Output Routines hbook files are in fact zebra RZ files 10 Input output error return codes are available vin the zebra communication vector IQUEST and the user should consult the RZ manual for their meaning Both disk and memory resident files are supported the latter being particularly useful in online applications where histogram data have to be shared between different processes hbook files are written in Zebra exchange format and thus need not be converted when transferred be tween different computer systems using binary ftp see section 8 5 or accessed over the network using a distributed file system such as AFS or NFS Reading and writing histograms to a direct access file CALL HRPUT ID CHFILE CHOPT Action Write a histogram to a given direct access file This routine cannot be used for Ntuples Input parameters ID Histogram identifier ID 0 writes all histograms in the current directory to the output file CHFILE Character variable or constant defining the filename If CHFILE the histogram is saved in the current working directory on disk CHOPT Character option specifying the desired option N Write the histogram to a New file 166 Chapter 8 Memory Management input output Routines Can be used together with ID 0 All histograms the current directory and all subdi
36. CHOLD Character variable with old column name CHNEW Character variable with new column name One dimensional convolution of Ntuple CALL HCONVOL ID1 ID2 ID3 IERROR Action Perform a one dimensional convolution of the Ntuple with respect to an other histograms must pre exist prior to calling this routine Input parameters 101 Ntuple identifier this Ntuple be 1 D or 2 D It is used as kernel for the convolution of ID2 ID2 Ntuple to be convoluted ID3 Ntuple resulting from the convolution of ID2 with ID1 Output parameters IERROR error return code Discussion This method scales badly for large histograms The best general algorithm would be to unpack the histograms add a suitable number of zeros do the two FFTs multiply the transforms do yet another FFT and stuff the resulting histogram back into HBOOK However for small histograms the naive method is probably faster especially if recoded in terms of lower level calls It will also work with 1 D and 2 D kernel histograms that do not have matched coordinate systems the FFT method implies equal binsize in X and Y for the kernel and the histogram to be folded This simple method uses HBOOK to avoid this in one X dimension at least corresponding to folding in a constant resolution term Example of use Original code written by Per Steinar Iversen PerSteinar Iversen fi uib no 3 7 Ntuple examples CALL CALL CALL CALL CALL CALL CALL
37. COMMON PAWC IPAW NWPAWC REAL RDATA 11 INTEGER CATEGORY FLAG AGE SERVICE CHILDREN GRADE STEP HRWEEK COST CHARACTER 4 DIVISION NATION 3 7 Ntuple examples 47 COMMON CERN CATEGORY FLAG AGE SERVICE CHILDREN GRADE STEP HRWEEK COST COMMON CERNC DIVISION NATIDN 4 DIVS 13 NATS 15 DATA DIVS AG DG FI PS SPS 5 TIS DATA NATS AT DK ES FR GB GR IT NO PT SE ZZ CALL HLIMIT NWPAWC open a new RZ file CALL HROPEN 1 MYFILE cern hbook N LRECL ISTAT book Ntuple CALL HBNT 10 CERN Population define Ntuple 1 block with 11 columns CALL HBNAME 10 CERN CATEGORY CATEGORY 100 600 I FLAG U 4 AGE 1 100 1 SERVICE 0 60 I 0 10 GRADE 3 14 I STEP O 15 I HRWEEK 20 44 I COST I CALL HBNAMC 10 CERN DIVISION DIVISION C NATION C open data file with staff information OPEN 2 FILE aptuple dat STATUS OLD read data and store in Ntuple 10 READ 2 10F4 0 F7 0 END 20 CATEGORY RDATA 1 DIVISION DIVS INT RDATA 2 FLAG RDATA 3 AGE RDATA 4 SERVICE RDATA 5 CHILDREN RDATA 6 GRADE RDATA 7 STEP RDATA 8 NATION
38. HISTO1 DAT 1024 ISTAT Open first HBOOK RZ file read only CALL HROPEN 2 HISTO2 HISTO2 DAT U 1024 ISTAT Open second HBOOK RZ file update CALL HCDIR HISTO1 9 Make HISTO1 current directory CALL HRIN 20 9999 0 Read ID 20 on file 1 CALL HCDIR HISTO2 9 Make HISTO2 current directory CALL HRIN 10 9999 0 Read ID 10 on file 2 CALL HROUT 20 ICYCLE Write ID 20 to file 2 CALL HREND HISTO1 Close file 1 CALL 5 027 Close file 2 In the previous example and also in figures 1 2 and 1 4 it is shown how an external file is available via a directory name inside hbook and paw and that one can change from one to the other file by merely changing directory with hbook routine HCDIR Using subdirectories The use of subdirectories both in memory and on disk is shown in the following examples Example of using subdirectories PROGRAM TEST INTEGER NWPAWC PARAMETER NWPAWC 15000 COMMON PAWC PAW NWPAWC CHARACTER 8 CHTAGS 5 DIMENSION EVENT 5 EQUIVALENCE EVENT 1 X EVENT 2 Y EVENT 3 Z EQUIVALENCE EVENT 4 EVENT 5 1 055 DATA CHTAGS X Y Z Energy Eloss Tell HBOOK how many words are in PAWC CALL HLIMIT NWPAWC CALL HROPEN 1 EXAMPLE EXAMPLE DAT N 1024 ISTAT 8 6 RZ directories files 173 IF ISTAT NE 0 GO TO 99 Make sub directory on disk as HR
39. tcp ip global section VMS X X X auam imis SHARE tcp ip shared memory Unix X X X Figure 8 3 Different kinds of hbook directories CALL HMDIR Action Make a new subdirectory below the current directory This command works with all five differ ent kinds of directories described in figure 8 3 8 3 Directories 161 Input parameters CHPATH Character variable or constant containing the name of the subdirectory CHOPT Character variable specifying the option chosen If CHOPT S then the current directory is changed to the new directory CALL HCDIR Action Change the current directory This command works with all five different kinds of directories described in figure 8 3 Input parameters CHPATH Character variable or constant containing the name of the directory which is to become the current directory default action if CHOPT CHOPT Character variable specifying the option chosen gt Set new directory R Read the name of the current directory Output Parameter CHPATH Character variable containing the name of the current directory CHOPT R Setting RZ directories CALL HCDIR C PAW CDET 9 Goto directory with given absolute pathname CALL HCDIR TPC Goto directory with given relative pathname weare nowin PAW CDET TPC CALL HCDIRC PAW CDET TPC Equivalent to 1 2 above CALL HCDIR 9
40. te Bid 5 2 Memory Size o ca Ra emm RE be 9 ub x EUR bale da ba baleen 8 21 Space Tequirements R9 B exe 2 X MIO Tr 8 4 Input Output Routines 8 5 Exchange of histograms between different 8 6 RZ directories and HBOOK 102 102 103 104 104 106 108 112 112 113 114 115 116 117 118 118 119 119 121 124 125 131 135 135 144 157 9 Global sections shared memory 9 1 9 2 9 3 9 4 93 Sharing histograms in memory on remote machines Memory communication 222225220562 A ord Mapping global sections on VMS 9 2 1 Using PAW as a presenter VMS systems global section Windows and Unix Sun and DecStation only shared 9 3 1 Using PAW and Unix shared memory Sun DecStation Access to remote files from PAW Using PAW asa presenter on Systems s e c so oo huq ne Ro URS X w Qusa 10 HBOOK Tabular Overview List of Figures 1 1 Schematic presentation of the various steps in the data analysis chain 12 Writing data to HBOOK with the creation ofa RZ file 1 3 Output generated by joWHTEST ces coz ROGER ee GG 1 4 Addi
41. variab hmapg global_name base_common offset 175 VARIAB HMAX ID 99 CALL 83 CALL HMCINI IDDATA IDMC IDWT NSRC CHOPT IERR 142 VARIAB HMCLNL FRAC 142 CALL HMCMLL IDD IDM IDW NSRC CHOPT IFIX FRAC FLIM START STEP UP PAR DPAR 141 CALL HMDIR CHPATH CHOPT 160 CALL HMERGE NFILES CHFIN CHFOUT 170 CALL HMERGIN 170 VARIAB HMIN ID 99 CALL HMINIM ID FMIN 83 CALL HNFORM CHFORM CHNAME LDIM CHTYPE XLOW XHIGH 29 184 Chapter 10 Tabular Overview Table 10 1 HBOOK Routine calling sequences cont Calling Sequence page CALL HNOENT ID NOENT 94 CALL HNORMA ID XNORM 84 CALL HNTDUP ID1 ID2 NEWBUF CHTITL CHOPT 41 LOGVAR HNTNEW ID 93 CALL HNTVDEF ID1 IVAR CHTAG BLOCK ITYPE 38 CALL HOPERA ID1 CHOPER ID2 1D3 C1 C2 102 CALL HOUTPU LOUT 87 CALL HPAGSZ NLINES 85 CALL HPAK ID CONTEN 63 CALL HPAKAD ID CONTEN 63 CALL HPAKE ID ERRORS 63 CALL HPARAM ID IC R2MIN MAXPOW COEFF ITERM NCO 128 CALL HPARMN X Y EY NP NVAR IC R2MIN MAXPOW COEFF ITERM NCO 131 CALL HPCHAR CHOPT CHAR 82 CALL HPDIR CHPATH CHOPT 163 CALL HPHIST ID CHOICE NUM 85 CALL HPHS ID 86 CALL HPHST ID 86 CALL HPONCE 87 CALL HPRINT ID 18 CALL HPRNT IDN 3l CALL HPROJ1 ID IDN ISEL FUN IFROM ITO IVARX 34 CALL HPROJ2 ID IDN ISEL FUN IFROM ITO IVARX IVARY 34 CALL HPROT ID CHOICE NUM 86 CALL HPSCAT ID 86 CALL HPTAB ID 86 CALL HQUAD ID CHOPT MODE SENSIT SM
42. 01 BIN WID 1000E 01 MEAN VALUE 1943E 02 R M S 8124E 01 Grade vs Step HBOOK ID 103 DATE 09 03 93 NO 3 CHANNELS 10 U O 1 0 1 123456789012 OVE OVE 15 4 16 14 7 15 13 22 14 12 J YFB23G 13 11 39 QJ6H8 12 10 3C YTL6JE 11 9 36E N9HD3 10 8 2K VEN85 9 7 38D NRB25 8 6 2GQ TD8 7 5 3S9 UM7 6 4 5I9P QKG44 5 3 298WW QK72 4 2 9J S NK5 3 1 TEJMYQM6 2 32A9GMNM2 1 UND UND LOW EDGE 10 11111 1 345678901234 ENTRIES 3354 PLOT I SATURATION INFINITY I 3354 I SCALE 2 3 A B STATISTICS Ts T STEP 1 00 0 000 00 Chapter 4 Advanced features for booking and editing operations 4 1 Overview of booking options 4 1 4 Histograms with non equidistant bins CALL ID CHTITL NCX XBINS VMX Action As but instead of giving the lower and upper limits an array XBINS of NCX 1 ele ments is provided XBINS 1 contains the lower edge of the first bin XBINS 2 contains the lower edge of the second bin and so on XBINS NCX 1 contains the upper edge of the last bin 41 2 Profile histograms CALL HBPROF ID CHTITL NCX XLOW YMIN YMAX CHOPT Action Create a profile histogram Profile hi
43. 1 110 zr TiS 11 1 er 1 I I 1 1 I I I I I I I I I I Tree 1 T I II I IT I 152 1 L E T I I I I 15 T I I I lt I sI eS I I 2 3 4 DATE 5 17 12 91 NO Id Ic IIS IP T sis 251 441 Is I I zI I I I If I lt I sl e 6 T 8 9 0 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 LOW EDGE 1 1111111111111 112224658012445755432099687543222121221233455666557776678686676664543343222221111 21124626818147606828212710478511552225771649871850922032539736953183588893942434650812591167574 111111111122222222223333333333444444444455555555556666666666777777777788888888889999999999 10 1 ENTRIES WID 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789 5000 0 1000 01 TEST HRNDM2 HBDDK ID 20 CHANNELS 100 U O 10 NO ALL CHANNELS MEAN VALUE 0 5000E 04 0 4834E 00 UNDERFLOW 0 0000 00 OVERFLOW 0 0000E 00 R M 5 0 2184E 00 DATE 17 12 91 NO 6 10 1 2 3 4 5 6 7 8 9 1 D 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 E ROBO ORO
44. 1 1 HBOOK ID 172 168 164 160 156 152 148 144 140 136 132 128 124 120 116 112 108 104 100 96 92 88 84 80 76 72 68 64 60 56 52 48 44 40 36 32 28 24 20 16 12 8 4 CHANNELS 100 10 1 CONTENTS 100 10 1 LOW EDGE 1 10 1 0 ENTRIES BIN WID 0 1 TITLE OF ID 2 HBDDK ID 84 82 80 78 76 74 72 70 68 66 64 62 60 58 56 54 52 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 CHANNELS 100 10 1 CONTENTS 10 1 LOW EDGE 1 10 1 0 HHH I I I I 0 0 1 2 3 4 6 7 8 9 0 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 111111111122222222223333333333444444444455555555556666666666777777777788888888889999999999 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789 HHHH HHHHHHHH I I Li II I T E I I I I I I I I I L I I I L T k t I II I I I I I I IS 1111111111111 112224658012445755432099687543222121 211246268181476068282127104785115522257716498 100 ALL CHANNELS 0 2825E 04 000E 01 MEAN VALUE 0 3087E 00 2 0 0 1 2 3 4 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 221233455666557776678686676664543343222221111 718509220325397369531
45. 10 33 3581 12 247 1 01 34 3726 12 042 I 0I 35 3864 11 747 10 36 4013 12 207 10 37 4161 12 166 10 38 4307 12 083 IOI 39 4444 11 705 I 0I 40 4556 10 583 10 LOW EDGE INTEGRAT ERRORS 100 1 1 1 1 2 3 10 1 1 1 1 2 3 3 5 6 T 30 2 9 5 1 1 2 2 3 3 5 06 x05 2 b 59 5 1 9 0 9 0 5 8 9 1 6 0 0 5 9 0 3 9 0 5 8 d 6 8 1 1 4 0 8 4 5 1 2 0 0 1 6 8 1 1 4 0 9 5 5 2 2 1 2 0 3 0 9 9 3 9 3 ENTRIES 40 ALL CHANNELS 0 4556E 04 UNDERFLOW 0 0000 00 OVERFLOW 0 0000E 00 BIN WID 0 1000E 01 MEAN VALUE 0 2331E 02 5 0 9558E 01 TEST OF BIG BIN HBDDK ID 2000 DATE 17 12 91 NO 13 13 25 0 8 RE 13 I I 12 75 12 5 12 25 12 I I 11 75 L I 11 5 I I 11 25 I Iz 41 51 0000 I I 10 75 I I 10 5 I I 10 25 I I 10 I I 9 75 I I 9 5 I I 9 25 I p 9 I I 8 75 I 8 5 I I I I 8 25 I I T 8 T 7 75 7 5 7 25 I f 0 n gt Erf 6 75 I I I i 6 5 6 25 6 5 75 5 5 I T ea 5 25 I 5 4 75 q 2 4 5 T 4 25 foes 4 3 75 T 3 25 3 2 75 2 5 2 25 222 I I 1 75 I I 1 5 I I 1 25 T
46. 22 22224344 4322 2 2 3 2 2 St th 36 85 2 2 23 433 82 33 3424834 35 825 23 227434724 2 3 2 3242 422 6 2 2242 34 8 2 4 2 235565622435 3 2 2 22243 33442332424 39434 2 2 33 775 2 33222223545235 33333 33 2 2 544 2 3 732433243422 4 2 32 75 2 53 4525556865446523 223 3 23 2 3223 4 3 524 3 423243 2 2 31 725 33 63224226465624664 233 23 23 23 233 52 5 7 34 33232 3 2 30 sf 23 85 2478547767234432 2 22 2 4 34 4243334247 3434242 45 3 29 675 2 25232 545975576 47A4 32 2 2 2 4452 24533544223 65323 2 2 2 22 28 65 2 23 22875334425488 324 2 22 2 2 3 32 242423 5 4363 3 22 2 3 27 625 2 423 255285447559545334 243 22 233434 34 3 332 24242 2 2 2 26 6 322 6363354545424255 2 3 2 33 2228433 4 32 422 2 25 575 3222236 272342322 2 Qtt 334 24248342434 3 229 2 24 55 2 3 3 6 665 22 5 2 2 3 2 2 2 3 222 2 2 2 23 525 43 4244 35 2 22 22 2 2 2 3222 02 4 4 2 2 22 5 2 3 3332 22 2 23 2 2 2 2 3 21 475 2333 2 2 2 2 tt 2 23 2 23 20 45 2 435 2 2 22 23 2 32 2 22 2 19 425 3332 233 3 2 3 2
47. 5000 words for large values of PNCX and a large number of points memory behaves roughly as 2 NP PNCX DOUBLE PRECISION Histograms and plots CALL HPARAM ID IC R2MIN MAXPOW COEFF ITERM NCO Input parameters ID Histogram or plot identifier IC Control word see below R2MIN Maximum required value of multiple correlation coefficient MAXPOW Maximum degrees of standard polynomials INTEGER array of size NDIM ITERM Acceptable function codes see explanation above INTEGER array of size lt PNBF see expla nation above Output parameters NCO number of regressors in final expression COEFF Coefficients of terms DOUBLE PRECISION array of size NCO ITERM Accepted regressors codes INTEGER array of size NDIM NCO or NCO see explanation above IC is a coded integer with the following fields IC Nx 10 R 10 C 10 B 10 T 10 W 10 7 P 10 8 S This switch controls the superimposition of the result when printing the histogram it is effective only for 1 dimensional histograms 1 Resulting parametric fit superimposed on histogram 0 Nosuperposition P This switch controls the amount of information printed during the fitting process 0 Minimal output the residual sum of squares is printed 1 Normal output in addition the problem characteristics and options are printed also the stan dard deviations and confidence intervals of the coefficients 2 extensive output the results of each iteration are printed wit
48. 86 HRECOV 28 HRENAME 37 HREND 27 29 147 148 150 150 151 HRENDF 148 150 HRENDF 150 HRENID 16 HRESET 16 HRFILE 19 143 148 148 150 151 153 HRGET 146 147 HRIN 139 143 147 149 149 153 HRNDM1 119 119 120 HRNDM2 119 HROPEN 17 23 27 140 147 147 148 150 151 HROTAT 82 HROUT 23 27 29 102 139 143 147 148 149 153 HRPUT 146 147 HRVAL 112 HSCALE 74 82 HSCR 150 HSELBF 112 114 115 HSETPR 112 115 115 HSMOOF 116 116 HSPFUN 116 118 11 116 117 117 HSPLI2 116 117 HSQUEZ 74 HSTAF 70 HSTAR 82 88 97 HSUM 87 HTABLE 69 82 HTITLE 4 70 HUNPAK 75 83 88 HUNPKE 84 HUWFUN 24 33 35 35 HX 83 HXE 84 191 HXI 85 HXY 83 HXYE 85 HXYIJ 85 I O 146 IBINX 58 IBINX O 58 IBINY 58 IBINY O 58 identifier 4 input 146 integer number 56 integer type 4 IQUEST communication vector 21 99 100 146 148 Kolmogorov test 90 91 KUIP 139 limits on fitted parameters 105 line printer 15 log likelihood 98 LREC 151 LRECL 17 18 mean value 81 88 memory 20 MIGRAD 104 105 minimisation 98 MINOS 99 101 125 MINUIT 100 101 103 109 125 mononomial 111 Monte Carlo statistics 120 138 multiply histograms 89 multiquadric 116 MZEBRA 4 NFPAR 103 nfs 150 NPST 69 NTUPLE 82 Ntuple 2 3 17 47 146 149 Column Wise Ntuple 17 18 21 25 27 28 33 35
49. 88 89 TABL 14 HIDOPT 70 70 71 HIE 84 84 HIF 85 HIGZ 10 139 HIJ 83 83 HIJE 85 85 HIJXY 86 HINDEX 69 143 HINTEG 82 HIPAK1 56 HISTDO 4 14 15 68 69 75 76 histogram 2 3 addition 89 copy 15 copy range 15 deletion 16 division 89 identifier 4 13 multiplication 89 operations 89 packing 56 57 profile 48 rebinning 86 rename 16 reset 16 substraction 89 title 13 HIX 86 HKIND 82 HLABEL v 53 53 54 57 58 60 HLDIR 143 148 HLIMAP 156 156 HLIMIT 4 17 23 139 140 140 156 HLNEXT 144 HLOCAT 53 140 INDEX HLOGAR 82 hmapg 154 HMAX 86 HMAXIM 73 82 125 126 126 HMCLNL 122 124 126 126 HMCMLL i 124 125 125 HMDIR 142 148 HMERGE 149 150 HMERGIN 150 HMIN 86 HMINIM 73 82 HNFORM i 24 26 26 HNOENT 30 82 HNORMA 73 82 HNTDUP 37 HNTNEW 81 81 HNTVDEF 34 HOPERA 89 89 149 HOUTPU 76 76 HPAGSZ 74 HPAK 56 57 95 HPAKAD 57 HPAKE 51 53 57 57 85 95 98 113 HPARAM 111 113 114 116 HPARMN 111 116 HPCHAR 72 HPDIR 144 HPHIST 75 75 HPHS 75 76 HPHST 76 HPLCAP 11 HPLEND 11 HPLINT 11 HPLOT 1 10 11 51 53 153 HPONCE 76 76 HPRCHA 82 HPRCON 82 HPRERR 82 HPRFUN 82 HPRHIS 82 HPRINT 15 15 68 69 75 76 144 HPRLOW 82 HPRNT 27 HPROJ1 30 30 HPROJ2 30 INDEX 0 75 HPRSTA 82 HPSCAT 75 75 HQUAD i 116 118 118 HRDIR 145 HREBIN
50. CALL HIPAK1 ID NID IV N Action Analogous to HFPAKI except that the user vector contains now integers instead of real num bers 4 2 Filling Operations 63 4 2 2 Global Filling A vector or matrix can be transferred into a histogram with a single call CALL ID CONTEN Action Transfer the contents of an array as channel contents into an histogram The original contents of the histogram are overwritten Input parameters ID an existing histogram identifier CONTEN a user array suitably dimensioned Remark In the case of a 1 dimensional histogram the dimension of the array must at least be equal to the number of histogram channels NCHAN DIMENSION CONTEN NX with NX NCHAN In the case of a 2 dimensional histogram the dimensions of the array must exactly be equal to the number of histogram channels NCHANX and NCHANY ie DIMENSION CONTEN with NX NCHAN and NY NCHANY Projections and slices if present for the given histogram are not filled CALL HPAKAD ID CONTEN Action Similar to HPAK but instead of overwriting the channel contents the array values are added to the respective channel contents CALL ID ERRORS Action Store the contents of an array as the errors for the bins of the 1 dimensional histogram for which the option HBARX has been invoked Input parameters ID histogram identifier ERRORS user array containing the errors to be assigned to the
51. CFIELD PREC IUPD ISTPAR NUMOLD CHARACTER 4 TYPE COMMON CMCC TYPE The code to book and fill the Ntuple would look like this Initialisation phase The calls to HROPEN HBNT and HBNAME may be placed in different initialisation routines In this example example the Ntuple will be stored in directory MYFILE CALL HROPEN 1 MYFILE geant ntup N 1024 ISTAT CALL HBNT 10 Geant Ntuple CALL HBNAME 10 RUN IDRUN IDRUN 16 IDEVT 16 CALL HBNAME 10 RUN IEORUN IEORUN 16 CALL HBNAME 10 VECT VECT VECT 6 CALL HBNAME 10 GEKIN GEKIN CALL HBNAME 10 INWVOL INWVOL INWVOL 1 7 ISTOP 1 7 CALL HBNAME 10 NUMED NUMED NUMED 10 CALL HBNAME 10 NSTEP NSTEP NSTEP 16 CALL HBNAMC 10 TYPE TYPE TYPE C To fill the Ntuple when the common blocks are filled just invoke routine HFNT which knows the addresses and the number of variables DU 10 I 1 1000000 CALL HFNT 10 10 CONTINUE At the end of the job proceed as usual CALL HROUT 10 ICYCLE CALL HREND MYFILE Disk resident Ntuples Histograms are never created directly on a disk file They are always created in the current directory in memory PAWC or PAWC subdir Histograms are saved on the disk file with a call of type CALL HROUT In case of disk resident Ntuples it is the same thing The Ntuple header data struct
52. COMMON PAWC in process PFILL and to COMMON PAWMAP PAWM nvords in PRESENT This process has also a COMMON PAWC which will be used as a working space common CALL HRFILE PAWM PFILL GN in process PRESENT will open a HBOOK global section The current directory is now set to PFILL Routine HCDIR may be used to change the current directory to lower level directories Using HRIN described below a histogram can now be copied from PFILL to PAWC of process PRESENT and invoke the printing or plotting routines of either HBOOK or HPLOT Tools exist for example in PAW to dynamically map global sections It should be noted however that this mechanism does not allow to write e g using routine HROUT from process PRESENT into PFILL It is possible to open more than one global section several processes PFILL 91 1 Memory communication CALL HCOPYM ID IPAWD IOFSET Action Copies one or more histograms from the PAW area to common PAWC Input parameters ID Identifier of the histogram 0 means copy all existing histograms IPAWD PAW area identifier IOFSET Offset of newly created histogram s i e new histogram s will have identifier s ID IOFSET 174 9 2 Mapping global sections VMS 175 92 Mapping global sections on VMS VALUE hcreateg global_name base_common size Action Function to create and map a global section The function first opens a file with UFO option using HST_OPEN_GBL then crea
53. Calculates and prints the parameter correlations from the error matrix SHOw COVariance Prints the external covariance error matrix SIMplex maxcalls tolerance Performs a function minimization using the simplex method of Nelder and Mead Minimization termi nates either when the function has been called approximately maxcalls times or when the estimated vertical distance to minimum EDM is less than tolerance The default value of tolerance is 0 1 UP see SET ERR 7 3 Deprecated fitting routines Fitting histograms Long version CALL ID FUN NP P CHI2 IC SIG COV ST PMI PMA Use HFITH instead Fitting histograms Short version CALL HFITS ID FUN NP P CHI2 IC SIG Use HFITH instead 7 4 Parametrization 125 Non equidistant points in a multi dimensional space Long version CALL HFITN X Y EY NPTS N1 NVAR FUN NP P CHI2 IC SIG COV Use HFITV instead Non equidistant points in a multi dimensional space Short version CALL HFIT1 X Y EY N FUN NP P CHI2 IC SIG Use HFITV instead Histogram Fitting with Special Functions CALL HFITEX AA BB CHI2 IC SIG Use HFITHN instead as CALL HFITHN ID E 2 PAR STEP PMIN PMAX SIGPAR CHI2 CALL HFITGA ID C AV SD CHI2 IC SIG Use HFITHN instead as CALL HFITHN ID G 3 PAR STEP PMIN PMAX SIGPAR CHI2 CALL HFITPO ID NP A CHI2 IC SIG Use HFITHN instead as CALL HFITHN ID Pn NP P
54. I 00 II O IIIIIIIIII I I 170 IIII I 14 I IIIII II I I III OIII LJ ITII I IIOII 13 I IIIII OI I IIO IIIO I IIIO I IIIII 12 I IIIIIIII I EELE OIII III IOIII 11 I OII II I I OI T II OI IIIII IIIOIIOI I I 10 0 100 II III II IIOOI IIIII IO T 9 IIII O EL OI II II OOIII II I III II 8 II III I I IIII II IOIO II I IIOI II IIOI OI 7 II II I IIII II 01 III II I III I I ITII II 6 IT I OIII I II 10 III III T LIE IOIIOIOIIO I 5 IOI 1000 0 0 IIIOI II III I 4 1010 IIIII 01100 IIO 01011 IO IIO II 3 IIII IIII IOOII 01 I I I I II I OI IOI 2 IIOII I OIIIIII II 0 01 01 1 001 0 10 10 0 CHANNELS 100 0 1 10 0 1 2 3 4 5 6 7 8 9 0 1 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 CONTENTS 10 1 11111 112121111111111 11 1111 1 111111 1 1124150410055936050897739471365552143344 963473821858200355998124109464568648634 23 21 1 LOW EDGE 1 111111111122222222223333333333444444444455555555556666666666777777777788888888889999999999 10 1 0 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789 ENTRIES 707 ALL CHANNELS 0 7070E 03 UNDERFLOW 0 0000 00 OVERFLOW 0 0000 00 BIN WID 0 1000 01 MEAN VALUE 0 4943E 00 R M 5 0 2244E 00 HIST FILLED WITH HFILL AND HRNDM2 HBOOK ID 210 SLICE X DATE 17 12 91 NO 7 SLICE X NO 3 YMIN 0 6667 00 0
55. ID 250 240 230 220 210 200 190 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 CHANNELS 100 10 1 CONTENTS 100 10 1 LOW EDGE 100 10 1 ENTRIES BIN WID EXAMPLE NO 10 1 2 HiHHHHHHHHHHHHHHHHHHH 111111111122222 4 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 Hi HH HH HH HiHHHHHHHBHHBHHH 111111111122222 DATE 17 12 91 I zr L E Bi zr Er I I I E I zt I I I gt L 5 6 7 HiHHHHHHHHHHHHHHBHHBHHH 111111111122222 123456789012345678901234 123456789012345678901234 123456789012345678901234 123456789012345678901234 000000000000000000000000 000000000000000000000000 000000000000000000000000 000000000000000000000000 NO 8 9 HiHHHHHHHHHHHHHHHHHHH 111111111122222 1 0 1 1111111111222222222233333333334444444444555555555566666666667777777777888888888899999999990 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 EXAMPLE SCATTER PLOT HBDDK ID CHANNELS 100 10 1 OVE N N IO ND NN G G w w w w w w G p D 0 O 00 O gt LOW
56. Ignores bins with zero contents in the comparison For the S option ignores bins with zero contents in either histogram For the C and A option ignores bins with zero contents in the reference histogram The default action is to consider all bins as significant D Debug printout dumps the critical variables in the comparisons along with indicators of its weight etc The default no options selected does the S option statistical comparison ignores underflow and overflow bins and automatically corrects for the difference in entries between ID1 and ID2 Output parameters NBAD The number of bins failing the compatibility test according to the criteria defined by TOL and CHOPT DIFFS An array of length the number of bins being compared which gives the results of the test bin by bin confidence levels for options S and C deviations for option A Results are passed back in the form 1 D DIFFS NX for no over or underflow or DIFFS 0 NX 1 for overflow and or underflow 2 D DIFFS NX NY or DIFFS O NX 1 O NY 1 When to use HDIFFB instead of HDIFF HDIFFB treats the histogram bins individually while HDIFF treats the histogram as a whole In HDIFF one is comparing the overall shapes of a probability distribution Typically an event is entered only in one channel and the choice of channel depends on a measured value of a continuous coordinate so that it makes sense for downward fluctuations in one bin to be considered as compensated
57. Information VARIAB HI 1 and VARIAB HIJ C ID I J Action These functions return the channel contents in a given histogram bin in the 1 dimensional and 2 dimensional case respectively Input parameters ID Histogram identifier I Bin number for X coordinate For 0 HI returns the number of underflows in X J HIJ only Bin number for Y coordinate For 750 HIJ returns the number of underflows in Y When NX NY are respectively the number of channels in X and Y and I NX 1 J NY 1 then HI HIJ returns the number of overflows VARIAB HX ID X and VARIAB HXY Action These functions return the channel contents in a given histogram of the bin which contains a given value in X 1 dimensional case or a given pair of X Y 2 dimensional case Input parameters ID Histogram identifier X value Y value 2 dimensional case i e HXY only 5 7 Errors CALL HUNPKE ID CONTEN CHOICE NUM Action Transfer the error contents of a histogram or a selected projection of a 2 dimensional histogram into the local array Input parameters ID Histogram identifier CHOICE Character variable selecting subhistograms irrelevant for the 1 dimensional case HIST the 2 dimensional histogram itself PROX X projection PROY Y projection SLIX X slice SLIY Y slice gt BANX X band BANY Y band CHOICE is equivalent to HIST NUM Serial order of the slice or band that is requested If N
58. Ntuples Prior to booking the RWN a new HBOOK RZ file is created using HROPEN The top directory name of this file is passed to routine HBOOKN when the Ntuple is booked Filling proceeds as before but now when the buffer in memory is full it is written to the HBOOK file and then reused for the next elements of the Ntuple This normally results in a more efficient utilisation of the memory both when the Ntuple is created and when it is reprocessed Recommended way of creating a RWN PROGRAM TEST PARAMETER NWPAWC 15000 COMMON PAWC PAW NWPAWC CHARACTER 8 CHTAGS 5 DIMENSION EVENT 5 EQUIVALENCE EVENT 1 X EVENT 2 EVENT 3 Z EQUIVALENCE EVENT 4 ENERGY EVENT 5 ELOSS DATA CHTAGS X Y Z Energy Eloss CALL HLIMIT NWPAWC CALL HROPEN 1 EXAMPLE EXAMPLE DAT N 1024 ISTAT IF ISTAT NE 0 GO TO 99 24 Chapter 3 Ntuples CALL HBOOKN 10 A Row Wise Ntuple 5 EXAMPLE 5000 CHTAGS CALL HBOOK1 100 Energy distribution 100 0 100 0 DO 10 I 1 10000 CALL RANNOR X Z SQRT X X Y Y ENERGY 50 10 ELOSS 10 ABS CALL 10 EVENT CALL HFILL 100 ENERGY 0 1 10 CONTINUE CALL HROUT O ICYCLE CALL HREND EXAMPLE 99 CONTINUE END l When the Ntuple is filled routine will automatically write the buffer to the directory the RZ file which was specified in the call to HBOOKN the top directory EXAM
59. The example below shows different uses of the label routines The input data are the same as those used for building the Ntuple on page 45 Three histograms are booked For the first one 11 the number of channels 13 is given explicitly and a call to HLABEL declares all the labels for that histogram Then a second histogram 12 is booked with one pre declared channel In fact this latter histogram will be filled with in a way completely identical to histogram 11 but channels will be dynamically added as new labels are encountered We also create a 2 D histogram 21 where for the y axis we again pre declare labels and we fill it with a call to HFC2 After the loop where the histograms are filled we tell HBOOK to order the labels in the second histogram 12 according to decreasing bin contents This shows that it is not necessary in the 1 D case to pre declare the labels of a histogram but that they can be added to a histogram the fly i e while filling The sorting order can be specified after the histogram is filled As stated earlier labels are only printed on graphical output devices so that one must use HPLOT HIGZ to see the effect of the label routines The calls to the HPLOT HIGZ routines used to generate the PostScript picture shown in Fig 4 1 are described in the HIGZ HPLOT manual Example of the use of the histogram label routines PROGRAM CERN PARAMETER NWPAWC 30000 COMMON PAWC IPAW NWPAWC REAL RD
60. WRITE 31 COVARIANCE MATRIX WRITE 31 gt 7 7 Fitting with finite Monte Carlo statistics 20 30 DO 20 1 6 WRITE 31 6 D12 4 1X COV I J J 1 1 CONTINUE Gaussian fit Prints first and last iterations AG 2 BG 0 4 CG 0 1 CALL HDELET 0 CALL HBFUN1 1 100 0 1 HFUNGA CALL HBOOK1 5 100 0 1 1000 DO 30 I 1 5000 XR HRNDM1 1 CALL HFILL 5 XR 0 1 CONTINUE PAR 1 200 PAR 2 0 4 PAR 3 0 1 CALL HFITHN 5 G 3 PAR 1 ST PMI PMA SIGPAR CHI2 CALL HPRINT 5 CALL HDELET 0 END FUNCTION HFUNF X COMMON HFPAR PAR 6 DOUBLE PRECISION 1 2 1 2 1 2 51 52 1 2 Force double precision calculation C1 PAR 1 C2 PAR 2 XM1 PAR 3 XM2 PAR 4 XS1 PAR 5 XS2 PAR 6 A12 0 5 X XM1 XS1 2 A22 0 5 X XM2 XS2 2 IF A1 LT 20 THEN X1 0 ELSEIF A1 GT 20 THEN X1 1 E5 ELSE X1 C1 EXP A1 ENDIF IF A2 LT 20 THEN X2 0 ELSEIF A2 GT 20 THEN X2 1 E5 ELSE 2 2 2 ENDIF HFUNF X1 X2 END FUNCTION HFUNFV X DIMENSION X Compute function value for 2 dim point X HFUNFV HFUNF X 1 HFUNF X 2 END 147 148 FUNCTION HFUNGA X COMMON HFGAUS AG BG DOUBLE PRECISION AG BG CG HFUNGA AG EXP 70 5 X BG CG 2 END Chapter 7 Fitting parameterization and smoothing 7 7 Fitting with finite Monte Carlo statistics 149 TITLE
61. X restricted to the Y interval YMI YMA Input parameters ID identifier of an existing 2 dimensional histogram YMI lower limit of Y interval YMA upper limit of Y interval VMX maximum value to be stored in 1 channel The same remarks as for HBPRO apply CALL HBANDY ID XMI XMA VMX Action As HBANDX but the projection is onto Y CALL HBSLIX 1ID NSLI VMX Action Books slices along Y of 2 dimensional histograms as NSLI 1 dimensional histograms Each slice is a projection onto X restricted to an interval along the Y axis Input parameters ID identifier of an existing 2 dimensional histogram NSLI number of slices VMX maximum value to be stored in 1 channel The same remarks as for HBPRO apply CALL HBSLIY ID NSLI VMX Action As HBSLIX but slices are projected onto Y 4 1 Overview of booking options 57 4 1 5 Statistics Mean value and standard deviation of 1 dimensional histograms are calculated at editing time using the channel contents If a more accurate calculation is desired or if more statistical information is needed the following option will provide it CALL HIDOPT ID STAT CALL HBARX ID Action Store the errors for 1 dimensional histograms X projections etc in memory and superimpose them on the plot during output This routine must be called after booking but before filling Input parameter ID identifier of an existing histogram ID 0 means all histograms already booked If ID
62. XMA XMI forces one word per channel 21 2 Two dimensional case CALL HBOOK2 ID CHTITL NX XMI XMA NY YMI YMA VMX Action Books a two dimensional histogram Input parameter description ID histogram identifier integer CHTITL histogram title character variable or constant up to 80 characters NX number of channels in X 16 2 2 Filling 17 XMI lower edge of first X channel XMA upper edge of last X channel NY number of channels in Y YMI lower edge of first Y channel YMA upper edge of last Y channel VMX maximum population to store in 1 cell Remarks Similar to HBOOKI apart from automatic binning By default a 2 dimensional histogram will be printed as a scatterplot If the option TABL is selected via CALL HIDOPT ID TABL the 2 dimensional histogram will be printed as a table When editing the table the number of columns NCOL used to write the content of one cell depends on the value of VMX as follows NCOL ALOG10 VMX 2 When VMX is zero the contents is printed in 10 columns in floating point format including sign If necessary all contents are multiplied by a power of 10 this number being reported at the bottom of the table 2 2 Filling CALL HFILL ID X Y WEIGHT Action Fills a 1 dimensional or a 2 dimensional histogram The channel which contains the value X and for two dimensionals the cell that contains the point X gets its contents increased by WEIGHT All boo
63. by upward fluctuations in another bin In HDIFFB each bin is considered independently except perhaps for an overall normalization factor which is the sum over all bins Thus HDIFFB is appropriate when It makes sense to identify a single channel as bad for example if the bin contents correspond to hits in a given detector element The data is heterogeneous for example if the contents are counts versus trigger bit You have already found a discrepancy on a shape with HDIFF and wish to focus on where dis agreement is worst 108 Chapter 6 Operations Histograms A plot of hits versus detector element where the detector elements cover some angular range is an example of a histogram which might be considered with either comparison utility The choice depends on the question you wish to answer If you want to know if the angular distribution looks the same use HDIFF If you want a report on bad detector elements use HDIFFB 6 3 1 Choice of TOL If you choose 0 05 for TOL you should expect 5 or so bad bins per trial from a histogram with 100 channels For monitoring you must compromise between the number of false messages you can tolerate based on the total number of channels you monitor and the amount of data you will need to collect to claim a channel is bad In general a somewhat smaller fraction of channels than TOL will be flagged as bad since for discrete distributions Poisson statistics
64. chain Although it is possible to define histograms interactively in a PAW session and then read the many thousands of events in general for large data samples the relevant variables are extracted from the Data Summary Files or DSTs and stored in histograms or an Ntuple Histograms require to make a certain choice as to the range of values for the plotted parameter because the binning or the coarseness of the distribution has to be specified when the histogram is defined booked Also only one and two dimensional histograms are possible hence the correlations between various parameters can be difficult to study Hence in many cases it Is more appropriate to store the value of the important parameters for each event in an Ntuple This approach preserves the correlation between the parameters and allows selection criteria to be applied on the reduced data sample at a later stage In general the time consuming job of analysing all events available on tape is run on a mainframe or CPU server and the important event parameters are stored in a Ntuple to allow further detailed study For convenience the Ntuple can be output to disk for each run and then at a later stage the Ntuples can be merged in order to allow a global interactive analysis of the complete data sample see Figure 1 1 A typical batch job in which data are analysed offline and some characteristics are stored in HBOOK is shown in Figure 1 2 HBOOK is initialised by a call to HLI
65. computation is actually carried on in universities or other research establishments Particle physicists from various countries are in close contact on a continental and world wide basis the infor mation exchanged being mainly via preprints and conferences The similarities in experimental devices and problems and the close collaboration favour the adoption of common software methodologies that sometimes develop into widely used standard packages Examples are the histograming fitting and data presentation package its graphic interface hplot 2 and the Physics Analysis Workstation paw system 3 which have been developed at CERN HBOOK is a subroutine package to handle statistical distributions histograms and Ntuples in a Fortran scientific computation environment It presents results graphically on the line printer and can optionally draw them on graphic output devices via the hplot package paw integrates the functionalities of the hbook and hplot and other packages into an interactive workstation environment and provides the user with a coherent and complete working environment from reading a mini DST via data analysis to preparing the final data presentation These packages are available from the CERN Program Library see the copyright page for conditions They are presently being used on several hundred different computer installations throughout the world 11 Data processing flow in particle experiments In the late
66. corresponds to a 2 dimensional histogram HBARX acts on all X projections slices bands where i binnumber n number of entries in bin W weight of event j in bin 2 Itis clear that the sum of the squares of weights in each bin must also be stored to perform this calculation However when filling with weight always equal to 1 errors can be calculated from bin contents only and HBARX HBARY need not be called The superimposition of error bars can be selected at output time using HIDOPT ERRO In both cases the values of errors can be printed under the contents via the editing option HIDOPT ID PERR The entry HPAKE permits user defined error bar setting CALL HBARY ID Action As HBARX it is used to act on Y projections of 2 dimensional histograms CALL HBAR2 ID Action This routine can be used to create the data structure to store errors for 2 D histograms like HBARX for 1 Ds By default the errors are set to the sqrt contents Input parameter ID identifier of an existing 2 D histogram ID 0 means all histograms already booked The routine HPAKE or the paw command PUT ERR may be used to fill errors If HBAR2 is not called before HPAKE then invokes HBAR2 automatically When 2 is called routines HFILL or HF2 will accumulate the sum of the squares of the weights The errors for 2 D histograms are used by the fit routines or the Histo FIT command The error bars are not drawn by the hp
67. dimensional case i e HIJXY only 5 10 99 5 10 Maximum Minimum VARIAB HMAX ID and VARIAB HMIN ID Action Returns the maximum or minimum channel contents of a histogram without underflow and overflow In the case of a 2 dimensional histogram the returned value does not take into account projec tions Input parameter ID Histogram identifier 5 11 Rebinning CALL HREBIN ID X Y EX EY N IFIRST ILAST Action The specified channels of a 1 dimensional histogram are cumulated rebinned into new bins The final contents of the new bin is the average of the original bins Input parameters ID Histogram identifier N Number of elements in the output arrays X Y EX EY IFIRST First histogram channel on which the rebinning has to be performed ILAST Last histogram channel on which the rebinning has to be performed Output Parameters X Array containing the new abscissa values Y Array containing the cumulated contents EX Array containing the X errors EY Array containing the Y errors The abscissa errors on the rebinned histogram are calculated to be half the bin width If the standard deviation on the abscissa values is instead required then specify N as a negative number In this case the returned abscissa error for each bin is the bin width divided by the square root of 12 This routine may also be used for histograms with unequal bin widths 100 Chapter
68. execution For example at initialization these estimates are just the starting step sizes as specified by the user After a MIGRAD or HESSE step the errors are usually quite accurate unless there has been a problem MINUIT when it prints out error values also gives some indication of how reliable it thinks they are For example those marked CURRENT GUESS ERROR are only working values not to be believed and APPROXIMATE ERROR means that they have been calculated but there is reason to believe that they may not be accurate If no mitigating adjective is given then at least MINUIT believes the errors are accurate although there is always a small chance that MINUIT has been fooled Some visible signs that MINUIT may have been fooled are Warning messages produced during the minimization or error analysis Failure to find new minimum Value of EDM too big estimated Distance to Minimum Correlation coefficients exactly equal to zero unless some parameters are known to be uncorrelated with the others Correlation coefficients very close to one greater than 0 99 This indicates both an exceptionally difficult problem and one which has been badly parameterized so that individual errors are not very meaningful because they are so highly correlated Parameter at limit This condition signalled by a MINUIT warning message may make both the function minimum and parameter errors unreliable See the discussion above Gett
69. file global section should be read into memory If a histogram identifier ID already exists in memory a message is printed and it is deleted from memory before reading the new histogram from the file or global section ICYCLE Cycle number If ICYCLE O then the lowest cycle is read To read the highest cycle use a large number e g 999999 When filling an Ntuple HBOOK creates a dummy header 1 which contains only the Ntuple definition This dummy header is used for the error recovery command it is a fully functional header except that the number of events is not necessarily correct For the purpose of reading Ntuples users should always use ICYCLE 999 to ensure they receive the correct quantity of data in for example subsequent calls to HGNTB IOFSET histogram which is read in memory will have the identifier IDN ID IOFSET Specifying IOFSET different of zero permits to have in memory copies of histograms with the same iden tifiers ID in different files This parameter may be very useful when HRIN is called together with routines such as HOPERA or HDIFF This facility also works for Ntuples 170 Chapter 8 Memory Management input output Routines Merging HBOOK files into a new file CALL HMERGE NFILES CHFIN CHFOUT Action Merges two or more HBOOK files with identical objects and directories into a new file His tograms are added and Ntuples are combined Works for CWN s and RWN s Input parameters NF
70. is returned If the histogram ID is empty or if the sum of its channel contents is not positive a message is printed and a flat distribution is assumed CALL HRNDM2 ID RX RY Action Returns a random point RX RY distributed according to the contents of a 2 dimensional histogram Input parameter ID Identifier of a 2 dimensional histogram Output parameters RX RY Random numbers Remark Same as HRNDMI These 2 entries can be used in conjunction with HBFUNI and HBFUN2 respectively 7 7 Fitting with finite Monte Carlo statistics Most of the following text is taken from 17 see this publication for more discussion and details of the algorithm and examples Analysis of results from HEP experiments often involves estimation of the composition of a sample of data based on Monte Carlo simulations of the various sources Data values generally of more than one dimension are binned and because the numbers of data points in many bins are small a x minimi sation is inappropriate so a maximum likelihood technique using Poisson statistics is often used This package incorporates the fact that the Monte Carlo statistics used are finite and thus subject to statistical fluctuations 136 Chapter 7 Fitting parameterization and smoothing The Problem A common problem arises in the analysis of experimental data There is a sample of real data each member of which consists of a set of values for example a
71. is returned CHTYPE Character variable specifying type of histogram TE m m mi po 1 dimensional 2 dimensional Ntuple subdirectory unknown CHTYPE Character variable containing title or subdirectory name IDH 0 1 CONTINUE Scan content of current directory CALL HLNEXT IDH CHTYPE CHTITL CHOPT IF IDH NE O THEN process GOTO 1 ENDIF CALL HRDIR MAXDIR CHDIR NDIR Action Returns the list of subdirectories of the current working directory This command works with all five different kinds of directories described in figure 8 3 Input parameter MAXDIR Length of the character array CHPATH Output parameters CHDIR Character array which will contain the names of the subdirectories of the current working directory NDIR Actual number of subdirectories present in the current working directory If this number is greater than MAXDIR only the first MAXDIR subdirectory names will be returned in array CHDIR The use of directories is illustrated below Example of use of directories PROGRAM MAIN COMMON PAWC H 20000 CALL HLIMIT 20000 CALL HBOOK1 10 Energy distribution 100 0 300 0 CALL USECAL 6 4 Input Output Routines 165 CALL HFILL 10 EDER 0 1 CALL HISTDO END SUBROUTINE USECAL Make a new directory ECAL and set the new current directory CALL HMDIR ECAL S Create a new histogram with ID 10 in the new directory CALL 00 1 10 My histogram 50
72. it forces you into the less accurate Gaussian approximation Thus it is preferable for example to have unweighted Monte Carlo events if you need to use HDIFFB to compare with data The only useful case is if the weighted histogram is the reference histogram in the C comparison which only makes sense if you have much better accuracy than your data 6 3 Bin by bin histogram comparisons 109 Using Profile histograms The N option is irrelevant for profile histograms The overflow underflow options are illegal for profile histograms because insufficient information is stored to calculate the error bars None of the test options 5 C check on the number of entries in a profile histogram bin To do that make a separate 1 dimensional histogram This has an unexpected effect when the number of entries are small Bins with no entries always pass the 5 and C options no data is compatible with any distribution so in such cases more bins pass than called for by TOL Values of DIFFS The value of DIFFS may depend somewhat on the value of TOL chosen as the approximation chosen to calculate DIFFS depends on both the number of entries and on the size of TOL how accurately DIFFS must be calcuated The 5 option sometimes returns a confidence level of 1 0 in the small statistics calculation i e there is no probability that the two numbers came from different distributions This is due to finite precision Values slightly higher than 1 0 w
73. lt u gt where 1 is the lower and lt u gt the upper limit of the arrays using this index variable In the above example the lower limit of NTRACK is 0 and the upper limit is 100 MAXTRK While filling a CWN HBOOK can also easily test for array out of bound errors since it knows the range of NTRACK Only the last dimension of a multi dimensional array may be variable and the index variable must be specified in the block where it is used Array lower bounds must just like the lower range of the index variable be 0 Multiple calls to HBNAME HBNAME may be called more than once per block as long as no data has been stored in the block New blocks can be added to an Ntuple at any time even after filling has started whereas existing blocks may only be extended before filling has started 3 3 3 Creating CHFORM dynamically CALL HNFORM CHFORM CHNAME LDIM CHTYPE XLOW XHIGH Action Assists with the formation of the character string CHFORM Input parameters CHFORM The character string to be started or appended to The string should be declared of sufficient length in the calling routine such that it can hold the fully expanded specifications of the Ntuple variables CHNAME Character variable specifying the name of the variable to be added to CHFORM If the variable is dimensioned then CHNAME should contain the dimension specification in brackets as usual For dimension spcifications that are to be computed at run time the
74. lt x lt 4 9 9 9 lt lt x lt 10 10 A 10 lt z lt 1l 11 B 11 x 12 12 12 z lt 13 overflow VMX lt x 4 3 Editing operations 85 Remarks The call has no effect on the projection of histogram ID he scale can be redefined several times 4 3 5 Page Control Plots are output on the line printer file each of them starting at the beginning of a new page The page size is an installation default One dimensional histograms take one page and are printed across the page All those defaults can be overwritten as follows CALL HSQUEZ YES NO Action Suppres reestablish page eject CALL HPAGSZ NLINES Action Changes the number of lines per page Input parameter NLINES Number of lines per page The initial value of this parameter is system dependent generally 56 4 3 6 Selective Editing Editing routines that draw histograms use a considerable amount of core due to the complexity of the tasks they have to perform If the editing is performed by HISTDO or HPRINT all the routines that deal with 1 dimensional his tograms rotated 1 dimensional histograms 2 dimensional histograms get loaded even if not used e g even in the case where only 1 dimensional in standard format are required In such cases selective editing options for different classes can be used to replace HISTDO or HPRINT CALL HPHIST ID CHOICE NUM Action Edits 1 dimensional histogram or projection sl
75. of each source actually present in the data sample you provide 2 The transformation of the P into the P the fractions of each source which were present in the data sample before the efficiencies were applied to the data This is implemented as follows The user or HMCMLL calls HMCLNL with the These trans formed into the P within HMCLNL using the normalisation factors calculated by HMCINI gt xo gt OP 7 7 Fitting with finite Monte Carlo statistics 141 where ccs N and HMCLNL calculates the correct log likelihood using the P and the normalised weight distributions HBOOK routines The following three routines are intended to help with problems of the above type Subroutine HMCMLL uses minuit to perform the log likelihood maximisation and return a set of fractions Functions HMCINI and HMCLNL are provided for those who wish to perform the fit themselves N B Real parameters and functions are all REAL 8 Double precision on most machines CALL HMCMLL IDD IDM IDW NSRC CHOPT IFIX FRAC FLIM START STEP UP PAR DPAR Action Fits the given Monte Carlo distributions to the data distribution using a binned maximum likelihood fit which includes the effect of both data and Monte Carlo statistics and allows weights to be provided for each Monte Carlo distribution The data Monte Carlo and weight distributions must be presented in identically bin
76. ok ok PK KOR ke ke ke Var numb Name Lower Upper gt 3k ok ok 5k K 2k 2k 2k 3k 2K 1 X 359595E 01 0 396836 01 2 Y 398909E 01 0 381000 01 3 2 0 748417E 03 0 162475E 02 gt K gt K gt K gt K gt K gt gt gt K K gt K gt K K K k k k k k k k gt Directory 30 N N TUPLE 10 1 TEST1 20 2 TEST2 HHH HH H 45 A more complex example CERN personnel statistics In order to explain the advantages of the Column Wise Ntuple format we consider a small data sample containing some characteristics of the CERN staff as they were in 1988 For each member of the staff there exists one entry in the file Each entry consists of 11 values as described in Table 3 1 Note how the constraints on the various variables shown in the table are expressed in the job when creating the Ntuple 46 Chapter 3 Ntuples Variable Name CATEGORY DIVISION FLAG AGE SERVICE CHILDREN GRADE STEP NATION HRWEEK COST Description and possible values Professional category integer between 100 and 600 100 199 Scientific staff 200 299 Engineering staff 300 399 Technical support staff 400 499 Crafts and trade support staff
77. or with automatic overflow on an RZ file Only single precision floating point numbers REAL 4 on 32 bit machines can be stored no data compression is provided Input parameters ID Identifier of the Ntuple CHTITL Character variable containing the title associated with the Ntuple NVAR Number of variables per event NVAR lt 512 CHRZPA Character variable containing the path name of a RZ file onto which the contents of the Ntuple can overflow nod Memory resident Ntuples A bank of NWBUFF words is created Further banks of the same size are added in a linear chain should additional space be required at filling time RZTOP Disk resident Ntuples recommended A disk resident Ntuple is created if the CHRZPA argument specifies the top direc tory name of an existing RZ file that has already been opened with HROPEN or HRFILE A bank of length NWBUFF is created as in the case of memory resident Ntuples However each time the bank becomes full it is automatically flushed to the RZ file rather than creating additional banks in memory NWBUFF Number of words for the primary allocation for the Ntuple CHTAGS Character array of length NVAR providing a short name up to eight characters tagging scheme for each variable Example of the declaration of a memory resident RWN 2 CHTAGS 5 DATA CHTAGS Px Py Pz Q2 NU CALL HBOOKN 10 My first Ntuple 5 1000 CHTAGS 3 2 2 Filling a RWN CAL
78. produce link produce SYS INPUT OPTIONS cern library packlib lib kernlib lib PSECT PAWC PAGE Figure 9 1 Visualise histograms in global section In addition to the facilities described in the previous section the standard version of PAW may be used as an online presenter on VMS systems using the mechanism of global sections It is possible for two processes to reference the same histograms using global sections For example the first process may be a histogram producer e g a monitoring task and the second process PAW As the histograms are being gradually filled by the first task PAW can view them and even reset them To use the global sections it is also necessary to page align the common which is in the global section This is achieved in the link step when making the process see example The relevant statements are SYS INPUT OPTIONS to tell the linker that some options follow the link statement and PSECT PAWC PAGE which is the option to page align the PAWC common 9 3 Windows Unix Sun and DecStation only shared memory 177 9 3 Windows and Unix Sun and DecStation only shared memory On Windows NT Windows 95 and on Unix systems with the exception of HP UX and SOLARIS it is possible to communicate between processes using shared memory In the histogram producer pro gram use routime HLIMAP instead of HLIMIT to initialize HBOOK With PAW use the command global sect to use shared memory CALL HLIMAP NWORDS CHNA
79. rectories in memory are written to the output file U Write the histogram to an already existing hbook file When an histogram with the same identifier already exists on the output file then a new cycle is added CALL ID CHFILE CHOPT Action Read a histogram from a given direct access file This routine cannot be used for Ntuples 6 4 Input Output Routines 167 Input parameters ID Histogram identifier 0 read all histograms into the current directory CHFILE Character variable or constant defining the input filename If CHFILE the histogram is read from the current working directory on disk CHOPT Character option specifying the desired option Add to the current histogram in memory Get complete tree not yet implemented Remarks The following remarks apply to both HRPUT and HRGET HRGET and HRPUT issue automatically Fortran OPEN and CLOSE calls With HRPUT the file is created with LREC 1024 machine words On Unix the filename CHFILE will be translated to lowercase Fortran logical unit 88 is used by these routines HRPUT calls HROPEN HROUT and HREND HRGET calls HROPEN HRIN and HREND Open an RZ direct access file or map a Global Section CALL HROPEN LUN CHTOP CHFILE CHOPT LREC ISTAT Action Open a direct access hbook file If several direct access files are opened they are identified by the top directory only Input parameters LUN Log
80. roo physics 1sa umich edu 54 4 1 Overview of booking options 55 If a bin has N data points all with the same value Y especially possible when dealing with integers the spread in Y for that bin is zero and the uncertainty assigned is also zero and the bin is ignored in making subsequent fits This is a problem If VY was the correct error in the case above then vY VN would be the correct error here In fact any bin with non zero number of entries N but with zero spread should have an uncertainty VY VN Yet is Y N really the correct uncertainty Probably it is only true in the case where the variable Y is some sort of counting statistics following a Poisson distribution This should probably correspond to the default case However Y can be any variable from an original Nntuple not necessarily distributed according to a Poisson distribution Therefore several settings for the option variable CHOPT are possible to determine how errors should be calculated 5 stands for the spread in the formulae below S N for S 40 Default for S 0 N 0 0 for N 0 Errorsare 5 for S 5 0 79 Y forS 0 N 0 i 0 for N 0 Errors are S N for S 5 0 ps 1 V12 N for S 0 N gt 0 0 for N 0 The third case above corresponds to integer Y values for which the uncertainty is 0 5 with the assump tion that the probability that Y takes any value between Y 0
81. safely via a PARAMETER statement as shown below PARAMETER NWPAWC 50000 COMMON PAWC HMEMOR NWPAWC Furthermore HBOOK must be informed of the storage limit via a call to HLIMIT This is discussed in detail in section 8 2 on page 158 In the case above this would correspond to CALL HLIMIT NWPAWC At execution time when histograms are booked they are accomodated in common PAWC in booking order up to the maximum size available Note that a call to HLIMIT will automatically initialise the ZEBRA system via a call to the routine MZEBRA If ZEBRA has already been initialised MZEBRA has already been called then HLIMIT should be called with a negative number indicating the number of words required e g CALL HLIMIT NWPAWC 1 3 1 HBOOK parameter conventions Histogram or Ntuple Identiers Histograms and Ntuples in HBOOK are identified by a positive or negative integer Thus the histogram identifier ID O is illegal at booking time However it is a convenient way to specify that the option or operation applies to all known histograms in the current working directory e g output input printing routines for which a zero identifier is meaningful are mentioned explicitly Parameter types In agreement with the Fortran standard when calling an HBOOK routine the type of each parameter must correspond to the one described in the routine s calling sequence in this manual Unless explicitly state
82. saving space the routine HDIFF has been provided and we believe it is the best test for comparison even on binned data However the values of PROB for binned data will be shifted slightly higher than expected depending on the effects of the binning For example when comparing two uniform distributions of 500 events in 100 bins the values of PROB instead of being exactly uniformly distributed between zero and one have a mean value of about 0 56 Since we are physicists we can apply a useful rule As long as the bin width is small compared with any significant physical effect for example the experimental resolution then the binning cannot have an important effect Therefore we believe that for all practical purposes the probability value PROB is calculated correctly provided the user is aware that value of PROB should not be expected to have exactly the correct distribution for binned data he user is responsible for seeing to it that the bin widths are small compared with any physical phenomena of interest he effect of binning if any is always to make the value of PROB slightly too big That is setting an acceptance criterion of PROB 0 05 will assure that at most 5 of truly compatible histograms are rejected and usually somewhat less The Confidence Level for Two dimensional Data The Kolmogorov Test for 2 dimensional data is not as well understood as for one dimension The basic problem is that it requires
83. set of Z decay events with inclusive leptons for each of which there is a value of p pt Evis or a set of measured particle tracks each with p E cos 0 You know that these arise from a number of sources the lepton events from direct b decays cascade b decays c decays and background the tracks from and p hadrons You wish to determine the proportions P of the different sources in the data There is no analytic form available for the distributions of these sources as functions of the r only samples of data generated by Monte Carlo simulation You therefore have to bin the data di viding the multidimensional space spanned by the z values into n bins This gives a set of numbers di d2 dn where d is the number of events in the real data that fall into bin 7 Let f P1 P5 P5 be the predicted number of events in the bin given by the strengths P and the numbers of Monte Carlo events aj from source 7 in bin 7 m fi Np 7 1 j 1 where Np is the total number in the data sample and the total number in the MC sample for source 5 TL Np gt d N Y aji 7 2 i 1 i 1 The P are then the actual proportions and should sum to unity It is convenient to incorporate these normalisation factors into the strength factors writing NpP N giving the equivalent form m fi pus 7 3 j 1 One approach is then to estimate the p by adjusting them to minimise d f 2 x x di
84. statistical errors HESSE and MINOS NP Number of parameters NP lt 25 PAR Array of dimension NP with initial values for the parameters STEP Array of dimension NP with initial step sizes for the parameters B option only PMIN Array of dimension NP with the lower bounds for the parameters B option only PMAX Array of dimension NP with the upper bounds for the parameters B option only Output parameters PAR Array of dimension NP with the final fitted values of the parameters SIGPAR Array of dimension NP with the standard deviations on the final fitted values of the parameters CHI2 Chisquared of the fit 7 1 4 Results of the fit When the fit is complete the parameters and the errors on the parameters are returned to the calling program By default unless option N is specified the fitted parameters the errors on these parameters their names see below the chi squared and the number of degrees of freedom of the fit are stored in a data structure associated to the histogram ID when routines HFITH and HFITHN are invoked For HFITH the value of the fitted function in each histogram channel is also stored in the histogram data structure The parameters are given the default names P1 P2 Pn For HFITHN the type of the function being fitted is stored instead of the fitted values for each channel The information stored in the associated data structure is used during the printing plotting phase I
85. the 1974 CERN School of Computing Godoysund Norway 1974 CERN Report 74 23 7 5 B Schorr Spline estimation of Distributions and Density Functions Technical Report DD 75 13 CERN 1975 7 5 B Schorr Etude du lissage d histogramme par la m thode des B splines et implementation dans Technical Report DD EE 78 3 CERN 1978 7 5 J Allison Multiquadratic Radial Basis Functions for Representing Multidimensional High Energy Physics Data Comp Phys Comm 77 377 395 1993 7 5 Roger Barlow and Christine Beeston Fitting using finite Monte Carlo Samples Comp Phys Comm 71 219 1993 7 7 7 7 186 BIBLIOGRAPHY 187 18 Roger Barlow Fitting using finite Monte Carlo Samples J Comp Phys 72 202 1987 7 7 19 CERN CSPACK Client Server Computing Package nProgram Library Q124 1991 8 3 Index W 102 Q 148 892 57 58 gt 5 54 U 57 103 common 153 3530h 116 access to histogram information 81 add histograms 89 analytic function 110 array 56 57 attribute 140 B splines 116 band 139 bin histogram rebinning 86 BLAC 72 block 26 BSIZE 23 change directory 151 channel contents 81 character type 4 CHFILE 147 148 Chisquare test 91 CHOPT 23 circular buffer 20 CLABX 58 CLABY 58 client 159 common PAWMAP 153 common PAWC 3 4 17 18 23 53 87 116 139 140 142 153 156 confidence level 92 Convolution Ntuple 37 covarian
86. the given expansion but for a residual namely uj The expansion itself is the linear combination of the regressors F computed at the 7 th data point The strategy of the two entries is to minimize the residual variance from fitting various possible regressors out of a set which is either system or user defined The previous expression can be rewritten in a more synthetical notation array of NP data points with matrix of regressors NP lines times NCO columns o Ne array of coefficients u array for the NP residuals As already said we want to use the smallest possible number of regressors for a given set of data points which yields the desired fit in the terms explained below That is to say that the rank of the matrix F should be NCO If it were smaller then some at least one of the columns could be represented as a linear combination of others and so rearranging the coefficients we could get rid of these regressors The residual variance is minimized under the following constraints 1 The NP values of the residuals should have a mean of 0 2 residuals should be independently distributed This means that their covariance matrix has the form of a positive diagonal matrix we call it D 3 The regressors should be linearly independent Hypothesis 2 implies that F F 1 exists where D F F is the covariance matrix of the coeffi cients The coefficients and regressors are determined iterative
87. the program above on the 3 7 Ntuple examples 21 CERN Ntuple should be compared with the table obtained during the creation run as shown on page 48 Output Generated HBOOK HBOOK CERN VERSION 4 17 HISTOGRAM AND PLOT INDEX 09 03 93 NO TITLE ID B C ENTRIES DIM NCHA LOWER UPPER ADDRESS LENGTH i 1 CERN Population 10 N 27174 37 2 Staff Age 101 32 3354 1 X 45 200E 02 650 02 26527 90 3 Number of years at CERN 102 32 3354 1 X 35 000E 00 350E 02 26432 83 4 Grade Step 103 32 3354 2 X 12 300 01 1 0 02 26347 298 16 000 00 160 02 26074 264 MEMORY UTILISATION MAXIMUM TOTAL SIZE OF COMMON PAWC 30000 52 FEO Ntuple ID 10 Entries 3354 CERN Population JE OSS A ACK AC ACI ACE Var numb Packing Range Block Name aA AACA ACACIA ACI AGE Ko 1 4 11 100 6001 CERN CATEGORY 2 Ux4 4 CERN FLAG 3 4 8 1 100 CERN 4 0 601 CERN SERVICE 5 4 5 0 101 CERN CHILDREN 6 4 5 3 14 CERN GRADE 7 4 5 0 151 CERN STEP 8 4 7 20 44 CERN HRWEEK 9 x I 4 CERN COST 10 C 4 CERN DIVISION 11 4 CERN NATION AA IA
88. the value at a given abscissa point Input parameters ID Identifier of an existing 1 dimensional histogram X Abscissa Number of knots when Nx 0 then 13 Degree of the splines when K gt 3 then 3 CALL HQUAD ID CHOPT MODE SENSIT SMOOTH NSIG CHISQ NDF FMIN FMAX IERR Action This routine fits multiquadric radial basis functions to the bin contents of a histogram or the event density of an Ntuple For Ntuples this is currently limited to simple ones 1 with 1 2 or 3 variables all events are used no selection mechanism is implemented Thus the recommended practice at the moment is to create a simple Ntuple and fill it from your master Ntuple with the NTUPLE LOOP command and an appropriate SELECT FOR function Routine HQUAD is called automatically in paw by the existing command SMOOTH For a complete description of the method see reference 16 Input parameters ID Histogram or Ntuple ID CHOPT Character variable containing option characters 0 Replace original histogram by smoothed 134 MODE Chapter 7 Fitting parameterization and smoothing 2 Donotreplace original histogram but store values of smoothed function and its parameters The fitted function is regenerated from the values or the parameters with the FUNC option HISTOGRAM PLOT for histograms or with NTUPLE DRAW for Ntuples V Verbose Mode of operation 0 Sameas MODE see below 3 find significant points a
89. thus the proportional error on the bin contents gt w2 wj is greater than the 1 v N obtained from unweighted Poisson statistics and this effect get worse as the spread of weights w 172 gets larger Fluctuations in a small number of events with large weights will swamp the information obtained from low weight events Thus in any application the spread in weights for a source in a bin should be small and this means that the resulting uncertainty in its value will also be small Some insight be gained by noting that in the set of Equations 7 19 7 22 the weights always appear together with the p Equation 7 20 can be multiplied by p to make this explicit Thus if the weights are all too high by some factor the strengths will be low by exactly the same factor So the error in the p estimates resulting from uncertainties in the weights is of the same order as that uncertainty and in any application this should be small In HMCINT the weight distributions provided are normalised so that N i i and the normalisation factors These should always be 1 unless there is an efficiency component to the distribution are preserved Inclusion of weights is then regarded as a two stage problem 1 The fitting of the reweighted Monte Carlo distributions to the data distribution in which the Monte Carlo normalisation is preserved to find a set of fractions These correspond to the fractions
90. with respect to p m 0 Vj 7 10 and those for the differentials with respect to Aj dipj 1 0 Vij 7 11 7 138 Chapter 7 Fitting parameterization and smoothing These m x n 1 simultaneous equations are nonlinear and coupled remembering that the f that appear in them are functions of the p and the A However they can be remarkably simplified Equations 7 11 can be rewritten 1 E 1 fi The left hand side depends only so write it as t 1 7 12 di 7 13 i fi The right hand side then becomes ds dc 7 14 HII 7 14 which is a great simplification for a given set of pj the n x m unknown quantities Aj are given by the n unknown quantities The t are given by Equation 7 13 If d is zero then t is 1 if not then di e j gt 1 pit 7 15 If these n equations are satisfied with Equation 7 14 used to define the A then all the m x n Equa tions 7 11 are satisfied The method adopted by HMCLNL is for a given set of p to solve equations 7 15 for the thus giving the A via equation 7 14 The log likelihood may then be calculated using equation 7 9 The maximum of the likelihood may then be found using numerical means HMCMLL uses MINUIT to perform this maximisation this is equivalent to solving equations 7 10 Although there are n equations 7 15 to be solved n
91. 0 CALL HBNAME 20 0 CLEAR CALL HBNAME 20 VECT V1 SET Enter user code here END File nt20p f REAL FUNCTION NT20 lt sk ok oR oK sk sk 5k oR PK 9k 5k ok OR PK 5k 9k FOR ROROROR kkk kkk k kkk k This file was generated by HUWFUN OO ok kkk kkk kkk kk N tuple Id 20 N tuple Title 1 block 20 variable N tuple Creation 11 06 92 18 46 10 lt sk ok oR oR sk sk 5k oR PK 9k K FOR lt COMMON PAWIDN IDNEVT VIDN1 VIDN2 VIDN3 VIDN 10 REAL V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15 V16 V17 V18 V19 V20 COMMON PAWCR4 V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15 V16 V17 V18 V19 V20 3 6 Ntuple operations 41 Enter user code here NT20 1 END 3 5 4 Optimizing event loops paw 15 able before starting the loop over the events to find out which are the columns of the CWN which are actually referenced in any given query command line selection expression or COMIS routine Only the columns which are referenced will be read from the file If you analyse Ntuple data without it is your own responsibility to find out and specify which are the columns referenced via the routines HGNTV or HGNTB if all variables in a block are ne
92. 0 1 1000 CALL HBFUN2 200 TEST OF HRNDM2 100 0 1 40 0 1 HTFUN2 CALL HSCALE 200 0 CALL HCOPY 200 20 CALL HBOOK2 210 HIST FILLED WITH HFILL AND HRNDM2 100 0 1 40 0 1 30 Filling DO 10 1 5000 X HRNDM1 100 CALL HFILL 110 X 0 1 CALL HRNDM2 200 X Y CALL HFILL 210 X Y 1 CONTINUE Save all histograms on file hexam dat CALL HRPUT O hexam dat N CALL HDELET 100 CALL HDELET 200 Printing CALL HPRINT 0 END FUNCTION HTFUN1 DOUBLE PRECISION HDFUN1 4 2 Filling Operations HTFUN1 HDFUN1 X END FUNCTION HTFUN2 X Y HTFUN2 HTFUN1 X HTFUN1 Y END DOUBLE PRECISION FUNCTION HDFUN1 X COMMON HDEXF C1 C2 XM1 XM2 XS1 XS2 DOUBLE PRECISION C1 C2 XM1 XM2 XS1 XS2 A1 A2 X1 X2 A12 0 5 X XM1 51 2 A2 0 5 X XM2 XS2 2 IF A1 LT 20 THEN X1 0 ELSEIF A1 GT 20 THEN X1 1 E5 ELSE X1 C1 EXP A1 ENDIF IF A2 LT 20 THEN X2 0 ELSEIF A2 GT 20 THEN X2 1 E5 ELSE X2 C2 EXP A2 ENDIF HDFUN1 X1 X2 END 69 TEST OF HBOOK m N IN N N GO G O dS gt dS gt O1 O O 00 00 00 0 CHANNELS Output Generated HRNDM1 ID 10 DATE 17 12 91 75 5 25 75 5 25 75 5 25 75 5 25 75 5 25 75 5 25 75 5 25 75 25 75 5 25 75 5 25
93. 0 GO TO 99 3 3 More general Ntuples Column Wise Ntuples CWN 25 3 33 More general Ntuples Column Wise Ntuples CWN A CWN suppotts the storage of the following data types floating point numbers REAL 4 and REAL 8 integers bit patterns unsigned integers booleans and character strings Data Compression Floating point numbers integers and bit patterns can be packed by specifying a range of values or by explicitly specifying the number of bits that should be used to store the data Booleans are always stored using one bit Unused trailing array elements will not be stored when an array depends on an index variable In that case only as many array elements will be stored as specified by the index variable For example the array definition NHITS NTRACK defines NHITS to depend on the index variable NTRACK When NTRACK is 16 the elements NHITS 1 16 are stored when NTRACK is 3 only the elements one to three NHITS 1 3 are stored etc Storage Model Column wise storage allows direct access to any column in the Ntuple Histogramming one column from a 300 column CWN requires reading only 1 300 of the total data set However this storage scheme requires one memory buffer per column as opposed to only one buffer in total for an RWN By default the buffer length is 1024 words in which case a 100 column Ntuple requires 409600 bytes of buffer space In general performance increases with buffer size Therefore one should tune th
94. 0 IIOIIIO OII I0 II 0 1111111111222222222233333333334 ALL CHANNELS MEAN VALUE 1234567890123456789012345678901234567890 0 4556 04 0 2331 02 1 9 2 2 0 8 2 2 4 2 4 0 UNDERFLOW R DAT 5 2 5 6 2 T 2 0 0000 00 0 9558 01 17 12 91 UNDERFLOW R M S 0 0000 00 0 9558 01 2 8 8 3 0 4 3 2 0 3 3 6 OVERFLOW NO 11 OVERFLOW 0 0000 00 0 0000 00 4 3 Editing operations TEST OF PRINTING OPTIONS 91 HBOOK ID 1000 DATE 17 12 91 NO 12 100 1 1 1 1 2 3 10 1 1 1 1 2 3 3 5 6 T 0 2 25 9 1 1 2 2 3 3 5 6 7 0 2 5 9 5 1 9 9 0 5 8 9 1 6 0 5 1 9 0 3 9 0 5 38 09 1 6 8 1 1 4 0 8 4 5 1 2 0 0 1 6 8 1 1 4 0 9 5 5 2 2 1 2 0 38 0 9 9 3 9 3 LOW EDGE INTEGRAT ERRORS mu oras usu sashes leslie sls lee lea 3 2 1 414 4 4 1 414 5 10 2 449 6 18 2 828 7 32 3 742 8 61 5 385 I 0 I 9 106 6 708 I 0 I 10 179 8 544 I 0 I 11 295 10 77 I 0 I 12 485 13 784 I 0I 13 725 15 492 IOI 14 1008 16 823 IOI 15 1336 18 111 IOI 16 1640 17 436 IOI 17 1925 16 882 IOI 18 2151 15 033 1 0 19 2337 13 638 10 20 2484 12 124 10 21 2608 11 136 10 22 2690 9 055 1 0 23 2738 6 928 I 0 I 24 2778 6 325 I 0 I 25 2825 6 856 I 0 I 26 2873 6 928 I 0 I 27 2916 6 557 I 0 I 28 2985 8 307 I 0 I 29 3079 9 695 10 30 3192 10 63 I 0I 31 3319 11 269 I 0I 32 3431 10 583
95. 000 You can use option Q to change this A file declared with HROPEN must be released with HREND HROPEN calls HRFILE internally CALL HRFILE LUN CHTOP CHOPT Action Establishes a temporary unique correspondance between a logical unit and a top directory name Users should call HROPEN instead of HRFILE By default HROPEN HRFILE creates new files option N with the maximum number of records set to a large number default 32000 If this is insufficient the user can override this value by specifying the Q option and setting IQUEST 10 to the actual number of records required up to a maximum of 65K Overriding the default record allocation COMMON QUEST IQUEST 100 Declare IQUEST communication vector IQUEST 10 65000 I require 65000 records CALL HROPEN 1 FILE file ext NQ 1024 ISTAT Call HROPEN Note that after a call to HROPEN HRFILE if CHTOP MYDST for example the current directory is set to MYDST If LUN is an existing file one can change the current directory to an existing subdirectory SUBDIR using CALL HCDIR SUBDIR setting the current directory CD to CHTOP SUBDIR contents of a directory is listed using routine HLDIR A new subdirectory can be created with routine HMDIR The current directory in memory PAWC and hence on the direct access files may be set by one of the routines HCDIR or HMDIR Note that when calling HCDIR or H
96. 1 12 13 14 15 16 17 Lamport A Document Preparation System 2nd Edition Addison Wesley 1994 document CN ASD Group HIGZ HPLOT Users Guide nProgram Library Q120 and Y251 CERN 1993 1 1 6 CN ASD Group PAW users guide nProgram Library Q121 CERN October 1993 1 3 various authors SUMX User s Manual nProgram Library Y200 CERN 1976 1973 Rev 1976 R Brun Hansroul and P Palazzi HBOOK users guide Version 1 2 nProgram Library Y250 CERN 1973 1 1 R Brun M Hansroul P Palazzi and B Peuchot HBOOK users guide Version 2 nProgram Library Y250 and DD 75 11 CERN 1975 1 1 R Brun I Ivanchencko and P Palazzi HBOOK users guide Version 3 nProgram Library Y250 DD 77 9 CERN 1977 1 1 R Brun I Ivanchencko D Lienart and P Palazzi HBOOK users guide Version 3 Revised nProgram Library Y250 and DD EE 81 1 CERN 1984 1 1 R Brun and D Lienart HBOOK users guide Version 4 nProgram Library Y250 CERN 1987 1 1 CN ASD Group and J Zoll ECP ZEBRA Users Guide nProgram Library 0100 CERN 1993 1 1 13 8 1 8 2 8 4 W T Eadie D Drijard F James M Roos and B Sadoulet Statistical Methods in Experimental Physics North Holland 1971 6 2 2 7 2 3 CN ASD Group MINUIT Users Guide nProgram Library D506 CERN 1993 7 1 J H Friedman Data Analysis Techniques for High Energy Particle Physics In CERN editor Proceedings of
97. 1 IF ABS A2 GT 0 0001 X2 C2 EXP A2 Return function value HTFUN1 X1 X2 RETURN END Figure 1 2 Writing data to HBOOK with the creation of a HBOOK RZ file Filled according to HTFUN1 Fill according to HTFUN2 HBOOK ID 110 DATE 02 09 89 2 ID 210 DATE 02 09 89 4 340 CHANNELS 100 0 330 I 10 0 320 II 310 II 300 1 ove 290 I 1 280 r E 3 32 270 I 1 928 2 422 2 22 2 2 260 I I NE 2 250 4 1 875 240 I I 185 230 I 1825 220 I 1 8 210 r I DS gt 1 2 E 4 7 8 E 200 1 I 1 190 I 1 180 170 160 150 140 130 CHANNELS 100 0 o 1 1 1234567890123456789012 CONTENTS 100 LOW EDGE 1 10 1 0 0123456789 UND UND ENTRIES BIN WID 0 10 Figure 1 3 Output generated by job HTEST 1 5 batch as the first step of the analysis 11 1 5 1 Adding some data to the RZ file A second run using program HTEST1 below shows how to add some data to the HBOOK RZ file created in the job HTEST Figure 1 2 After opening the file HTEST DAT created in the previous run in update mode U option with the name EXAM2 a new directory NTUPLE is created known as EXAM2 NTUPLE as seen in the output of HLDIR command at the end of the output One dimensional 10 and two dimensional 20 histograms and an Ntuple 30 are booked Each Ntuple element or event is char acterised by three variab
98. 100 VZERO X 51 50 HPAK 1 X HPHIST 1 HIST 1 VZERO Y 50 146 o o X X 10 Chapter 7 Fitting parameterization and smoothing CALL HPAK 2 Y CALL HPHIST 2 HIST 1 adds 1 and 2 Identifier 3 is created and will contain result of addition CALL HOPERA 1 2 3 1 1 CALL HCOPY 3 4 PAR 1 PAR 2 PAR 3 PAR 4 PAR 5 PAR 6 Fits 3 with function HFUNF similar to example 2 Initializes parameters Prints results of the last iteration Superimpose result of fit to the histogram The result of this fit can be compared with the initial parameters of example 2 40 20 O CALL HFITH 3 HFUNF V 6 PAR 1 ST PMI PMA SIGPAR CHI2 CALL HPHIST 3 HIST 1 NY 0 Fits a two dimensional distribution xf yf with HFITN initialize parameters Prints results of the last iteration Errors EY automatically computed as SQRT yf DO 10 J 1 40 DO 5 I 1 100 CONT HIJ 210 1 J IF CONT EQ 0 GOTO 5 NY NY 1 YF NY CONT EY NY SQRT CONT CALL HIJXY 210 1 J X1 X2 XF NY 1 X140 005 2 2 0 0125 CONTINUE CONTINUE PAR 1 PAR 2 PAR 3 PAR 4 PAR 5 PAR 6 43 T 07 12 I O O O O CALL HFITV NY NY 1 XF YF EY HFUNFV V 6 PAR 1 ST PMI PMA SIGPAR CHI2 Get covariance matrix of last fit from Minuit Minuit parameters on 4 byte machines are Double precision CALL MNEMAT COV 6
99. 1000 01 26 I 25 24 II ITI II 23 II II II I 22 I 21 OI II II I 20 IO II IO I 19 II 00 OI I 18 II IIIIIII 0 17 IIIIIIIIII I II 16 I IIIIIIIIIII 15 IIIII IIII LP Ep 14 I 0 OOII II II 13 01 0 I 1110 II 0 12 I ILII I L I O 11 I I I Or IIII 10 IIOI I IL II III TII IL ITIII I 9 I IIO 010 10 III IIOI I 8 I III IIIIO IIIII IT II 001 I I 7 0 III 10111 0 0 I IIIO 0 I 6 I OI IIIII I I IIIIII II O IIIIIII IIIIII 5 I III I 0100 ITIITTIOIO 111111111110 4 De IIIIIOII IIIIIIOO III I I 00 11000001 1111 It T 3 0 I IIIOI 0100011 0 OOIIIIII IOII 18 xL 2 I IIIOIIIO OOIIOIIOIIIOIII 0 I II IIIIIII IOIOO IIOO IO 1 0 OOIO I IO TI I0 I OI II OOII OI CHANNELS 100 0 1 10 0 1 2 3 4 5 6 7 8 9 0 1 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 CONTENTS 10 11 221111121111 1111 1 1 3112133273069103994904423575582243213233324149575927931268388974473344444512322 1122 12 LOW EDGE 1 111111111122222222223333333333444444444455555555556666666666777777777788888888889999999999 10 1 0 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789 ENTRIES 542 ALL CHANNELS 0 5420E 03 UNDERFLOW 0 0000 00 OVERFLOW 0 0000E 00 BIN WID 0 1000E 01 MEAN VALUE 0 4760E 00 5 0 2167E 00 43 Editing ope
100. 12 91 2 2 2 4 5 T 0 6 2 2 8 8 3 0 4 3 2 0 NO 3 3 6 10 LOW EDGE I I 1 1 1 I 1 1 I I I I 1 1 1 1 I 1 I I 1 1 O O P gt gt O O QY gt QO N N WWWWWWWWWWNNNNNNNNN O O 5 Q gt O OON O Q Q gt 40 LOW EDGE 100 10 1 ENTRIES BIN WID I I 0 I 01 01 IOI 10 10 1 0 1 0 1 0 I 0 I 1 0 1 0 1 1 3 6 2 40 0 1000E 01 TEST OF PRINTING OPTIONS HBOOK 354 316 281 251 223 199 177 158 141 125 112 100 O S Q O O O NNNWWW Q O O p Q OQ gt O HE O O ND gt O1 CO LOW EDGE ENTRIES BIN WID ID 814 228 838 189 872 526 828 489 254 893 202 125 433 795 096 234 119 668 811 481 623 184 119 387 953 783 849 125 589 22 913 943 079 31 623 012 467 981 548 162 818 512 239 10 1 II II II 00 1000 HHOHH 10 01 40 1000 01 HHOH HOH HOH NER ALL CHANNELS MEAN VALUE or 0100 I II 01001 10110 Lees HOH 0 1 6 0 1 7 6 0 4556 04 0 2331 02 0010001
101. 22032539736953183588893942434650812591167574 111111111122222222223333333333444444444455555555556666666666777777777788888888889999999999 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789 5000 ALL CHANNELS 0 5000E 04 UNDERFLOW 0 0000E 00 OVERFLOW 0 0000E 00 1000E 01 MEAN VALUE 0 4834E 00 R M S 0 2184E 00 0 7284E 02 I I I I I I I I 1 DATE 17 12 91 NO 19 I I 0 II IIII OIIII III IOI III IOI 00 I II I I III I 01 I I II 0 I 00 II OI I I I I 0 III I I O I III IO I II I I 0 TI 1 0 TI 01 I 10 10 TIT III IIO 01 OI III I I I I I II I 100 OIOI II 1011 IOI IIIII III IIIOII 0 001 OO II I IOI I OI 0 I I I III II OI I I 0 OI 11 0 00 110 0 II I I 0 OI O IOI IOI I I 0 IOI OI I II I OII OI 0 I 1 0 O 0 IO O I 01 IIO 0 0 1 2 3 4 5 6 7 8 9 0 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 1111111111111 112224658012445755432099687543222121221233455666557776678686676664543343222221111 2112462681814760682821271047851155222577164987185092203253973695318358889394243465081
102. 234567890123456789 I I ENTRIES 5000 PLOT SATURATION 31 5000 SCALE 2 3 A B STATISTICS I 2 IT STEP 1 00 MINIMUM 0 000 I I More booking examples SUBROUTINE HEXAM3 Get all histograms saved in example 2 CALL HROPEN 1 HEXAM hexam dat U 1024 ISTAT CALL HRIN 0 9999 0 CALL HMDIR HEXAM3 S Print an index of all histograms that are now in memory CALL HINDEX Reset hist 110 and 210 adds more options CALL HRESET 110 CALL HRESET 210 CALL HIDOPT 110 STAT CALL HBARX 210 CALL HBPROX 210 0 CALL HBSLIX 210 3 1000 CALL HBANDY 210 0 1 0 5 0 CALL HIDOPT O 1EVL New filling DO 10 I 1 2000 74 Chapter 4 Advanced features for booking editing operations CALL HFILL 110 HRNDM1 10 0 1 CALL HRNDM2 20 X Y CALL HFILL 210 X Y 1 10 CONTINUE Print new contents using specialized printing routines Same result could be obtained using HISTDO HPRINT 0 HPHS CALL HPHIST 110 HIST 1 CALL HPSCAT 210 CALL 210 PROX 1 CALL 210 BANY 1 CALL 210 SLIX 0 Save all histograms in new directory HEXAM3 CALL HROUT O ICYCLE gt CALL HREND HEXAM CLOSE 1 END Output Generated 1 TEST OF HRNDM1 100 32 i 100 0 000 00 0 100 01 64912 146 2 TEST HRNDM1 10 32 100 1
103. 2591167574 111111111122222222223333333333444444444455555555556666666666777777777788888888889999999999 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789 5000 1000E 01 0 9674E 02 ALL CHANNELS MEAN VALUE 0 5000E 04 0 4834E 00 UNDERFLOW R M S 0 0000 00 0 2184 00 OVERFLOW 0 0000E 00 Chapter 8 Memory Management and input output Routines 81 Memory usage and ZEBRA The hbook system uses the zebra data manager to store its data elements ina COMMON block PAWC shared with the kuip and higz packages when the latter are also used as is the case in paw In fact the first task of a hbook user is to declare the length of this common to zebra by a call to HLIMIT as is seen in figures 1 2 and 1 4 In the PAWC data store the hbook higz and kuip packages have all their own division see 10 for more details on the notion of divisions as follows see figure 8 1 LINKS Some locations at the beginning of PAWC for zebra pointers WORKS Working space or division 1 used by the various packages storing information in PAWC HBOOK Division 2 of the store Reserved to hbook HIGZ division reserved for the higz graphics package This division only exists when higz is called KUIP division reserved for the kuip user interface package This division only exists when kuip is called SYSTEM The zebra system division It contains some tables as well as the Input Ou
104. 3456789012345678901234567890123456789012345678901234567890 111111111211211121111111 1 112233456889131356586199288608541122964655231111 1 2224268062313614000760053587389243868095597245890427768955738341 11 1 111111111122222222223333333333444444444455555555556666666666777777777788888888889999999999 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789 0 0000E 00 OVERFLOW 0 0000 00 0 9985E 01 5000 ALL CHANNELS 0 5000E 04 UNDERFLOW 0 3984 00 R M S 0 6987 02 153 Example of parametrization and smoothing SUBROUTINE 6 PARAMETRIZATION E SMOOTHING gt R Brun DOUBLE PRECISION COEFF DIMENSION ITERM 15 COEFF 15 Get hist 110 from data base CALL HRGET 110 hexam dat Find best parametrization of histogram in terms of powers of shifted Tchebychev polynomials also produces the corresponding fortran function here on standard output 154 Chapter 7 Fitting parameterization and smoothing CALL 110 1 CALL HSETPR PNBX 15 CALL HSETPR PNCX 15 CALL HSETPR PLUN 31 CALL HPARAM 1 3011 1 14 COEFF ITERM NCO CALL HPRINT 1 ID 2 is smoothed with B splines Statistical errors sqrt of contents are drawn CALL HCOPY 110 2 CALL HSPLI1 2 2 14 3 CHI2 CALL HIDOPT 2 ERRO CALL HPHIST 2 HIST 1 END Output Genera
105. 36 43 149 convolution 37 disk resident 19 20 duplicate 37 192 identifier 4 memory resident 19 20 operation 37 rename column 37 reset 16 Row Wise Ntuple 17 19 20 22 27 31 35 37 39 149 Ntuple type 81 null hypothesis 91 NWBUFF 17 20 NWPAWC 140 one dimensional histogram 13 online 146 OS9 159 output 146 overflow 88 packing 4 13 56 57 parameter errors fit 105 parameter type 4 parametrization 110 116 pathname 151 PAW 1 17 20 22 27 30 34 36 43 51 53 70 99 103 104 107 118 139 150 151 153 156 158 server 159 PAW 151 PAWC common 3 4 17 18 23 53 87 116 139 140 142 153 156 common 153 51 PFUN 52 Poisson distribution 98 polynomial fit 100 presenter 155 157 159 print 14 profile histogram 48 projection 56 139 QUEST see IQUEST random number generation 119 120 real type 4 rebinning 86 INDEX regressor 111 remote file 158 login 158 159 shell 158 159 Rename column in Ntuple 37 Reset histogram 16 Ntuple 16 resize command VMS 151 RLOGIN 158 159 ROTA 75 76 RSHELL 158 159 RWN see Ntuple Row Wise Ntuple RZ file 17 RZ package of ZEBRA 146 RZPURG 149 saturation 91 scatter plot 2 server 159 shared memory 156 157 slice 56 Smirnov Cramer Von Mises test 91 smoothing 116 119 standard deviation 81 88 STAR 72 STAT 51 55 70 88 89 subscract histogra
106. 5 Accessing Information Example CALL HREBIN 25 11 85 This call will regroup channels 11 to 85 three by three 25 bins and return new abscissa contents and error values in the output arrays In this case the errors in X will be equal to 1 5 BINWIDTH CALL HREBIN ID X Y EX EY NCHAN 1 NCHAN This example shows a convenient way using one subroutine call to return the abscissa contents and errors for 1 dimensional histogram Note that in this case the errors in X are equal to 0 5 BINWIDTH 5 12 Integrated contents VARIAB HSUM ID Action Returns the integrated contents of a histogram without underflow and overflow In the case of a 2 dimensional histogram the returned value does not take into account projections Input parameter ID Histogram identifier 5 13 Histogram definition CALL HDUMP ID Action Prints a dump of the HBOOK storage area corresponding to a given histogram Input parameter ID Histogram identifier 0 will dump the whole of the HBOOK central memory storage area CALL HGIVE ID CHTITL NX XMI XMA NY YMI YMA NWT Action Returns the booking parameters and address of a given histogram Input parameter ID Histogram identifier cannot be zero Output Parameters CHTITL Histogram title must be declared CHARACTER 80 NX Number of channels in X XMI Lower edge of first X channel XMA Upper edge of last X channel NY Number of c
107. 5 and Y 0 5 is uniform the same argument goes for Y uniformly distributed between Y and Y 1 this could be useful for instance for the case where Y are ADC measurements 4 1 3 Rounding CALL HBINSZ YES NO Action Round the bin size for bookings of subsequent histograms to a reasonable value i e 1 1 5 2 2 5 4 5 times an integer power of 10 HBINSZ controls a switch that when on rounds the binsize still respecting the number of bins The switch is initially off Input parameters YES enable the reasonable rounding feature disable the reasonable rounding feature 41 4 Projections Slices Bands 56 Chapter 4 Advanced features for booking editing operations CALL ID VMX Action Books the projections of a 2 dimensional histogram as two 1 dimensional histograms Input parameters ID identifier of an existing 2 dimensional histogram ID 0 means book projections for all existing 2 dimensional histograms VMX upper limit of single channel content Remark if ID does not exist or is a 1 dimensional histogram the call does nothing see for details about VMX booking of projections can be executed only after the 2 dimensional histogram with identifier ID has been booked CALL HBPROX ID VMX and CALL HBPROY ID VMX Action Books projection onto X or Y only See HBPRO for more details CALL HBANDX ID YMI YMA VMX Action Books a projection onto
108. 555544443333222 2233455666666665543322 2222222333333333333222222 Pate ee eh So ede i Oe te 0000000000111111111122222222223333333333444444444455555555556666666666777777777788888888889999999999 71 72 Chapter 4 Advanced features for booking and editing operations 0 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789 ENTRIES 4000 PLOT I I SATURATION INFINITY I 422 3271 SCALE 2 3 A B STATISTICS I I STEP 0 400 01 MINIMUM 0 000 4 2 Filling Operations 73 HIST FILLED WITH HFILL AND HRNDM2 HBOOK ID 210 DATE 17 12 91 NO 7 CHANNELS 100 U 0 10 10 NO 1 2 3 4 5 6 7 8 9 1 D 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 E gt K ok ok ok ok ok ok ok ok CO KOR R a a OVE OVE 975 40 95 224 2 2 2 39 925 2 24 ttt 38 9 2222 3 33 2 4 2 2 37 875 2
109. 5555666666555554443332222 23445789 AABCCCCBBA987 6543222 2222333344455555666666555554443332222 233456789ABBBBBBA98765443222 222233344445555555555555544443332222 2234567889 98876543322 2222333344445555555555444433332222 2334567789999998776544322 22223333344444444444444333332222 223345567778877765543322 2222233333333443333333322222 i aksa 222222233333333332222222 2222222222222222 Se oo te eee oe ettttt 4 4 22222222222222 44 4 4 4 23344566777777665543322 2222223333333333333333222222 233456789 98765443222 222233344445555555555555544443332222 2345689BCDFFGHHGGFDCB98754432222222233344455667777888888887777665544433222 234578ACEGHJKLLLLKJHGECA97654332222333445566778899AAAAAAAAAA99887766554433222 2235689BDGIKLNODOONLKIGECA8754433333334455677899AABBBCCCCCCBBBAA998776554433222 2235689BDGIKLNODOONLKIGECA8754433333334455677899AABBBCCCCCCBBBAA998776554433222 234578ACEFHJKLLLLKJHGECA97654332222333445566778899AAAAAAAAAA99887766554433222 2345689ACDEFGGGGFEDCB98754432222222223344455666777888888887776665544433222 223456789AABBBBAA9876543322 22223333444455555555
110. 67890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 111123234456566654443432111 1 1 11 11211112233223333322332222122111111 1 11 3154368221187867616584443348583959815682574502969683732245966025146893294712079898422 111111111122222222223333333333444444444455555555556666666666777777777788888888889999999999 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789 2000 0 1000 01 ALL CHANNELS MEAN VALUE WITH HFILL AND HRNDM2 U N D 210 0 0 1 2 3 0 2000E 04 0 4911E 00 4 UNDERFLOW R M DATE 5 S 0 0000 00 0 2207 00 17 12 91 6 0 NI NO VERFLOW EQUIVAL 2 8 0 0000E 00 0 2000E 04 9 10 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 RO 0 0 ooo IOI IIIa AI ka ak 4 4 4 4 ES 2 22 4 2 2 2 3 42 2 2 5 2
111. 83588893942434650812591167574 111111111122222222223333333333444444444455555555556666666666777777777788888888889999999999 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789 Output Generated DATE 18 05 92 HHHHI HHHH UNDERFLOW 0 0000 00 OVERFLOW 0 0000E 00 R M 5 0 7466E 01 DATE 18 05 92 NO 15 I gt IT Ec II I Tels II IL I Lote LL TA 1 TL t X T Tzi 1 T Ket I I I I I I I I St 1 I I I I I I I I SI 1 1815 ES I rc L I I I I 1 Il I TL Tes III ISTE II I I I I I I I I I I I 5 6 T 8 9 NO 14 150 Chapter 7 Fitting parameterization and smoothing ENTRIES BIN WID 100 ALL CHANNELS 0 1000E 01 MEAN VALUE 0 2175E 04 UNDERFLOW 0 7102 00 R M S 0 0000 00 OVERFLOW 0 0000 00 0 1063E 00 7 7 Fitting with finite Monte Carlo statistics MINUIT RELEASE 90 10 INITIALIZED DIMENSIONS 100 50 0 89 15 1 SET EPS 0 1000 06 FLOATING POINT NUMBERS ASSUMED ACCURATE TO 0 100E 06 Function minimization by SUBROUTINE HFITH Variable metric method ID 3 CHOPT V Convergence when estimated distance to minimum EDM LT 0 10 03 PARAMETER DEFINITIONS NO NAME
112. 999999 1 CALL HPR0J2 20 30 0 0 1 999999 1 2 CALL HPRINT 0O CALL HROUT 10 ICYCLE CALL HROUT 20 ICYCLE 9 CALL HLDIR CALL HREND HEXAM7 CLOSE 1 END Output Generated TEST1 HBOOK ID 10 DATE 17 12 91 0 20 250 gt Tim 240 lI I 230 220 set TS 210 1 200 T 190 esr I 180 II I aL 170 160 150 T I 140 i gt lt 130 I 120 I I 110 T I 100 90 T 80 I T 70 AT Ket 60 50 e251 e 40 ga S 30 I 20 E S I 10 I I I CHANNELS 100 0 1 10 0 1 2 3 4 5 6 7 8 9 0 1 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 CONTENTS 100 111111111111122222222222222222222211111111111 10 1 1111221234344665789911044677997990122303341234324100018734232120186756443432222111111 1 1591794631142995679730577637087033910061276900757760757337734725809812493999812692748547445127656864 LOW EDGE 1 3222222222222222211111111111111111 111111111111111112222222222222222 0 0988776554432211099887665543322100998776654433211000112334456677899001223345566788990112234455677889 0 0482604826048260482604826048260482604826048260482606284062840628406284062840628406284062840628406284 ENTRIES 10000 ALL CHANNELS 0 9979 04 UNDERFLOW 0 1000 02 OVERFLOW
113. AR STEP PMIN PMAX SIGPAR CHI2 where 1 in the second argument Pn 7 4 Parametrization In analyzing experimental data it is sometimes very important to be able to parametrize relationships among data by means of linear combinations of elementary functions One of these expansions is the well known Taylor series which is an expansion of an analytic function using as elementary functions regressors the powers of the independent variables In the case of the Taylor series the coefficients of the linear combination are a well known expression involving the derivatives of the function to be represented at a given initial point Even if the Taylor series is very powerful for its noticeable features and its analytical simplicity from the point of view of the numerical analist it might be not the best expansion in terms of elementary functions Ideally one would like to use the smallest possible number of regressors in order to describe the relationship among data with a given precision and this is not always guaranteed using the Taylor series Another feature of the monomials is that they do not form a complete orthonormal set of functions in the sense of the Hilbert spaces while other functions which possess this feature may be more computationally convenient to use The entries HPARAM for histograms and scatter plots and HPARMN for n dimensional distributions perform regressions on the data in order to find the best parametrizat
114. ATA 11 CHARACTER 4 CHDIV CHDIVS 13 CHNAT CHNATS 15 DATA CHDIVS AG DG EF EP FI LEP PE PS SPS ST 15 DATA CHNATS CH DE DK ES FR GB GR PIT CNL NO SE ZZ CALL HLIMIT NWPAWC OPEN 11 FILE aptuple dat STATUS OLD OPEN 12 file hlabexa ps form formatted status unknown CALL HBOOK1 11 Example HLABEL explicit list 13 1 14 0 CALL HBOOK1 12 Example HLABEL implicit list 1 0 1 0 CALL HBOOK2 21 Example HLABEL 2 D 13 2 15 13 1 14 0 CALL HLABEL 11 13 CHDIVS 66 Chapter 4 Advanced features for booking editing operations CALL HLABEL 21 13 CHDIVS NY Loop over input data DO 10 IEVENT 1 99999 READ 11 10F4 0 F7 0 END 20 RDATA CHDIV CHDIVS INT RDATA 2 IGRADE RDATA 7 CALL HFC1 11 0 CHDIV 1 CALL HFC1 12 0 CHDIV 1 CALL HFC2 21 IGRADE 0 CHDIV 1 10 CONTINUE 20 CALL HLABEL 12 0 SV Call the HPLOT HIGZ routines to print the histos showing the labels CALL HPLINT 0 CALL HPLCAP 12 CALL HPLSET VSIZ 0 20 CALL HPLSET NDVX 13 05 CALL HPLSET HCOL 1105 CALL HPLSET BCOL 1 5 CALL HPLSET FON 60 CALL HPLOPT NBOX 1 CALL HPLZON 2 2 1 CALL HPLOT 11 0 CAL
115. BLAC when HIDOPT ID BLAC is called FUNC when HBFUNI HFUNC or HIDOPT ID STAR have been called gt STAR when HBFUNI HFUNC HIDOPT STAR have been called CHAR Character chosen Example CALL HPCHAR STAR Replaces the asterisk with a dot in all histograms with the HIDOPT STAR option selected CALL HBIGBI ID NCOL Action For a given 1 dimensional histogram prints one channel over a certain number of columns Input parameters ID Histogram identifier NCOL Number of columns to be used per bin NCOL 0 meams use the full width of the page Remark HBIGBI will be applied to histograms output across the page only i e if NCHAN NCOL lt 100 If this relation is not fulfilled then the value of NCOL will be reduced till it obeys the inequality No restrictions if the histogram is printed down the page HIDOPT ID ROTA If the histogram is 2 dimensional the bigbin option is selected on all its projections etc It can be redefined at any time 4 3 Editing operations 83 4 3 4 Scale Definition and Normalization Note that whenever a multiplication by a power of ten appears in the output it means that the quantity it refers to has been multiplied by that factor before being printed The scaling of the contents while outputing a 1 dimensional histogram is chosen by default to be linear and to span the interval between the minimum and the maximum of th
116. CALL CALL HBOOK1 1 Kernel 1 1D 100 5 0 5 0 0 0 HBOOK2 2 Kernel 2 2D 100 5 0 5 0 100 0 0 100 0 0 0 HBPRO 2 0 0 HBOOK2 3 Kernel 3 2D 100 5 0 5 0 100 0 0 100 0 0 0 HBPRO 3 0 0 HBOOK1 4 Function 100 0 0 100 0 0 0 HBOOK1 5 Result 1 100 10 0 110 0 0 0 HBOOK1 6 Result 2 100 10 0 110 0 0 0 HBOOK1 7 Result 3 100 10 0 110 0 0 0 DO 10 I 1 100000 CALL RANNOR A B CALL HFILL 1 A 0 0 1 0 CALL HFILL 1 B 0 0 1 0 CALL RANNOR A B CALL HFILL 2 A 100 0 RNDM I 1 0 CALL HFILL 2 B 100 0 RNDM I 1 0 CALL RANNOR A B CALL HFILL 3 A 100 0 SQRT RNDM I 1 1 0 CALL HFILL 3 B 100 0 SQRT RNDM I 1 1 0 y 30 0 RNDM I 0 5 50 0 CALL HFILL 4 X 0 0 1 0 10 CONTINUE CALL CALL CALL HCONVOL 1 4 5 TERROR HCONVOL 2 4 6 IERROR HCONVOL 3 4 7 IERROR 43 37 Ntuple examples The first example shows the use of Row Wise Ntuples containing only floating point data Chapter 3 Ntuples Creating and using a RWN SUBROUTINE HEXAM7 DIMENSION X 3 CHARACTER 8 CHTAGS 3 DATA CHTAGS X CALL HROPEN 1 HEXAM7 hexam dat U 1024 15 CALL HBOOK1 10 TEST1 100 3 3 0 CALL 2 20 TEST2 20 3 3 20 3 3 250 CALL HBOOKN 30 N TUPLE 3 HEXAM7 1000 CHTAGS DO 10 1 10000 CALL RANNOR A B 1 X 2 B X 3 A A B B CALL HFN 30 X 10 CONTINUE CALL HROUT 30 ICYCLE 9 CALL HPR0J1 10 30 0 0 1
117. CHI2 115 CALL HFIT1 X Y EY N FUN NP P CHI2 IC SIG 125 CALL HFN ID X 22 CALL HFNOV ID X 23 CALL HFNT ID 31 CALL HFNTB ID CHBLOK 24 CALL 1 ID NID V N 62 CALL HFUNC ID FUN 58 variab hfree global size base common offset 175 CALL 1 ID X WEIGHT 61 CALL 1 ID X WEIGHT ERRORS 61 CALL HF2 ID X Y WEIGHT 61 CALL HGFIT ID NFPAR NPFITS FITCHI FITPAR FITSIG FITNAM 117 CALL HGIVE ID CHTITL NX XMI XMA NY YMI YMA NWT LOC 100 CALL HGIVEN ID CHTITL NVAR CHTAG RLOW RHIGH 35 CALL HGN ID IDN IDNEVT X IERROR CALL ID IDNEVT X IERROR 35 CALL HGNPAR ID CHROUT 35 183 Table 10 1 Routine calling sequences cont Calling Sequence page CALL HGNT ID IROW IERR 37 CALL HGNTB ID CHBLOK IROW IERR 37 CALL HGNTF ID IROW IERR 38 CALL HGNTV ID CHVAR NVAR IROW IERR 38 VARIAB HI ID I 96 CALL HIDALL IDVECT N 93 CALL HIDOPT ID CHOPT 80 CALL HID1 IDVECT N 93 CALL HID2 IDVECT N 93 VARIAB HIE ID I 97 VARIAB HIF ID I 98 VARIAB HIJ ID I J 96 VARIAB HIJE ID I J 97 CALL HIJXY ID I J X Y 98 CALL HINDEX 80 CALL HIPAK1 ID NID IV N 62 CALL HISTDO 18 CALL HIX 1 98 CALL HKIND ID KIND CHOPT 94 CALL HLABEL ID NLAB CLAB CHOPT 60 CALL HLDIR CHPATH CHOPT 161 CALL HLIMAP NWORDS CHNAME 177 CALL HLIMIT NWPAW 158 CALL HLNEXT IDH CHTYPE CHTITL CHOPT 163 CALL HLOCAT ID LOC 158
118. CMLL SET UP VALUE TO 1 20 MCMLL FOR 2 FREE PARAMETERS MINOS MINUIT TASK HBOOK New 11 maximisation FCN 8319 763 FROM MINOS STATUS SUCCESSFUL 72 CALLS 119 TOTAL EDM 0 66 08 STRATEGY 1 ERROR MATRIX ACCURATE EXT PARAMETER PARABOLIC MINOS ERRORS NO NAME VALUE ERROR NEGATIVE POSITIVE 1 P1 0 64665 0 11579 0 11144 0 12598 2 P2 0 35335 0 10932 0 11560 0 10891 ERR DEF 1 2 7 7 4 Example of fits SUBROUTINE 5 7 7 Fitting with finite Monte Carlo statistics 145 50 70 60 50 40 50 20 10 ID Entries D TO S 20 25 MC dist rae 60 20 40 50 20 2 ID Entries qi 1572029 Data dist x x Figure 7 1 Monte Carlo distributions left and data distribution right OPERATIONS ON HISTOGRAMS AND FITTING gt R Brun modified by M Goossens COMMON HFPAR PAR 6 COMMON HFGAUS AG BG DOUBLE PRECISION AG BG CG DIMENSION X 100 Y 100 DIMENSION XF 4000 2 YF 4000 EY 4000 SIGPAR 6 DOUBLE PRECISION COV 6 6 EXTERNAL HFUNF HFUNFV HFUNGA CHARACTER 12 TITL1 DATA CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL TITL1 TITLE OF ID1 GET hist 110 from data base HRGET 110 hexam dat HRGET 210 hexam dat 2 HBOOK1 1 TITL1 100 0 1 0 HCOPY 1 2 TITLE OF ID 2 Gets information from ID 110 and fills new IDs 1 2 HUNPAK 110 X HIST 1 UCOPY X Y
119. COMMON offset Offset with respect to BASE COMMON of the mapped section in words i e BASE COMMON OFFSET is the first word The function value returned is equal to the global section length pages if the procedure was successful or is an errorcode lt 0 if an error occurred 176 Chapter 9 Global sections shared memory 9 2 1 Using PAW as a presenter on VMS systems global section PROGRAM PRODUCE PARAMETER MAXPAGES 100 COMMON PAWC IPAWC 128 MAXPAGES CHARACTER 8 GNAME PAW gt edit produce macro produce ntimes 100 nt ntimes zone 1 2 INTEGER 4 HCREATEG histo plot 10 K histo plot 20 K GNAME GTEST loop WAIT_TIME 1 histo plot 10 U NUMEVT 1000 histo plot 20 U pip Create Global section wait 4 NPAGES HCREATEG GNAME IPAWC 128 MAXPAGES nt nt 1 5 0 THEN if gt 0 goto loop PRINT 1000 GNAME return 1000 FORMAT Global Section A created PAW global sect GTEST ELSE IERROR NPAGES PRINT 2000 TERROR PAW gt exec produce ntimes 20 2000 Global Section Error I6 GO TO 99 ENDIF CALL HLIMIT 128 NPAGES Book histos CALL HBOOK1 10 Testi 50 4 4 0 CALL HBOOK1 20 Test2 50 4 4 0 Fill histos DO 20 I 1 NUMEVT DO 10 1 1 100 CALL RANNOR A B CALL HFILL 10 A 0 1 CALL HFILL 20 B 0 1 10 CONTINUE CALL LIB WAIT WAIT TIME 20 CONTINUE 99 STOP END fort
120. D 20 HMAXIM KIND 5 Automatic binning KIND 21 HMINIM KIND 6 Variable bin sizes KIND 22 HINTEG KIND 7 KIND 23 H2PAGE KIND 8 Profile histogram KIND 24 HIEVLI KIND 9 HBARX KIND 25 HPRSTA KIND 10 KIND 26 HLOGAR KIND 11 HERROR KIND 27 HBLACK KIND 12 HFUNC KIND 28 HSTAR KIND 13 HROTAT KIND 29 HPRCHA KIND 14 HPRFUN KIND 30 HPRCON KIND 15 HPRLOW KIND 31 HPRERR KIND 16 HPRHIS Output parameter KIND Integer array of dimension 32 which will contain the information returned about histogram ID See above for a detailed explanation of its contents 5 6 Contents CALL HUNPAK ID CONTEN CHOICE NUM Action Transfer the contents of a histogram or a selected projection of a 2 dimensional histogram into a local array Input parameters ID Histogram identifier CHOICE Character variable selecting subhistograms irrelevant for the 1 dimensional case HIST 2 dimensional histogram itself Default CHOICE is equivalent to HIST PROX X projection PROY Y projection PSLIX X slice SLIY Y slice gt BANX X band BANY Y band NUM Serial order of the slice or band that is requested If NUM 0 it is assumed to be 1 Output Parameter CONTEN Array to be dimensioned at least to the number of channels of the histogram or projection ie DIMENSION CONTEN NX in the 1 dimensional case and DIMENSION CONTEN NX NY in the 2 dimensional case 96 Chapter 5 Accessing
121. EDGE 0 0 ENTRIES 100 ALL CHANNELS 0 1200 05 0 1000 01 MEAN VALUE 0 5433E 02 1 20 Uo NO 1 2 3 4 D U R INDERFLOW M S 0 0000 00 0 2854 02 DATE 17 12 91 5 6 7 OVERFLOW NO 8 9 0 0000 00 10 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 KK KK k 9IR 8GO TELS 6CIOU 5AFKPU 48CGK0S 369CFILORU 2468ACEGIKMOQS 23456789ABCDEFGHIJK 9IR 8G0 TELS 6CIOU 48CGK0 369CFILO 2468ACEGIK 23456789ABCDEF 9 860 TEL 6 48CG 369CF 2468ACE 23456789A 9 8G 6 48 369 2468 2345 9IR 8GO TELS 6CIOU 5AFKPU 48CGKOS 369CFILORU 2468ACEGIKMOQS 23456789ABCDEFGHI JK 9IR 8G0 TELS 6CIOU 48CGK0 369CFILO 2468ACEGIK 23456789ABCDEF 9 860 TEL 6CI 48CG 369CF 2468ACE 23456789A 9 8G 6 48 369 2468 2345 9IR 860 TELS 6CIOU SAFKPU A48CGKOS 369CFILORU 2468ACEGIKMOQS 23456789ABCDEFGHIJK 9IR 8G0 TELS 6CIOU 5AFKP 48CGKD 369CFILO 2468ACEGIK 23456789ABCDEF 91 860 TEL 6 48CG 369CF 2468ACE 23456789A 9 8G 6
122. HBOOK Alignment of variables declared in CHFORM Variables declared must always be aligned on a word boundary In other words all variables including character strings must be declared in the calling program with alength that is a multiple of 4 bytes Character variable names not their contents are limited to a maximum of 32 characters Variable length Ntuple rows Variable length Ntuple rows and looping over array components are also supported to optimize Ntuple storage and Ntuple plotting Variable row length occurs when arrays in the Ntuple depend on an index variable which varies 3 3 More general Ntuples Column Wise Ntuples CWN 29 Example of a variable row length CWN definition PARAMETER MAXTRK 100 MAXHIT 300 COMMON CMTRK NTRACK NHITS MAXTRK PX MAXTRK PZ MAXTRK XHITS MAXHIT MAXTRK YHITS MAXHIT MAXTRK ZHITS MAXHIT MAXTRK CALL HBNAME ID VARBLOK2 NTRACK 2NTRACK 0 100 NHITS NTRACK 0 300 gt PX NTRACK PY NTRACK PZ NTRACK XHITS 300 NTRACK YHITS 300 NTRACK ZHITS 300 NTRACK In this example the number of elements to store in one Ntuple row depends on the number of tracks NTRACK The call to HBNAME declares NTRACK to be an index variable and that the size of the Ntuple row depends on the value of this index variable Ranges of index variables in a CWN The range of an index variable is specified using lt 1 gt
123. HPDIR CHPATH CHOPT Action Print the contents of a directory This routine calls HPRINT This routine works only for direc tories in local memory or remote RZ files accessed opened via XZRZOP see the CSPACK manual 19 for more information Input parameters CHPATH Character variable or constant specifying the pathname of the directory to be printed CHPATH stands for the current directory CHOPT Character variable specifying the option chosen gt Print the contents of the top directory I Print an index T Print the complete directory tree i e the top directory and its subdirectories Printing list of histograms CALL HPDIR PAWC T Print list of all histograms in PAWC CALL HPDIR C Print list of all histograms in current directory CALL 0 Print histograms current directory CALL HLNEXT IDH CHTYPE CHTITL CHOPT Action Scan the contents of the current directory in memory or on an RZ file Input parameters IDH Must be zero for first call CHTYPE Character variable specifying items to be scanned 1 include 1 D histograms 2 include 2 D histograms W include Ntuples D include subdirectories gt include everything i e equivalent to 12ND 164 Chapter 8 Memory Management input output Routines Output parameters IDH On return contains identifier of next histogram When all histograms are processed a value of Zero
124. I 1 I I 75 L I 5 I I 25 92 Chapter 4 Advanced features for booking editing operations CHANNELS 10 0 1 2 1 1 4 7 9 0 1 2 3 5 6 7 8 9 0 ENTRIES 20 ALL CHANNELS 0 1282E 03 UNDERFLOW 0 0000 00 OVERFLOW 0 0000E 00 BIN WID 0 5000E 01 MEAN VALUE 0 4963E 00 5 0 2391 00 Chapter 5 Accessing Information The information contained in a histogram ntuple can be made available in local Fortran variables with the commands described below It is possible to access channel contents all together or individually and also mean value and standard deviation of 1 dimensional distributions 5 1 Testing if a histogram exists in memory LOGVAR HEXIST ID Action Returns a logical value of TRUE if and histogram exists and FALSE otherwise Input parameter ID Histogram identifier Remark HEXIST has to be declared LOGICAL in the calling routine 5 2 Testing if a ntuple is RWN or a CWN LOGVAR HNTNEW ID Action Returns a logical value of TRUE if IDis a CWN and FALSE otherwise Input parameter ID Ntuple identifier Remark HNTNEW has to be declared LOGICAL in the calling routine 5 3 List of histograms CALL HID1 IDVECT N Action Returns the number and identifiers of all existing 1 dimensional histograms Output Parameters IDVECT Array which will contain the histogram identifiers in booking order Its dimension should be at least equal to the nu
125. ID3 IERROR HCOPY ID1 ID2 CHTITL HCOPYM ID IPAWD IOFSET HCOPYR ID1 ID2 CHTITL IBINX1 IBINX2 IBINY1 IBINY2 CHOPT variab hcreateg global name base common size CALL CALL CALL HDDIR CHPATH HDELET ID HDERIV DERIV 181 page 59 56 56 37 57 57 57 58 82 35 27 27 26 54 22 30 16 16 56 54 56 56 26 56 56 161 83 42 18 174 19 175 163 19 118 182 Chapter 10 Tabular Overview Table 10 1 HBOOK Routine calling sequences cont Calling Sequence page CALL HDIFF ID1 ID2 PROB CHOPT 103 CALL HDIFFB ID1 ID2 TOL NBINS CHOPT NBAD DIFFS 106 CALL HDUMP ID 100 CALL HERMES LERR 87 LOGVAR HEXIST ID 93 CALL ID IBIN CLAB W CHOPT 64 CALL HFC2 ID IBINX CLABX IBINY CLABY W CHOPT 64 CALL HFF1 ID NID X WEIGHT 62 CALL HFF2 ID NID X Y W 62 CALL HFILL ID X Y WEIGHT 17 CALL HFINAM ID CHPNAM NPAR 116 CALL HFITEX ID AA BB CHI2 IC SIG 125 CALL HFITGA ID C AV SD CHI2 IC SIG 125 CALL HFITH ID FUN CHOPT NP PARAM STEP SIGPAR CH2 113 CALL HFITHN ID CHFUN CHOPT NP PAR STEP SIGPAR CHI2 114 CALL ID FUN NP P CHI2 IC SIG COV ST PMI PMA 124 CALL HFITN X Y EY NPTS N1 NVAR FUN NP P CHI2 IC SIG COV 125 CALL HFITPO ID NP A CHI2 IC SIG 125 CALL HFITS ID FUN NP P CHI2 IC SIG 124 CALL HFITV N NDIM NVAR X Y EY FUN CHOPT NP PARAM STEP PMIN SIGPAR
126. III I OVE Ii p p i E INO N N IO IND N INO N G w w w w w w w 4 00 gt o Q gt Q O 75 76 Chapter 4 Advanced features for booking editing operations 16 OIII I IOI OI I OIIOIII OI 14 110 L OI TI L IIOII I IIIIO IT I 12 01 IIO IOII III I I II IOII 10 EI IIIOIIOIOI 0 100 8 I OI II OIIII I 0 II I 6 OIIO 0 I 010 I I IIOII 4 IO I I Tet 001001 I 2 00 I 110000 CHANNELS 100 0 1 10 0 1 2 3 4 5 6 7 8 9 0 1 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 CONTENTS 10 1112234335545656654443331111 111 1111131222223233242323222231111111 111 1 115475274447031969770012586101693260270696854072602204137731817684481677649975290445442121 LOW EDGE 1 111111111122222222223333333333444444444455555555556666666666777777777788888888889999999999 10 1 0 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789 ENTRIES 2000 ALL CHANNELS 0 2000E 04 UNDERFLOW 0 0000 00 OVERFLOW 0 0000E 00 BIN WID 0 1000E 01 MEAN VALUE 0 4847E 00 R M 5 0 2204E 00 HIST FILLED WITH HFILL AND HRNDM2 HBDDK ID 210 BAND Y DATE 17 12 91 N 4 BAND Y ND XMIN 0 1000 00
127. ILES Number of input files to be merged CHFIN Character array e g CHARACTER 8 CHFIN 10 for 10 files whose names are not longer than 8 characters containing the name s of the file s to be merged CHFOUT Character variable with the name of the output file CALL HMERGIN Action Identical to HMERGE but the routine prompts interactively for the names of the input and output files The paw command NTUPLE HMERGE calls this routine Scratching histogram in a file CALL HSCR ID ICYCLE CHOPT Action Scratch delete a histogram from the current directory in the direct access file Input parameters ID Histogram identifier ID 0 means scratch all histograms in the current directory ICYCLE Cycle number If ICYCLE O then all cycles are deleted CHOPT Character variable specifying options selected gt Only possible value not used at present Close a file CALL HREND Action Closes direct access file if no longer needed or when options or 2 are specified in HRFILE Input parameter CHTOP Character variable specifying the name of the top directory associated with the file to be closed This should correspond to the name declared with HRFILE After this call the system bank associated to this file is deleted call to HREND is obligatory when the file has been modified HREND uses C IO To force fortran I O HROPEN should be called with option F and the file should be closed with instea
128. L HEN ID X Action Fills a RWN Input parameters ID Identifier of the Ntuple X Array of dimension NVAR containing the values for the current event 3 2 Row Wise Ntuples RWN 23 Memory resident Ntuples When RWN 15 booked HBOOK reserves space in memory in which to store the data as specified by the NWBUFF argument of routine HBOOKN As the RWN is filled a call to HEN this space will be successively used until full At that time a new memory allocation will be made and the process continues If this data is then written to disk it appears as one enormous logical record In addition it most cases the last block of data will not be completely filled thus wasting space If one tries to reprocess this RWN at a later date e g with paw there must be enough space in memory to store the entire Ntuple This often gives rise to problems and so the following alternative method is recommended Circular buffer In an online environment you often want to have the last N events inside a buffer so that the experiment can be monitored continuously To make it easier to handle this case you can use routine HENOV which fills a circular buffer in memory with RWN events and when the buffer is full overwrites the oldest Ntuple CALL HFNOV ID X Action Fills a circular buffer with RWNs Input parameters ID Identifier of the Ntuple X Array of dimension NVAR containing the values for the current event Disk resident
129. L HPLOT 12 0 CALL HPLZON 1 2 2 S CALL HPLOPT GRID 1 CALL HPLOT 21 BOX gt 0 CALL HPLEND END 4 2 Filling Operations 67 500 500 300 300 200 200 100 100 0 DD DG EF FI LEP PE PS SPS ST 5 LEP PS EF SPS ST EP DD TIS AG FI PE TH DG Example HLABEL explicit list Example HLABEL implicit list 5 ST SPS PS PE LEP FI EP EF DG DD AG Example HLABEL 2 D Figure 4 1 Example of the use of HLABEL he top left picture shows the contents of the histogram ordered alphabetically by label he top right picture shows the same histogram but with the bins ordered by decreasing contents irrespective of their label he lower picture shows a two dimensional histogram where the ordinate Y axis ordered alpha betically 68 Chapter 4 Advanced features for booking editing operations 10 Example of booking options SUBROUTINE HEXAM2 TEST OF SOME BOOKING OPTIONS USING HBODK RANDOM NUMBER GENERATORS gt R Brun COMMON HDEXF C1 C2 XM1 XM2 XS1 XS2 DOUBLE PRECISION 1 2 1 2 51 52 EXTERNAL HTFUN1 HTFUN2 Booking C1 1 C2 0 5 XM1 0 3 XM2 0 7 XS1 0 07 XS2 0 12 CALL HBFUN1 100 TEST OF HRNDM1 100 0 1 HTFUN1 CALL HIDOPT 100 STAR CALL HCOPY 100 10 CALL HBOOK1 110 THIS HISTOGRAM IS FILLED ACCORDING TO THE FUNCT ION HTFUN1 100
130. L on a 2 dimensional histogram except that projections bands slices are not filled HBARY is ignored as well Input parameters ID histogram identifier X value of the abscissa Y value of the ordinate WEIGHT event weight 62 Chapter 4 Advanced features for booking editing operations CALL HFF1 ID NID X WEIGHT Action Analogous to HF1 with the same restrictions Cannot be used for variable bin width histograms Input parameters ID histogram identifier NID is a histogram specific variable that has to be provided by the user Before the first call NID must be initialized to 0 In subsequent calls to the constant NID must then be used in order to skip the calcula tion of the histogram address X value of the abscissa WEIGHT event weight Output parameter NID After the first call to HFF1 NID will contain the current address of histogram ID CALL HFF2 1ID NID X Y W Action Analogous to HF2 with the use of the parameter NID as explained for CALL HFPAK1 ID NID V N Action Fill an histogram using the contents of a vector Input parameters ID histogram identifier V array containing the values to be entered into the histogram N length dimension of the array V Input output parameter NID address of histogram see HFF1 This subroutine has the same effect as DO 10 I 1 N 10 CALL HFF1 ID NID V I 1 where the array V of N words must have been filled previously by the user
131. LDIM argument is used and a used as a placeholder in the dimension specification for replacement by HNFORM at run time See the examples 30 Chapter 3 Ntuples LDIM Dimension s of the variable If the variable in CHNAME is not dimensioned or its dimensions are hard coded in CHNAME then LDIM should be set to 0 If there is one placeholder in the dimension specification in CHNAME then LDIM should be set to the value of that dimension For more than one placeholder LDIM should be an integer array of appropriate size See the examples CHTYPE Acharacter variable specifying the type and bit packing to be used for the variable in CHNAME Possible values for the type R I U L C 4 32 The bit packing number should 99 99 appear after XLOW The lowest value that the variable in CHNAME may take This may be specified as either a real or integer value XHIGH The highest value that the variable in CHNAME may take If XHIGH is less than or equal to XLOW then no limits will be encoded by CHFORM The following example shows how HNFORM may be used to aid the creation of an Ntuple Example of booking an Ntuple with HNFORM and HBNAME PARAMETER MAXTRK 100 MAXHIT 300 COMMON CMTRK NTRACK NHITS MAXTRK PX MAXTRK PY MAXTRK PZ MAXTRK XHITS MAXHIT MAXTRK YHITS MAXHIT MAXTRK ZHITS MAXHIT MAXTRK CHARACTER 500 CHFDRM CHFORM CALL HNFORM CHFORM NTRACK 0 0 REAL MAXTRK CALL HNF
132. LT 0 10E 03 PARA N MIGR MIGR EIGE MINU MIGR FCN EXT NO WN CHIS cov 0 5 0 9 0 4 0 1 0 2 0 1 METER DEFINITIONS 0 VALUE STEP SIZE LIMITS 1 P1 3 0000 0 90000 no limits 2 2 1 0000 0 30000 limits 3 P3 0 30000 0 90000E 01 no limits PA 0 70000 0 21000 no limits 5 P5 0 70000E 01 0 21000 01 no limits 6 P6 0 12000 0 36000E 01 no limits 4 SET PRINT 0 0000 5 MIGRAD 1160 1 000 INE ACCURACY LIMITS FURTHER IMPROVEMENT AD MINIMIZATION HAS CONVERGED AD WILL VERIFY CONVERGENCE AND ERROR MATRIX NVALUES OF SECOND DERIVATIVE MATRIX 0 1596 01 0 6458E 00 0 3800 00 0 7478 00 0 1277E 01 0 5837E 01 IT WARNING IN HESSE MATRIX FORCED POS DEF BY ADDING 1 6018 TO DIAGONAL AD TERMINATED WITHOUT CONVERGENCE 1709 709 FROM MIGRAD STATUS FAILED EDM 0 41 02 STRATEGY 1 197 CALLS 198 TOTAL ERR MATRIX NOT POS DEF PARAMETER APPROXIMATE STEP FIRST NAME VALUE ERROR SIZE DERIVATIVE Pi 2 4709 0 73263E 01 0 00000 4 1109 P2 1 8247 0 37237E 01 0 00000 8 5400 P3 0 27725 0 24789E 02 0 00000 125 59 P4 0 70933 0 51778E 02 0 00000 132 72 P5 0 90472E 01 0 47875E 02 0 00000 302 38 6 0 21181 0 75383E 02 0 00000 63 830 QUARE 0 9282 00 NPFIT 1848 ARIANCE MATRIX 367E 02
133. M the variables their type size and possibly range or packing bits can all be specified at the same time Note however that variable names should be unique even when they are in different blocks The routine HNFORM see below can be used to ease the task of generating the CHFORM character string In the simplest case CHFORM corresponds to the COMMON declaration For example COMMON CEXAM IEVENT ISWIT 10 IFINIT 20 NEVENT NRNDM 2 can be described by the following CHFORM CHFORM IEVENT ISWIT 10 IFINIT 20 NEVENT NRNDM 2 28 Chapter 3 Ntuples in this case the Fortran type conventions are followed and the default sizes are taken Note that to get a nice one to one correspondance between the COMMON and the CHFORM statements the dimensions of the variables are specified in the COMMON and not in a DIMENSION statement The default type and size of a variable can be overridden by extending the variable name with t s t typeof variable lt s gt values default routine R floating point 4 8 4 HBNAME I integer 4 8 4 HBNAME U unsigned integer 4 8 4 HBNAME L logical 4 4 HBNAME C character 4 lt s lt 32 multiple of 4 4 HBNAMC Packing variables in a CWN Significant data storage savings can be achieved in the Ntuple when the range of a type U I or R variable is known In such cases the number of bits required to store all possible values of the variable is calculated by and the data suitably packe
134. ME Action The routine maps a file to a shared memory area Input parameters NWORDS Number of words for the shared area If NWORDS 0 an existing shared memory is attached and becomes the current HBOOK direc tory In this case HLIMIT must have been called previously CHNAME Character variable CHARACTER 4 specifying the name given to the shared area histograms Ntuples etc in this area have a structure similar to the PAWC common Example with pre existing shared area Program toy Parameter nwpaw 100000 common pawc paw call hlimit nwpaw call hlimap 0 TEST 1 read id call hrin id 9999 0 call hprint id call hdelet id if id ne 0 go to 1 end Note that HBOOK does not delete the shared memory when the job finishes that reamins the user s responsability 178 Chapter 9 Global sections shared memory 9 3 1 Using PAW and Unix shared memory Sun and DecStation only Program hserver HBOOK program creating a shared memory PAW edit shared i area called TEST macro shared ntimes 100 Routine HIME replaces HLIMIT histo plot 1 K NWORDS is the amount of space requested do nt 1 ntimes in the shared area histo plot 1 U t wait 271 parameter nwords 50000 endo return call hlimap nwords TEST PAW gt global_sect TEST PAW gt exec shared ntimes 15 call hbooki 1 testi 100 3 3 0 call hcopy 1 2 test2 call hcopy 1 3 test3
135. MIT which declares a length of 20000 words 1 5 batch as the first step of the analysis 9 for the length of the PAWC dynamic store Then the one and two dimensional histograms 110 and 210 filled respectively according to the functions HTFUN1 and HTFUN2 and the histograms are output to a newly created file HTEST DAT The output generated by the program is shown in Figure 1 3 10 Chapter 1 Introduction PROGRAM HTEST PARAMETER NWPAWC 20000 COMMON PAWC H NWPAWC EXTERNAL HTFUN1 HTFUN2 CALL HLIMIT NWPAWC Book histograms and declare functions CALL HBFUN1 100 Test of HRNDM1 100 0 1 HTFUN1 CALL HBOOK1 110 Filled according to HTFUN1 100 0 1 1000 CALL HBFUN2 200 Test of HRNDM2 100 0 1 40 0 1 HTFUN2 CALL HSCALE 200 0 CALL HBOOK2 210 Filled according to HTFUN2 100 0 1 40 0 1 30 Fill histograms DO 10 1 10000 X HRNDM1 100 CALL HFILL 110 X 0 1 CALL HRNDM2 200 X Y CALL HFILL 210 X Y 1 10 CONTINUE Save all histograms on file HTEST DAT CALL HRPUT O HTEST DAT N CALL HDELET 100 CALL HDELET 200 CALL HPRINT O END FUNCTION HTFUN2 X Y Two dimensional gaussian HTFUN2 HTFUN1 X HTFUN1 RETURN END FUNCTION HTFUN1 X Constants for gaussians DATA C1 C2 1 0 5 DATA XM1 XM2 0 3 0 7 DATA 51 52 0 07 0 12 Calculate the gaussians A1 0 5 X XM1 XS1 2 A2 0 5 X XM2 XS2 2 X1 C1 X2 C2 IF ABS A1 GT 0 0001 X1 2C1 EXP A
136. N tuple Title CERN Population Creation 12 06 92 11 46 34 K K 3K INTEGER CATEGORY FLAG AGE SERVICE CHILDREN GRADE STEP HRWEEK COST COMMON CERN CATEGORY FLAG AGE SERVICE CHILDREN GRADE STEP HRWEEK COST CHARACTER DIVISION 4 NATION 4 COMMON CERN1 DIVISION NATION CHARACTER 8 VAR 4 CALL HBNAME 10 0 CLEAR Clear addresses in Ntuple CALL HBNAME 10 CERN CATEGORY SET Set addresses for variables CATEGORY CALL HBNAMC 10 CERN DIVISION SET Set addresses for variables DIVISION xc Enter user code here book the histograms CALL 00 1 101 Staff Age 45 20 65 0 CALL 00 1 102 Number of years at CERN 35 0 35 0 CALL 00 2 103 Grade vs Step 12 3 15 16 0 16 0 CALL HBIGBI 101 2 CALL HBIGBI 102 2 get number of entries CALL HNOENT 10 NLOOP read only the four desired columns VAR 1 VAR 2 SERVICE VAR 3 GRADE VAR 4 STEP CALL HGNTV 10 VAR 4 1 IER DO 10 I 1 NLOOP IF I NE 1 CALL HGNTF 10 I IER IF IER NE 0 THEN PRINT Error reading row I ENDIF CALL HFILL 101 FLOAT AGE O 1 CALL HFILL 102 FLOAT SERVICE O 1 CALL HFILL 103 FLOAT GRADE FLOAT STEP 1 10 CONTINUE CALL HISTDO END l The summary table about the Ntuple shown below as obtained by running
137. NBF number of basic functions must be set by the user via a call to HSETPR see below User regressors values are to be re turned by the user supplied DOUBLE PRECISION function HBASFT IBF X where IBF is the user defined regressor code in the sense explained above 10 times the regressor code plus 2 The regressor code number can vary from 1 to PNBF number of basic functions used for the parametrization PNBF has to be specified by the user before calling HPARAM via a call to the routine HSETPR described below in the case that the switches B or C of the control param eter IC have the value 2 The parameter X is an array of length NDIM defining the coordinate where the regressor should be calculated switch controls the selection of the regressors Regressors are selected by the system The parameter PSEL and the array MAXPOW help the user in controlling the total degree of each regressor see below for each elementary function or for each regressor the logical function HSELBF ELEF gets called once before the beginning of the actual fitting procedure to set up the table of available elementary functions or regressors IELEF is the code of the regressor or of the function being tested for acceptance A value of TRUE returned will cause the regressor elementary function to be accepted The default version of this function which is supplied in HBOOK always returns the value TRUE while the user may want to write his own version of this func
138. No I Evtno I NPos I NNeg I call HLDIR KO T Nothing yet on KO call HCDIR KO gt Useless HFNT remembers that buffers written to KO call HFNT 1000 call HLDIR T This will not show anything on However if you call HLDIR TA you will see all Ntuple extensions in the case you have many calls to HFNT In this particular example everything is still in memory call HCDIR KO Useless you are already here call HLDIRC K0 same as call hldir 2 279 call RZLDIR call HROUT 0 icycle If you call HLDIR 9 here you will see the header If you call HLDIR A here you will see the header and your Ntuple extensions call HREND KO 3 4 Making projections of a RWN 34 Chapter 3 Ntuples CALL HPROJ1 ID IDN ISEL FUN IFROM ITO IVARX Action Fill an existing one dimensional histogram with data from a RWN Input parameters ID Identifier of 1 dimensional histogram which must have been previously booked with IDN Identifier of the RWN Ntuple ISEL Selection flag 0 No selection criterion Events between IFROM and ITO histogrammed with weight one 0 Function FUN is called for each event between IFROM and ITP they are histogrammed with a weight equal to the value of FUN FUN User function to be declared EXTERNAL in the calling routine It has as paramet
139. OI I IIIIIIIII IO I 7 I00 I IIII II IOOIII III II III IIOIO OI I 6 OII I I I00I OO I OIIIO OI IO IOI IIIIIIII I III 5 III I OIIO IIII IIIIOI I IO I I I III OIIII 4 IIIO IIII IIIO III II I II I I 0 IIIO00 I 3 Ts OF 01 10 I 20 41 I IIOIII I 2 1100 I II OI I I O IIIIIIO I 1 0011 001 0 CHANNELS 100 0 1 10 0 1 2 3 4 5 6 7 8 9 0 1 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 4 2 Filling Operations CONTENTS LOW EDGE 10 1 ENTRIES BIN WID 10 1 1111221221222111 11 11 11226471745235063882418799235665 6634 236775603165390062286416969199797478253444112 1 77 1 11111 111 1 111111111122222222223333333333444444444455555555556666666666777777777788888888889999999999 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567 890123456789 751 0 1000 01 ALL CHANNELS MEAN VALUE 0 7510 03 0 4820 00 UNDERFLOW R M S 0 0000 00 OVERFLOW 0 0000 00 0 2188 00 78 Chapter 4 Advanced features for booking editing operations HIST FILLED WITH HFILL AND HRNDM2 HBDDK ID 210 SLICE X DATE 17 12 91 NO 6 SLICE X NO 2 YMIN 0 3333 00 0 6667 00 25 E 24 LOIGI I I 23 I III I b 22 21 20 IO OIIII 19 II IIIIIOII O I I 0 18 IIIIOIII III I I T 17 II IIIIIIIOOIIIO I I II Ts 16 II IOIIIIIIIIIII I T I II I 15
140. OOTH NSIG CHISQ NDF FMIN FMAX IERR 133 CALL HRDIR MAXDIR CHDIR NDIR 164 CALL HREBIN ID X Y EX EY N IFIRST ILAST 99 CALL HRECOV ID CHOPT 31 CALL HRENAME ID1 CHOLD CHNEW 42 CALL HREND CHTOP 170 CALL HRENID IDOLD IDNEW 19 CALL HRESET ID CHTITL 19 CALL HRFILE LUN CHTOP CHOPT 168 CALL HRGET ID CHFILE CHOPT 166 CALL HRIN ID ICYCLE IOFSET 169 Table 10 1 Routine calling sequences cont Calling Sequence VARIAB HRNDM1 ID CALL HRNDM2 ID RX RY CALL HROPEN LUN CHTOP CHFILE CHOPT LREC ISTAT CALL HROUT ID ICYCLE CHOPT CALL HRPUT ID CHFILE CHOPT CALL HSCALE ID FACTOR CALL HSCR ID ICYCLE CHOPT CALL HSETPR CHNAME VALUE CALL HSMOOF ID ICASE CHI2 VARIAB HSPFUN ID X N K CALL HSPLI1 ID IC N K CHI2 CALL HSPLI2 ID NX NY KX KY CALL HSQUEZ YES NO CALL HSTAF CHOPT VARIAB HSTATI ID ICASE CHOICE NUM VARIAB HSUM ID CALL HTITLE CHGTIT CALL HUNPAK ID CONTEN CHOICE NUM CALL HUNPKE ID CONTEN CHOICE NUM CALL HUWFUN LUN ID CHFUN CHFILE ITRUNC CHOPT VARIAB HX ID X VARIAB HXE ID X CALL HXI ID X I VARIAB HXY ID X Y VARIAB HXYE ID X Y CALL HXYIJ ID X Y I JX 185 page 135 135 167 169 165 84 170 130 132 133 132 133 85 82 101 100 80 95 96 39 96 97 98 96 97 98 Bibliography 1 2 3 4 5 6 7 8 9 10 1
141. ORM CHFORM NHITS NTRACK 0 0 REAL MAXHIT CALL HNFORM CHFORM PX NTRACK 0 0 0 CALL HNFORM CHFORM PY NTRACK 0 0 0 CALL HNFORM CHFORM PZ NTRACK 0 0 0 CALL HNFORM CHFORM XHITS NTRACK MAXHIT 0 0 CALL HNFORM CHFORM YHITS NTRACK MAXHIT 0 0 CALL HNFORM CHFORM ZHITS NTRACK MAXHIT 0 0 LFORM INDEX CHFORM 1 CALL HBNAME ID VARBLOK2 NTRACK CHFORM LFORM Alternative way of booking a CWN CALL HBOOKNC ID CHTITL NVAR BLOCK TUPLE CHTAGS Action Provides a way to define a CWN similar to HBOOKN for a RWN Input parameters ID Identifier of the CWN If it does not already exist it is created CHTITL Character variable specifying the name of the Ntuple not used if it already exists 3 3 More general Ntuples Column Wise Ntuples CWN 31 NVAR Number of variables per event maximum 200 BLOCK of the block inside the CWN default is Block1 TUPLE Array of dimension NVAR that will contain values at filling time CHTAGS Character array of length NVAR providing a short name up to eight characters tagging scheme for each variable 3 3 4 Filling a CWN CALL ID Action Fill a CWN Input parameter ID Identifier of the CWN CALL HFNTB ID CHBLOK Action Fill the named block CHBLOK in a CWN Input parameters ID Identifier of the Ntuple CHBLOK Character variable specifying the block th
142. OUT does not do this for us CALL HMDIR US S CALL HCDIR PAWC Make sub directory in memory CALL HMDIR US S CALL HCDIR PAWC US gt Book Ntuple 14 histogram CALL HBOOKN 10 A simple Ntuple 5 EXAMPLE 5000 CHTAGS CALL HBOOK1 100 Energy distribution 100 0 100 0 Fill the Ntuple and histogram DO 10 I 1 1000 CALL RANNOR X Y Z SQRT X X Y Y ENERGY 50 10 ELOSS 10 ABS CALL HFN 10 EVENT CALL HFILL 100 ENERGY O 1 10 CONTINUE Juggle top directories order of these calls is important CALL HCDIR PAWC 9 CALL HCDIR EXAMPLE gt Write out everything to disk CALL HROUT 0 ICYCLE T Flush remaining buffers to disk CALL HREND EXAMPLE 99 CONTINUE END Chapter 9 Global sections and shared memory 9 1 Sharing histograms in memory on remote machines When is used in data acquisition system environment global sections be an interesting alternative to disk input output The following example is a simple illustration of this facility Let us assume two processes exist 1 PFILL the process filling some histograms in COMMON PAWC directly 2 PRESENT process activated from time to time to visualize the histograms created and filled by PFILL No hand shaking mechanism is required A global section is created this is system dependent This global section is mapped to
143. Overview ot booking options 2 2 2 2 552 5854 OS 54 4 1 1 Histograms with non equidistant bins 54 4 2 Profile Distogramis s es saog aoe da den 54 4153 22522222022 wo oem Den Pu 55 41 4 Projections Slices Bands 2 2 2 2 4 4 44 55 41 5 SANSS bow RR yo oa Pe k e d 57 4 1 6 Function Representation scs 222 n o eR y RR Ex UR 57 4 1 7 Reserve array in Memory e olo aoo s RR ROG BOR AUR Roy ow 59 4 1 8 Axis labels and histograms 2 2 59 42 Ens Operations 22222 22 2 41644 4 60 42 1 Past Pilling BninesS 222 9939 X9 ow Re go IR x XE a 60 3 22 Global oua rom REB E EE 63 4 2 3 Filling histograms using character variables 64 43 Edine operations sr sle soi o9 9 X SU m ex m 78 43 1 Index and General Tile 222222224528 wm ER we da 79 4 3 2 What to Print 1 dimensional histogram 80 4 3 3 Graphic Choices 1 dimensional 82 4 3 4 Scale Definition and Normalization 83 4355 Pags Conwell 222222252496 do Redes 85 430 Selective BGG ul euo e memos OR Re RR ORC E Re e 85 4 3 7 Printing after System Error Recovery
144. PLE in the example above If the current directory CD is different will save and later automatically restore the CD The Ntuple created by the program shown above can be processed by pav as follows Reading an RWN in a PAW session PAW gt Histo file 1 example dat PAW gt Histo plot 100 PAW gt Ntuple plot 10 energy gt gt PAW gt Ntuple plot 10 eloss lt 50 PAW gt Ntuple plot 10 1 x lt 2 and sqrt z gt 1 By default HROPEN creates a file that can be extended up to 32000 blocks i e 128 Mbytes for a record length LREC of 1024 words If one wishes to create very large Ntuples one should make two changes to the above procedure A large value should be used for the record length of the file e g 8192 words the maximum on most machines N B the maximum record length on VMS systems is 8191 words If access mode RELATIVE is used the maximum is 4095 words This remark does not apply to a CWN as described later Option Q HROPEN should be used to override the default number of records allowed This can be achieved as by changing the previous call to HROPEN as follows Writing very large Ntuple files COMMON QUEST IQUEST 100 CALL HLIMIT 150000 Create HBOOK file with the maximum record length 32756 bytes and maximum number of records 65000 IQUEST 10 65000 CALL HROPEN 1 EXAMPLE EXAMPLE DAT NQ 8192 ISTAT IF ISTAT NE
145. Performs some error checking and sets up a dummy weight histogram if necessary Input parameters IDDATA Data histogram identifier IFIXMC Array of dimension NSRC containing 17 ifa IDMC Array of dimension NSRC containing Monte Carlo histogram identifiers IDWT Array of dimension NSRC containing weight histogram identifiers W option only NSRC Number of Monte Carlo sources CHOPT W Use the weight histograms provided For non existent weight histograms and if the W option is not requested a dummy weight histogram in which all entries are 1 is booked IERR Error flag set to 1 if the parameters sent to HMCINI were not usable e g incom patibility between data and MC histograms number of MC sources less than 2 0 otherwise VARIAB HMCLNL Action HMCLNL is a double precision function giving the log likelihood including effect of both data and Monte Carlo statistics that the data distribution arose from a distribution given by combining the Monte Carlo distributions weighted by the weights provided using the fractions given in FRAC HMCINI must be called before this function may be used Input parameters FRAC Array of dimension NSRC containing the fraction of each Monte Carlo distribution you wish to assume is in the data distribution in order to calculate the log likelihood 7 7 Fitting with finite Monte Carlo statistics 143 PROGRAM MCSTAT PARAMETER NPAWC 10000 COMMON PAWC H NPAWC IN
146. RDS LOC Action Reserves an array in the memory storage area managed by HBOOK Input parameters ID identifier of the array pseudo histogram NWORDS length of the array Output Parameters LOC Address minus one in the internal hbook common block PAWC of the 1st element of the array 1 COMMON PAWC NWPAW IXPAWC IHDIV IXHIGZ IXKU FENC 5 LMAIN HCV 9989 DIMENSION IQ 2 Q 2 LQ 8000 EQUIVALENCE LQ 1 LMAIN 1Q 1 LQ 9 Q 1 IQC12 IADDR Q LOC 1 Remark At any time the address of preudo histogram ID can be obtained with HLOCAT ID LOC 4 1 8 Axis labels and histograms A set of routines HLABEL HFC1 and HFC2 allows one to associate labels with histogram channels This association can be made before or after a histogram is filled but it has the advantage that the label information get stored in the histogram data structure so that it is available for all future plots in an automatic way in the HPLOT and PAW packages Printing histograms with associated alphanumeric labels is not implemented in the line printer oriented routines of HBOOK 60 Chapter 4 Advanced features for booking editing operations CALL HLABEL ID NLAB CLAB CHOPT Action Associates alphanumeric labels with a histogram This routine can be called for a histogram after it has been filled and then the labels specified will be shown on the respective axes The routine can also be called before a histogram is filled an
147. RFILE on a direct access file the current directory in memory will be the latest current directory set Writing to a file 6 4 Input Output Routines 169 CALL HROUT ID ICYCLE CHOPT Action Write a histogram from the current directory in memory onto the current directory on the direct access file Input parameters ID Histogram identifier ID 0 means write all histograms from the current directory in memory CHOPT Character variable specifying the options selected W Create on the direct access file the same directory tree as in memory T Write the whole directory tree hanging from the current directory if ID 0 Output parameter ICYCLE Cycle number The first time a given histogram with identifier ID is stored on a directory on a direct access file ICYCLE is set to 1 If the histogram identifier ID already exists on the direct access file then the call to HROUT will increment the cycle number ICYCLE by one Experienced users may invoke routines from the zebra RZ package to purge a directory i e delete all versions of an identifier but the most recent one using routine RZPURG Reading from a direct access file or global section CALL HRIN ID ICYCLE IOFSET Action Read a histogram from the current directory on the direct access file or global section into the current directory in memory Input parameters ID Histogram identifier ID 0 means that all histograms from the current directory on the direct access
148. ST 14 specifies the upper limit in Y 2 D User function value is taken from HCFITD FITPAD 24 FITFUN see section 7 1 5 calculations are performed in double precision Verbose mode Results are printed after each iteration By default only final results are printed W Set the event weights equal to one By default weights taken according to statistical errors NP Number of parameters NP lt 25 PARAM Array of dimension NP with initial values for the parameters STEP Array of dimension NP with initial step sizes for the parameters B option only PMIN Array of dimension NP with the lower bounds for the parameters B option only 114 Chapter 7 Fitting parameterization and smoothing PMAX Array of dimension NP with the upper bounds for the parameters B option only Output parameters PARAM Array of dimension NP with the final fitted values of the parameters SIGPAR Array of dimension NP with the standard deviations on the final fitted values of the parameters CHI2 Chisquared of the fit 7 1 2 Fitting one dimensional histograms with special functions CALL HFITHN ID CHFUN CHOPT PAR STEP PMIN PMAX SIGPAR CHI2 Action Fits the given special function to the contents of a one dimensional histogram and optionally superimposes it to the histogram when editing Input parameters ID Histogram identifier CHFUN Character variable specifying the desired parametric func
149. TEGER NMCSRC PARAMETER NMCSRC 2 declarations for HMCMLL Example of use of HMCMLL INTEGER IDDATA IDMC NMCSRC IDWT NMCSRC IFIXMC NMCSRC DOUBLE PRECISION FLIM 2 NMCSRC FSTART NMCSRO FSTEP NMCSRC FUP FRAC NMCSRC ANS NMCSRC DANS NMCSRC DATA IDDATA IDMC IDWT 10 1301 1302 1351 1352 CALL HLIMIT NPAWC Set UP to correspond to 70 confidence level for 2 parameter fit FUP 1 2 Read in your data Monte Carlo and Weight histograms CALL HRGET 10 HMCHIS PAW DO 20 JSRC 1 NMCSRC CALL HRGET IDMC JSRC HMCHIS PAW 9 CALL HRGET IDWT JSRC HMCHIS PAW 9 20 CONTINUE perform log likelihood maximisation and error analysis using user weights setting limits on the fractions WRITE 6 1000 1000 FORMAT Fit with error analysis use user weights limits FLIM 1 1 0 0 FLIM 2 1 1 0D0 FLIM 1 2 0 0 FLIM 2 2 1 0D0 CALL HMCMLL IDDATA IDMC IDWT NMCSRC EWL IFIXMC FRAC FLIM FSTART FSTEP FUP ANS DANS END The program fits the first two histograms shown 1302 is dotted to the second The weights for the first distribution are all 1 for the second they are all 0 8 Output Generated Fit with error analysis use user weightsand limits MINUIT RELEASE 93 08 INITIALIZED DIMENSIONS 100 50 EPSMAC MCMLL You have 2 free fractions and 0 fixed PARAMETER DEFINITIONS NO NAME VALUE 1 P1 d 0 50000 2 2 i 0 50000
150. UM O it is assumed to be 1 5 7 Errors 97 Output Parameter CONTEN Array to be dimensioned at least to the number of channels of the histogram or projection ie DIMENSION CONTEN NX in the 1 dimensional case and DIMENSION CONTEN NX NY in the 2 dimensional case VARIAB HIE ID I Action Returns the value of the error that has been stored in a given 1 dimensional histogram channel This corresponds to the square root of the sum of the squares of the weights Input parameters ID Histogram identifier I Channel bin number When has not been called HIE returns the square root of the contents of the given channel VARIAB ID X Action Analogous to HIE but referring to the channel that contains a given X value Input parameters ID Histogram identifier X X value The same remark as for HIE applies VARIAB HIJE 1 Action Returns the value of the error that has been stored in a given 2 dimensional histogram channel This is usually the square root of the contents of the channel unless the user has filled his own values for the errors using HPAKE Input parameters ID Histogram identifier I Channel number in X ordinate J Channel number in Y ordinate VARIAB HXYE ID X Y Action The same as for HIJE except that the cell that contains both X and Y is computed and the error in that cell returned Input parameters ID Histogram identifier X X value of point Y Y
151. VALUE STEP SIZE LIMITS f 2Pp1 40 000 12 000 no limits 2 9 2 20 000 6 0000 no limits 0 40000 0 12000 limits 4 0 60000 0 18000 limits 5 5 2 0 10000 0 30000 01 1 5 6 0 10000 0 30000E 01 no limits 2 SET PRINT 0 0000 3 MIGRAD 1160 1 000 MIGRAD MINIMIZATION HAS CONVERGED MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX FCN 81 55959 FROM MIGRAD STATUS CONVERGED 391 CALLS 392 TOTAL EDM 0 21 05 STRATEGY 1 ERROR MATRIX ACCURATE EXT PARAMETER STEP FIRST NO NAME VALUE ERROR SIZE DERIVATIVE Pi 154 37 3 8591 97447 0 16735E 03 P2 74 934 2 1210 51925 0 16237E 03 P3 0 30351 0 15347E 02 76783 03 0 91430 0 70017 0 29587E 02 17713E 02 0 19339 P5 0 69299E 01 0 12334E 02 28758E 03 0 39057 P6 0 11985 0 27357E 02 62656 03 0 52392 CHISQUARE 0 9164 00 NPFIT 95 OnRWNE oooooo TITLE OF 1 1 HBOOK ID 3 DATE 18 05 92 NO 172 168 164 160 156 I 152 I I 148 I I 144 140 136 132 I I 128 I 124 120 zo 116 112 108 I 104 1 100 96 92 88 I 84 80 76 I 72 I 68 I I I I 16 T T I I I I II I I I I I I 1 44 I 40 I 36 I I I I ni
152. X 100 0 000 00 0 100 01 64764 146 I 3 THIS HISTOGRAM IS FILLED ACCORDING TO TH 110 10 5000 1 X 100 0 000 00 0 100 01 64605 89 4 E FUNCTION HTFUN1 4 TEST HRNDM2 200 32 052 100 000 00 0 100 01 64523 4328 40 0 000 00 100E 01 60218 4296 oo 100E 01 60193 4328 100 01 55888 4296 TEST OF HRNDM2 20 32 4000 2 100 40 000 00 000 00 100 01 55858 763 1100 01 55123 726 6 5 FILLED WITH HFILL HRNDM2 210 5 5000 2 100 40 000 00 000 00 MEMORY UTILISATION MAXIMUM TOTAL SIZE OF COMMON PAWC 80000 THIS HISTOGRAM IS FILLED ACCORDING 0 THE FUNCTION HTFUN1 HBOOK ID 110 DATE 17 12 91 NO 68 66 64 60 58 56 54 52 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 mu 16 II I I o N HHHHHH 1 H H FF TEE E ES HHHH Ed E HHHHH HHHHH I 14 12 10 4 2 Filling Operations 2 CHANNELS 10 1 CONTENTS 1 LOW EDGE 10 1 ENTRIES BIN WID HIST FILLED HBOOK I CHANNELS 10 1 OVE 975 95 925 875 85 825 1775 175 725 675 65 625 575 55 525 475 45 425 1375 135 1325 1275 125 1225 1175 115 1125 1075 105 1025 UND LOW EDGE ENTRIES SCALE 0 0 1 0 1 1 0 D 0 0 1 2 3 4 5 6 7 8 9 1 0 12345
153. XXXXXXXXXXXXXXXXXXXXXX52XX 32 XXXXXXXXXXXXXXXXXXXXXXXXX 2 28 TXXXXXXXXXXXXXXXXXXXXXXXXX7 5 X 7 2XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX2 X 24 2XXXXXXXXXXXXXXXXXXXXXXXXXXXX2X X X2 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX X25 20 X5XX5XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 7 16 5 7 12 77 8 5 5727 4 5225XX5XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX CONTENTS 100 1111111111111 10 112224658012445755432099687543222121221233455666557776678686676664543343222221111 1 21124626818147606828212710478511552225771649871850922032539736953183588893942434650812591167574 90 TEST OF PRINTING OPTIONS 1000 HBDDK 100 10 1 ID 1 6 3 2 4 8 6 4 8 0 9 6 1 1 2 1 2 8 1 4 4 1 6 0 Chapter 4 Advanced features for booking editing operations 1 T 6 1 9 2 2 0 8 DAT 2 2 4 E 17
154. XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXEXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXTX 12 TXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX7T 8 5 BXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX5727 4 5225XX5bXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX CHANNELS 100 0 1 10 0 2 3 4 5 6 7 8 9 0 1 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 CONTENTS 100 1111111111111 10 112224658012445755432099687543222121221233455666557776678686676664543343222221111 1 21124626818147606828212710478511552225771649871850922032539736953183588893942434650812591167574 THIS HISTOGRAM IS FILLED ACCORDING TO THE FUNCTION HTFUN1 HBOOK ID 110 DATE 17 12 91 NO 9 100 XXXXXXXXXXXXX 96 XXXXXXXXXXXXX 7 92 XXXXXXXXXXXXX7X 88 XXXXXXXXXXXXXXXX 84 XXXXXXXXXXXXXXXX 5 27 80 XXXXXXXXXXXXXXXX X 2 X 5 76 XXXXXXXXXXXXXXXX X X2X 2X X X 72 XXXXXXXXXXXXXXXX XX XXX2 XX X X 2 68 XXXXXXXXXXXXXXXX2XX 2 XXXX2XXXX2XXXX 64 XXXXXXXXXXXXXXXXXXX 75 60 X XXXXXXXXXXXXXXXXXXX XXX 56 XXXXXXXXXXXXXXXXXXXXX XXX2XXXXXXXXXXXXXXXX 5 52 XXXXXXXXXXXXXXXXXXXXXX X5XXXXXXXXXXXXXXXXXXXX2X 48 SXXXXXXXXXXXXXXXXXXXXXX2 XXXXXXXXXXXXXXXXXXXXXXXX 44 XXXXXXXXXXXXXXXXXXXXXXXX SXXXXXXXXXXXXXXXXXXXXXXXX5 X 40 XXXXXXXXXXXXXXXXXXXXXXXX2 TXXXXXXXXXXXXXXXXXXXXXXXXXX X 36 XXXXXXXXXXXXXXXXXXXXXXXXX XXXXX
155. a CALL HNTVDEF ID1 IVAR CHTAG BLOCK ITYPE Action Returns the definition as given in HBNAME for the variable with index IVAR in Ntuple ID1 The Ntuple must already be in memory 3 5 Get information about Ntuple 39 3 5 3 Generate a user function HBOOK can automatically produce a skeleton user selection function which includes the Ntuple dec 1 via the calls HBNT HBNAME and and can be used later run to access the elements of the Ntuple Two cases are available one for use in batch and the other for use with paw In the first case the common block names will be those specifed by the user in the call to HBNAME or HBNAMC For paw these common names are PAWCR4 PAWCR8 and PAWCCH for storing the single precision LOGICAL INTEGER and REAL 4 double precision REAL 8 and COMPLEX and CHARACTER data respectively CALL HUWFUN LUN ID CHFUN ITRUNC CHOPT Action Write an user function or subroutine to access an Ntuple Input parameters LUN Logical unit used to write the user routine LUN must be opened before this call ID Identifier of the Ntuple CHFUN Character variable specifying the routine name ITRUNC All variable names will be truncated to ITRUNC characters ITRUNC 0 is no truncation CHOPT Character variable specifying the desired options BO Make an user subroutine for batch usage i e with HBNAME and HBNAMC calls default P Make a pav selection function
156. ameter parno will be bounded between lolim and uplim Limits can be specified in either order MINUIT will take the smaller as lolim and the larger as uplim However if lolim is equal to uplim an error condition results SET PARameter parno value Sets the value of parameter parno to value The parameter in question may be variable fixed or constant but must be defined SET PRIntout level Sets the print level determining how much output MINUIT will produce The allowed values and their meanings are displayed after a SHOw PRInt command Possible values for level are 1 No output except from SHOW commands 124 Chapter 7 Fitting parameterization and smoothing 0 Minimum output no starting values or intermediate results 1 Default value normal output 2 Additional output giving intermediate results 3 Maximum output showing progress of minimizations SET STRategy level Sets the strategy to be used in calculating first and second derivatives and in certain minimization meth ods In general low values of level mean fewer function calls and high values mean more reliable minimization Currently allowed values are 0 1 default and 2 SHOw XXXX SET XXXX commands have a corresponding SHOw XXXX command In addition the SHOw commands listed starting here have no corresponding SET command for obvious reasons The full list of SHOw commands is printed in response to the command HELP SHOw SHOw CORrelations
157. aracters see HPCHAR CONT 1 Dim histogram is printed with the contour option STAR 1 Dim histogram is printed with a at the Y value see HPCHAR SCAT Print a 2 Dim histogram as a scatter plot TABL Print a 2 Dim histogram as a table PROS Plot errors as the Spread of each bin in Y for profile histograms PROE Plot errors as the mean of each bin in Y for profile histograms STAT Mean value and RMS computed at filling time double precision NSTA Mean value and RMS computed from bin contents only ERRO Errors bars printed as SQRT contents NERR Do not print print error bars INTE Print the values of integrated contents bin by bin NINT Do not print integrated contents LOGY 1 Dim histogram is printed in Log scale in Y LINY Dim histogram is printed in linear scale in Y PCHA Print channel numbers NPCH Do not print channel numbers PCON Print bin contents NPCO Do not print bin contents PLOW Print values of low edge of the bins NPLO Do not print the low edge PERR Print the values of the errors for each bin NPER Do not print the values of the errors PFUN Print the values of the associated function bin by bin NPFU Do not print the values of the associated function PHIS Printthe histogram profile NPHI Do not print the histogram profile PSTA Print the values of statistics entriesymean RMS NPST Do not print values of statistics ROTA Print histogram rotated by 90 degrees NROT Print his
158. ary function either standard or user defined is identified by a three digit code let s say nnm The last digit m is a one digit code specifying the kind of regressor used with the following meaning O Standard elementary function 1 User provided elementary function 2 User provided regressor The first two digits define the function number In the first two cases we have NDIM NCO of these codes arranged in an array so that the first NDIM codes are the code of the elementary functions to be multiplied to obtain the first regressor For system defined elementary functions nn is the degree of the polynomial For user provided regressors the meaning of this code is user defined in the sense that the user is free to give any meaning he wishes to this code in the routine he has to supply In the case of user provided regressors we will have just NCO regressor codes in the array ITERM at the end of the fitting process Only one code is needed to define a user given regressor whereas NDIM codes are needed to specify a regressor composed of elementary functions The parametrization routines will select the most efficient subset of regressors out of the set selected by the user in the sense of the criteria specified above Once the initial set of regressors has been specified the user still has the opportunity to tell the system how to make a further selection among those regressors before the fitting process actually starts maximu
159. ases a call is made to routine HFILL Finally a call to HISTDO writes an index with information about all histograms as well as a lineprinter representation of the histograms on standard output Example of how to produce simple histograms PROGRAM HSIMPLE PARAMETER NWPAWC 10000 COMMON PAWC H NWPAWC CALL HLIMIT NWPAWC Set global title CALL HTITLE C EXAMPLE NO 1 Book 1 4 histogram and scatter plot CALL HBOOK1 10 EXAMPLE OF 1 DIM HISTOGRAM 100 1 101 0 CALL HBOOK2 20 EXAMPLE SCATTER PLOT 100 0 1 40 1 41 30 Fill 1 dim histogram DO 10 I 1 100 10 00 1 25 CALL HFILL 10 FLOAT I 40 5 0 W 10 CONTINUE Fill scatter plot X 0 005 DO 30 I 1 100 X X 0 01 DO 20 J 1 40 Y J IW MOD 1 25 MOD J 10 IWMAX J MOD 1 25 10 IF IW GT IW 0 CALL HFILL 20 X Y FLOAT IW 20 CONTINUE 30 CONTINUE Print all histograms with an index CALL HISTDO END Output Generated 6 Chapter 1 Introduction EXAMPLE 1 HBDDK HBODK CERN VERSIDN 4 13 HISTOGRAM AND PLOT INDEX 17 12 91 NO TITLE ID B C ENTRIES DIM NCHA LOWER UPPER ADDRESS LENGTH 1 EXAMPLE OF 1 DIM HISTOGRAM 10 32 100 1 X 100 0 100 01 0 101 03 79369 149 2 EXAMPLE SCATTER PLOT 20 5 400 2 X 100 0 000E 00 0 100E 01 79217 760 Y 40 0 100E 01 0 410E 02 78482 726 MEMORY UTILISATION MAXIMUM TOTAL SIZE OF COMMON PAWC 80000 1 4 basic example EXAMPLE ND EXAMPLE OF 1 DIM HISTOGRAM HBDDK
160. at is to be filled CALL HPRNT ID Action Print the definition of the CWN ID as defined by the calls to HBNAME and or HBNAMC Input parameter ID Identifier of the CWN Recovery procedure The Ntuple header containing the essential definitions associated with an Ntuple are now written to the output file when the first buffer is written If the job producing the Ntuple does not terminate in a clean way i e the job crashs or you forgot to call it is now possible to rebuild the Ntuple header from the information available in the file Note however that the events corresponding to the last Ntuple buffer in memory are lost CALL HRECOV ID CHOPT Action Recover the information associated with a CWN Input parameters ID Identifier of the CWN CHOPT Character variable specifying the option desired At present Not used at present should be specified 32 Chapter 3 Ntuples Example of saving contents of common variables in an Ntuple COMMON GCFLAG IDEBUG IDEMIN IDEMAX ITEST IDRUN IDEVT IEDRUN IEOTRI IEVENT ISWIT 10 IFINIT 20 NEVENT NRNDM 2 COMMON GCTRAK VECT 7 GETOT GEKIN VOUT 7 NMEC LMEC MAXMEC NAMEC MAXMEC NSTEP MAXNST DESTEP DESTEL SAFETY SLENG STEP 5 SFIELD TOFG GEKRAT UPWGHT IGNEXT INWVOL ISTOP IGAUTO IEKBIN ILOSL IMULL INGOTO NLDOWN NLEVIN NLVSAV ISTORY COMMON GCTMED NUMED NATMED 5 ISVOL IFIELD FIELDM TMAXFD DMAXMS DEEMAX EPSIL STMIN
161. ata tapes would be written huge re construction programs would extract interesting data from those tapes and transfer them to DSTs Then to make the analysis more manageable various physicists would write their own mini DST with a re duced fraction of the information from the DST They would run these m j DSTs through HBOOK whose functionality had increased substantially in the meantime 7 8 Hence various tens of one or two dimensional histograms would be booked in the initialization phase and the interesting parameters would be read sequentially from the DST and be binned in the histograms or scatter plots Doing this was very efficient memory wise although 2 dim histograms could still be very costly but of course all correlations not explicitly plotted were lost 2 Chapter 1 Introduction HBOOK in those days still had its own memory management but with version 4 9 which became available in 1984 the ZEBRA data memory manager was introduced This not only allowed the use of all memory managament facilities of ZEBRA but at the same time it became possible to use the sequential FZ and random access RZ 101 input output possiblities of that system This allows histograms to be saved and transferred to other systems in an easy way At about the same time Ntuples somewhat similar in functionality to events as written on a miniDST were implemented This way the complete correlation matrix between the various Ntuple elements
162. before the first call to HGNF for a given RWN When accessing more than one row of an Ntuple it is more efficient to call HGNPAR and then HGNF for each row that is required than to call HGN 36 CAL L HGNF ID IDNEVT X IERROR Chapter 3 Ntuples Action Copy the contents of an Ntuple event into an array The routine HGNPAR must have been called prior to the first call to HGNF for a given Ntuple Input ID parameters Identifier of the Ntuple IDNEVT Event number Output parameters X IERRO Array to contain variables for the event chosen R Error return code This routine returns in the vector X the contents of the row IDNEVT or Ntuple ID The vector X must have be of size NVAR as specified in the call to HBOOKN Te Bo Fi 10 9001 T 20 c Example of access to RWN information PROGRAM TEST INTEGER NWPAWC PARAMETER NWPAWC 15000 MTUPLE 5 COMMON PAWC PAW NWPAWC 80 CHTITL CHARACTER 8 CHTAGS MTUPLE CHTAGZ MTUPLE DIMENSION RLOW MTUPLE RHIGH MTUPLE EQUIVALENCE EVENT 1 X EVENT 2 EVENT 3 Z EQUIVALENCE EVENT 4 ENERGY EVENT 5 ELOSS DATA CHTAGS X Y Z Energy Eloss 11 HBOOK how many words are in PAWC CALL HLIMIT NWPAWC ok Ntuple CALL HBOOKN 10 A Row Wise Ntuple 5 5000 CHTAGS 11 the Ntuple DO 10 1 1000 CALL RANNOR X Y Z SQRT X X Y Y ENERGY 50 10
163. bin in the comparisons If the O option is used this is automatic L Left underflow bin Same as above but the X Axis underflow is used The U option uses this automatically Top overflow bin Same as R but for the Y Axis Bottom underflow bin Option L for the Y Axis 6 3 Bin by bin histogram comparisons 107 S Statistical comparison Calculates the probability that both bins were produced from a distribution with the same mean This probability is referred to in TOL and DIFFS C Compatibility test Considers bins of the reference histogram ID1 as perfectly describing the true distribution Calculates the probability that the data from ID2 was produced from that distribution For 1 or 2 dimensional histograms the Poisson mean is deduced from ID1 For profile histograms the test assumes a Gaussian with mean and standard deviation given by the ID1 The C option should be used when comparing data to a function a well known reference or a calibration distribution A Absolute test Like the C test except that TOL and DIFFS are in terms of the number of standard deviations rather probability The test is on the number of standard deviations by which the data from ID2 deviates from the mean Both the mean and the standard deviation are deduced from ID1 Error bars must be on for this option This forbids overflow bins underflow bins and 2 dimensional histograms The A option ignores bins with zero contents in reference histogram Z
164. cale can be selected Various alternative output choices are illustrated in the examples About 120 subroutines are directly accessible to the user program via Fortran calls of the type CALL H P1 P2 1 3 What should know before you start 3 This is the only interface between a Fortran program and the dynamic data structure managed by which thus remains hidden from the average user The functionality of HBOOK The various user routines of HBOOK can be subdivided by functionality as follows Booking Declare a one or two dimensional histogram or a Ntuple Projections Project two dimensional distributions onto both axes Ntuples Way of writing micro data summary files for further processing This allows projections of individual variables or correlation plots Selection mechanisms may be defined Function representation Associates a real function of 1 or 2 variables to a histogram Filling Enter a data value into a given histogram table or Ntuple Access to information Transfer of numerical values from HBOOK managed memory to For tran variables and back Arithmetic operations On histograms and Ntuples Fitting Least squares and maximum likelihood fits of parametric functions to histogramed data Monte Carlo testing Fitting with finite Monte Carlo statistics Differences between histograms Statistical tests on the compatibility in shape between histograms using the Kolmogorov test Param
165. can be reconstructed at will The last few years multi Mflop machines have become available on the desktop and farms of analysis machines are being set up to interactively reconstruct events directly from the raw data as registered in the experimental setup hence bypassing the batch reconstruction step The first Ntuple implementation can be thought of as a static large two dimensional array one dimension representing the number of events and the other a number of characteristics floating point numbers stored for each event With the present version of HBOOK Ntuples can contain complex substructures of different data types which allow a certain dynamicity Moreover tools have been developed to dynamically share data between various processes Unix or global sections VMS This makes it now possible to sample events as they are registered in the experimental setup or when the computing power is available to reconstruct vizualise and analize events in real time as they are recorded in the experimental apparatus It is expected that this will progressively eliminate the intermediate Batch DST analysis step and allow with the help of Monte Carlo events and calibration data an almost immediate response to the data taking needs of a large experiment 1 2 and its output options The HBOOK system consists of a few hundred Fortran subroutines which enable the user to symboli cally define fill and output one and two dimen
166. cannot mix types Not enough bins in DIFFS to hold result The parameter NBINS is less that the number of bins in the histograms Number of channels is different The number of channels in the two histograms to compare are different They must be the same before the routine will process the data U O L R T B Option with weighted events HBOOK does not compute an error bar for over under flow bins thus it may not be used with weighted events U O L R T B Option with profile histograms HBOOK does not compute an error bar for over under flow bins thus it may not be used with profile histograms 6 3 Bin by bin histogram comparisons 111 Weighted options and no HBARX The user had not told to figure the error bars for the histograms Therefore the operations will not be valid A option with no error bars on reference histogram The user has not told HBOOK to compute error bars for the reference histogram This error is also returned when the user attempts to select the A option to compare 2 dimensional histograms Statistical comments The methods used for the 5 and C mode are correct for unweighted events and Poisson statistics for one or two dimensional histograms For weighted events a Gaussian approximation is used which results in DIFFS values which are too low when there are fewer than 25 or so equivalent events defined under HSTATT per bin This is caused by either few entries by wide f
167. ce matrix 111 current directory 21 151 CWN see Ntuple Column Wise Ntuple cycle 149 150 data acquisition system 153 data structure 139 data summary tape 17 188 DecStation 156 Deprecated routines 110 difference between histograms 90 direct access file 146 directory 142 151 change 151 current 21 151 divide histograms 89 DST 1 7 see data summary tape Duplicate Ntuples 37 EDM 107 109 elementary function 110 equivalent event 88 ERRO 51 error 57 139 return codes see IQUEST errors on fitted parameters 105 exchange mode 150 existence of histogram 81 expansion of function 110 exponential fit 100 F test 112 fit 98 exponential 100 gaussian 100 polynomial 100 fitting 98 103 fitting Monte Carlo statistics 120 138 floating number 56 Fortran 81 Fortran convention 4 FPARAM 115 ftp 150 FUN 103 gaussian fit 100 global section 153 155 157 global sect 155 157 H1EVLI 82 INDEX H2PAGE 82 HARRAY 15 53 HBANDX 50 50 HBANDY 50 HBAR2 51 51 HBARX 51 51 53 55 57 82 84 89 91 98 113 142 HBARY 51 51 55 82 HBASFT 114 HBFUN1 51 72 120 HBFUN2 52 120 HBIGBI 72 72 82 HBINSZ 49 49 HBLACK 82 HBNAMC 17 22 24 24 27 33 35 HBNAME 17 22 23 23 24 27 33 35 HBNT 17 22 23 23 24 27 29 34 142 HBOOK 1 10 53 103 139 140 142 143 146 147 150 151 HBOOK1 4 13 30 48 50 51 70 82 142 00
168. d For example an integer run number IRUN which takes values from 8000 to 8007 should be specified as IRUN 8000 8007 and HBOOK will automatically use 3 bits to store the variable in the resulting Ntuple By the same token if the variable is known to only require a certain number of bits then this should also be indicated in CHFORM by adding that number after the type specification using lt b gt for types U and I and lt b gt lt min gt lt max gt for type R For example if IRUN takes values between 0 and 10 then the declaration should be IRUN I 4 4 4 bits are allocated Note that the type declaration simply describes how the variable is stored in memory when the HBOOK program is run and is not necessarily a description of its size in the resulting Ntuple Floating points are packed into an integer using IPACK R lt min gt lt max gt lt min gt 2 lt b gt 1 0 5 When the bit packing specifier b is not given HBOOK will store the variable using the number of bytes given by lt s gt or the default see the table above for a list of defaults for each type In case the default type and size of a variable should be used the packing bits can be specified as 11 lt gt If the bit packing specifier is given then it must be in the range 1 lt b lt 8 lt s gt where lt s gt either appears in the CHFORM declaration or is the assumed default Logical variables are always stored in 1 bit by
169. d in this case when filling a certain order can be imposed By default the entries will be automatically ordered Input parameters ID Histogram identifier NLAB Number of labels CHOPT Character variable specifying the option desired gt As N below N Add NLAB new labels read in CLAB to histogram ID R Read labels into in from histogram ID Y X axis is being treated default Y Y axis is being treated 92 Z axis is being treated 959 Sorting order of the labels S default as SA SA alphabetically SE reverse alphabetical order SD by increasing channel contents after filling SV by decreasing channel contents after filling T Modify replace NLAB existing labels read from CLAB in histogram ID Input Output parameter CLAB Character variable array with NLAB elements input and output Notes For one dimensional histograms HLABEL can be called at any time For two dimensional histograms one must call HLABEL with option N for each axis between the call to HBOOK2 and the first call to HFC2 4 2 Filling Operations It is possible to speed up the filling process with the loss of some protection and to globally transfer an array or a matrix to a histogram 4 2 1 Fast Filling Entries If the program that is using HBOOK fills many histograms several times a substantial fraction of time can be spent by HFILL in searching for the histogram it has to fill deciding wh
170. d of HREND A Fortran CLOSE statement should follow a call to HRENDF 8 5 Exchange of histograms between different 171 8 5 Exchange of histograms between different machines hbook files are by default created in exchange mode They can be transported between machines using the standard binary FTP or they can be NFS mounted in a heterogeneous environment Transfer between Unix machines with FTP ftp remote ftp bin ftp get remote hbook Running FTP on a VAX VMS systen ftp remote ftp gt bin ftp gt get remote hbook ftp quit resize s 4096 remote hbook 1 The resize command does not copy the file It simply changes the header information from 512 byte records to 4096 bytes In case the block size of the hbook file is not 1024 words LREC parameter of routine HROPEN i e 4096 bytes specify the corresponding value as parameter to the resize command The resize tool is available on request from the CERN Program Library Proposed hbook file naming convention Users are encouraged to name their hbook files with the suffix hbook so that the paw browser will be able to recognize these files automatically 8 6 RZ directories and HBOOK files Another advantage of the use of zebra in hbook is that zebra s direct access RZ package is available The RZ package allows data structures to be uniquely addressed via pathnames which are based on Unix file names Related data structures ar
171. d otherwise parameters whose names start with I J K L Mor N are integer the rest real with the exception of those beginning with the string CH which correspond to character constants Data packing booking commands that reserve space for histograms or plots require the packing parameter VMX It corresponds to the estimated maximum population of a single bin on the basis of which a suitable number of bits per channel will be allocated This allows several channels to be packed in one machine word and thus to require less storage space at the expense of packing and unpacking processing time A value 0 0 signals that no packing is to be performed and that each histogram channel will occupy one machine word 1 4 basic example 5 1 4 A basic example Below a simple example is given describing how to use HBOOK for booking filling and printing simple histograms After telling HBOOK the length of the PAWC common block to be 10000 words with a call to HLIMIT a global title to appear on all histograms is specified by calling HTITLE Next a 100 bin one dimensional histogram with identifier 10 is booked with a call to HBOOKI followed by the booking using a call to HBOOK2 of a two dimensional histogram with identifier 20 and consisting of 100 times 40 cells The DO loop labelled 10 fills the one dimensional histogram 10 while the nested DO loops labelled 20 and 30 look after filling the two dimensional histogram 20 In both c
172. e so it slows down the computation a little bit and more importantly it introduces additional numerical inaccuracy into the problem in addition to what is introduced in the numerical calculation of the FCN value The effects of non linearity and numerical roundoff both become more important as the external value gets closer to one of the limits expressed as the distance to nearest limit divided by distance between limits The user must therefore be aware of the fact that for example if he puts limits of 0 1019 on a parameter then the values 0 0 and 1 0 will be indistinguishable to the accuracy of most machines The transformation also affects the parameter error matrix of course so MINUIT does a transformation of the error matrix and the parabolic parameter errors when there are parameter limits Users should however realize that the transformation is only a linear approximation and that it cannot give a mean ingful result if one or more parameters is very close to a limit where OP x OPint 0 Therefore it is recommended that 7 2 Basic concepts of MINUIT 119 Limits on variable parameters should be used only when needed in order to prevent the parameter from taking on unphysical values When satisfactory minimum has been found using limits the limits should then be removed if possible in order to perform or re perform the error analysis without limits 7 2 2 How to get the right answer from MINUIT MINUIT offer
173. e a routine is referenced are in normal type In the description of the routines a following the name of a parameter indicates that this is an output parameter If another precedes a parameter in the calling sequence the parameter in question is both an input and output parameter Some informations about HBOOK can also be found on the Web in the PAW frequently asked ques tions page http wwwinfo cern ch asdcgi listpawfaqs pl This document has been produced using IATEX 1 with the cernman style option developed at CERN A C interface is also distributed by the CERN Program Library created using the tool f2h Table of Contents 1 Introduction 1 1 Data processing flow in particle 1 2 HBOOK and its output options gt se ss e cesa eataa ea ea ka EStG 13 What you should know before yo statt 1 3 0 BOOK parameter conventions o lt es ses kx s RUE w a LA example oou ere wo om os X EUER HE 1 5 batch as the first step of the analysis 1 5 1 Adding some datatothe RZ 8 1 6 HPLOT interface for high quality graphics o 2 One and two dimensional histograms Basics 2 TOONS ium al alte RR eh ba Q eed bale 2 1 1 One dimensional 2 40404 2 80 90 20 Be 2 RR SUR E v EORR VU S 212 Two dim
174. e addressed from a directory Routine HROPEN issues a the Fortran OPEN statement and declares the RZ top directory Example of using HROPEN CALL HROPEN LUN HISTO1 HISTOS DAT CHOPT LRECL ISTAT 172 Chapter 8 Memory Management input output Routines In this example HROPEN issues a Fortran direct access open statement for the file HISTOS DAT If on input LRECL contains the value 0 HROPEN will automatically determine the record length of the file provided that the file already exists Each time a RZ file is opened via a call to HROPEN or HRFILE a supplementary top directory is created with a name specified in the calling sequence This means that the user can more easily keep track of his data and also the same histogram identifiers can be used in various files what makes life easier if one wants to study various data samples with the same program since they can be addressed by changing to the relevant file by a call to HCDIR first For more information on the RZ package see the zebra RZ manual In the case of the second call to HROPEN where update mode is requested it is the users responsibility to ensure that write acess is enabled i e the file is opened with the SHARED attribute VAX VMS systems etc A Fortran CLOSE statement is also required for each file after calling HREND Further details of hbook s usage of zebra RZ files are given below Defining hbook files CALL HROPEN 1 HISTO1
175. e buffer size using routine HBSET as a function of the number of columns and the amount of available memory Highest efficiency is obtained when setting the buffer size equal to the record length of the RZ HBOOK file as specified in the call to HROPEN A further advantage of column wise storage is that a CWN can easily be extended with one or more new columns Columns are logically grouped into blocks physically however all columns are independent Blocks allow users to extend a CWN with private columns or to group relevant columns together New blocks can even be defined after a CWN has been filled The newly created blocks can be filled using routine HFNTB For example a given experiment might define a number of standard Ntuples These would be booked in a section of the code that would not normally be touched by an individual physicist However with a CWN a user may easily add one or more blocks of information as required for their particular analysis Note that arrays are treated as a single column This means that a CWN will behave like a RWN with the addition of data typing and compression if only one array of NVAR elements is declared This is not recommended as one thereby loses the direct column access capabilities of a CWN Performance Accessing a relatively small number of the total number of defined columns results in a huge increase in performance compared to a RWN However reading a complete CWN will take slightly longer tha
176. e contents of the channels The options described below allow the choice of a logarithmic contents scale the definition of the limits of the scale the choice of the minimum step of the scale to be an integer the choice of the same scale for several histograms so that they can be compared more easily the normalisation of the total contents to a given value If the identifier corresponds to a 2 dimensional histogram they act on projections slices bands if any CALL HMAXIM 1 and CALL Action scale limits for histogram not calculated automatically but they as set to the specified values The histogram contents are left intact Input parameters ID Histogram identifier ID 0 Meams apply limit to all existing histograms FMAX FMIN Maximum minimum for contents scale of given histogram When FMAX lt FMIN then the maximum and minimum values of the scale are computed automatically These routines can be called as often as desired for a given histogram CALL IDVECT N Action Compare the contents of all histograms whose identifiers are contained in array IDVECT and assign them the same vertical scale The comparison is made on the basis of the contents at the time routine is called Input parameters IDVECT Array of N elements that contain the identifiers of the histograms to be compared The array must be dimensioned in the calling program to a
177. e stopped IMProve maxcalls If a previous minimization has converged and the current values of the parameters therefore correspond to a local minimum of the function this command requests a search for additional distinct local minima The optional argument maxcalls specifies the approximate maximum number of function calls after which the calculation will be stopped maxcalls tolerance Causes minimization of the function by the method of Migrad the most efficient and complete single method recommended for general functions see also MINImize The minimization produces as a by product the error matrix of the parameters which is usually reliable unless warning messages are produced The optional argument maxcalls specifies the approximate maximum number of function calls after which the calculation will be stopped even if it has not yet converged The optional argument tolerance specifies required tolerance on the function value at the minimum The default tolerance is 0 1 Minimization will stop when the estimated vertical distance to the minimum EDM is less than 0 001 tolerance UP see SET ERR MINImize maxcalls tolerance Causes minimization of the function by the method of Migrad as does the MIGrad command but switches to the SIMplex method if Migrad fails to converge Arguments are as for MIGrad MINOs maxcalls parno parno Causes a Minos error analysis to be performed on the paramete
178. ector of point I of the distribution Parameters of the parametric function F Parametric function to be fitted to the data points Remarks If no errors are specified by the user they are taken to be the square root of the bin contents In this case empty channels are ignored by the fitting procedure If at least one of C 1 0 then ECI is set to 1 for all channels cells If errors are correctly defined via HBARX or HPA KE then all channels will be taken into account The minimization algorithm requires the calculation of derivatives of the function with respect to the parameters and this is normally done numerically by the fitting routine If the analytical expression of the derivatives is known the fit can be speeded up by making use of this information see option D in the control flag of the various fitting routines For a log likelihood fit the likelihood is formed by determining the Poisson probability that given a number of entries in a particualar bin the fit would predict its value This is then done for each bin and the sum of the logs is taken as the likelihood 112 7 1 Fitting 113 7 1 1 One and two dimensional distributions CALL HFITH ID FUN PARAM STEP PMIN PMAX SIGPAR CHI2 Action Fits a given parametric function to the contents of a 1 or 2 dimensional histogram and option ally superimposes it to the 1 dimensional histogram when editing
179. eded This optimization can be very important Assume for instance that a 100 Mbyte file contains an Ntuple consisting of 300 columns and that 3 columns are referenced Then without optimization the complete 100 Mbyte file will have to be read while by specifying the columns used only 1 Mbyte will be input 3 6 Ntuple operations Duplicate Ntuples CALL HNTDUP ID1 ID2 NEWBUF CHTITL CHOPT Action Duplicate the definition of an Ntuple into a new Ntuple with the same definitions as the original one but with 0 entries Input parameters Identifier of original Ntuple ID2 Identifier of new Ntuple NEWBUF Buffer size NEWBUF O use buffer size of ID1 NEWBUF O use current buffer size 10000 for RWN s NEWBUF O use actually specified value as buffer size CHTITL Character variable specifying the the new title for the duplicate Ntuple If CHTITL use the original title CHOPT Character variable specifying the desired option CHOPT gt use original value disk or memory resident CHOPT M make the Ntuple memory resident CHOPT A interactive mode sets the addresses to PAWCRA 42 Chapter 3 Ntuples Rename a column in an Ntuple CALL ID1 CHOLD CHNEW Action Renames a column in an Ntuple CHOLD of Ntuple ID into CHNEW Duplicate the definition of an Ntuple into a new Ntuple with the same definitions as the original one but with 0 entries Input parameters 1 Identifier of Ntuple
180. emory 9 5 Using PAW as a presenter on OS9 systems The technique described in previous sections may also be used to access HBOOK histograms being filled by a monitoring task on OS9 systems from a standard PAW session running on a machine with the TCP IP software INDIRECT PAWC PROGRAM PRODUCE Monitoring task MT1 in processor OP2 2 PARAMETER NWPAW 10000 COMMON PAWC IPAWC CALL PAW Server one server per client Book histos a computer runningon shared code with TCP IP one OS9 node CALL HBOOK1 10 TEST1 50 3 3 0 Apollos SUNs 59 CALL HBOOK1 20 TEST2 50 3 3 0 IBM Central VAX gt Fill histos NUMEVT 10000 DO 20 I 1 NUMEVT E DO 10 J 1 100 ems CALL RANNOR A B OP1 OP2 OS9 processors CALL HFILL 10 A 0 1 MT1 MT2 Monitoring tasks CALL HFILL 20 B 0 1 10 CONTINUE 20 CONTINUE Figure 9 3 Visualising histograms on OS9 modules i from PAW 99 STOP END Example of how to access OS9 modules from PAW PAW gt rlogin O OPALO1 connect to an 059 machine PAW gt rshell module OP2 MT1 PAW server connects to OP2 MT1 Processor OP2 Monitoring Task MT1 PAW gt histo plot 10 plot histogram 10 PAW gt hrin 0 read all histograms into PAWC PAW gt Histo File 1 local dat 1024 N create a new file local dat on the client machi
181. ensional ece fee at ho ew EE a Ep 22 PI e REESE X Se ee dodo kd ys mcn RM 2 44 Copy renume Tesetand delete 2 444648 864468 be Rx ET 3 Ntuples 31 CWN and RWN Two kinds of Ntuples 32 Row Wise Ntuples RWN 241 ocra 04 4 40 RE bog Rode y deb 62 252 Coes ey S eb S hui e drag EU 3 3 general Ntuples Column Wise Ntuples 22 3 3 2 Describing the columns 3 3 3 Create CHFORM dynamically 2 PuhngpqCWN uo C SE ew eee Pede he xo Be eee ee 3 4 Making projections ofa RWN c edocs a e asa u Kw pw ey eee 3 5 Getintonmation about an Ntupl us ae eon m w n w ee 3 5 1 Retrieve the contents of a RWN into 3 5 2 Retrieve the contents of aC WN into a common block 22 2 Generate B USEFTUBGHOH uus x uoo xb OR daca bares oos loops u once ay km A sa 6 Npe apertos 2222 2252 vn woe Xem 4 569 ee tiple examples 2 2 222 2 2 4 6 4 E 11 13 16 16 16 16 17 18 18 iii 4 Advanced features for booking and editing operations 54
182. er CALL HFUNC ID FUN Action Samples the function FUN which must have been declared EXTERNAL at the centre of the bins of a histogram The function will be superimposed onto the histogram at editing time and its values optionally printed out see HIDOPT PFUN Input parameters ID identifier of an existing 1 dimensional histogram ID 0 signals that the function should be calculated for all existing 1 dimensional histograms FUN External real function e g REAL FUNCTION FUN X The function parameter X will be the central value of a histogram bin The user must return the corresponding function at that point as a value in FUN 4 1 Overview of booking options 59 Remark Not existing for 2 dimensional histograms Function FUN cannot contain any call to an entry of the HBOOK package HFUNC can be called several times for the same histogram identifier ID If the latter case the values of the old function will be overwritten by the new one The chi squared 7 as defined below will be printed along with the statistical information at the bottom of the histogram with Nen number of channels of histogram C i contents of channel i F i value of function at centre of channel i Ne 2 C i F i n number of entries in channel i l 1 2 W weight of event 7 in channel i i e square root of contents C or as given by HBARX HPAKE 4 1 7 Reserve array in memory CALL HARRAY ID NWO
183. ers the array of variables X and the selection flag ISEL If FUN 0 no filling takes place for that event IFROM Event number where the histogramming has to start ITO Event number where the histogramming has to end IVARX Sequence number in the Ntuple of the variable to be histogrammed Example of the use of a one dimensional Ntuple projection PROGRAM MAIN EXTERNAL WFUNC CALL HPR0J1 10 20 1 WFUNC 0 0 4 FUNCTION WFUNC X ISEL DIMENSION X WFUNC 0 IF ISEL EQ 1 THEN IF X 2 2 X 3 2 LT 0 WFUNC 1 ELSEIF ISEL EQ 2 THEN IF X 2 2 X 3 2 GT 5 WFUNC 1 ELSE WFUNC X 5 ENDIF END Note that in an interactive session with paw the user function FUN can be defined interactively using a Fortran like syntax without recompilation and relinking CALL HPROJ2 ID IDN ISEL FUN IFROM ITO IVARX IVARY Action Same action as HPROJI but filling a previously booked 2 dimensional histogram or a profile histogram Variable X IVARX will be projected onto the X axis onto the Y axis for all entries in the Ntuple between IFROM and ITO inclusive The number of entries in an Ntuple can be obtained by HNOENT 3 5 Get information about an Ntuple 35 3 5 Get information about an Ntuple CALL HGIVEN ID CHTITL NVAR CHTAG RLOW RHIGH Action Routine to provide information about an Ntuple Input parameters ID Identifier of the Ntuple NVAR Dimension of arrays TAGS RLOW and RHIGH Output parame
184. es not produce all the numerical information of the HBOOK output routines It is not restricted by the line printer s poor resolution and unique character sets but it uses the full graphics capabilities of the targeted output device HPLOT can access an HBOOK data structure and transform it into drawings using the HIGZ graphics package Some of the available options are Predefined ISO standard paper size A4 A3 etc horizontal or vertical orientation with suitable margins Other sizes are also possible Combination of several plots on the same page either by windowing or superimposition or both with different symbols to distinguish them Titles on the axes and text anywhere on the picture using various fonts containing e g Greek or special characters Three dimensional surface representations for two dimensional histograms with hidden line and hidden surface removal Colour if the hardware allows it hatching grey levels As a simple example of the use of HPLOT let us consider a program similar to the one in Figure 1 4 After opening a file on unit 10 to write the metafile output Fortran OPEN statement we book then fill the Ntuple projections and finally plot them The call to HPLINT initialises HPLOT and HPLCAP redirects the metafile output to unit 10 The parameters given to HPLOT instruct the program to output all histograms in the current working directory to the metafile using standard opt
185. eterization Expresses relationships between as linear combinations of elementary functions Smoothing Splines or other algorithms Random number generation Based on experimental distributions Archiving Information is stored on mass storage for further reference in subse quent programs Editing Choice of the form of presentation of the histogramed data 1 3 What you should know before you start The basic data elements of HBOOK are the histogram one and two dimensional and the Ntuple The user identifies his data elements using a single integer Each of the elements has a number of attributes associated with it The package is organised as part of a library from which at load time unsatisfied externals are searched and loaded In this way only those subroutines actually used will be loaded therefore minimising the space occupied in memory by the code Unfortunately given the way Fortran works and although the package is structured as much as possible in the sense of selective loading some unused subroutines will usually be present HBOOK uses the ZEBRA 10 data structure management package to manage its memory see chapter 8 The working space of is an array allocated to the labelled common PAWC ZE BRA terms this is a ZEBRA store It is thus necessary to reserve as many locations as required with a 4 Chapter 1 Introduction declarative statement in the main program The actual length of the common is defined most
186. evel for rejection of already included regres sors by default it is set to 1 A higher value makes it more difficult for regressors to remain in the regression The value of PFLV has to be gt 0 PLUN This parameter indicates the logical unit for writing the Fortran code of the function FPARAM X which gives the value of the parametrization at point X This Fortran code can be compiled and used in subsequent jobs By default no code is written PNBX Maximum number of regressors that may be entered as input to the fitting process after selec tion By default PNBX is set to 500 setting PNBX to an appropriate value will avoid wasting space in dynamic area PAWC This parameter may be set to the same value of PNBF or PNEF whichever is appropriate to save space PNCX Maximum number of regressors that may appear in the final expression of the parametrization this number has to be lt 50 Default setting is 50 The same remark applies as for PNBX Distributions CALL HPARMN X Y EY NP NVAR IC R2MIN MAXPOW COEFF ITERM NCO Input parameters X Coordinates of data points array of size NP NVAR Y Data to fit array of length NP EY Errors on data array of length NP NP Number of points to fit NVAR Dimension of X space MAXPOW see HPARAM IC see HPARAM R2MIN see HPARAM Output parameters See HPARAM The only difference concerns option W of IC where Oerrors are taken from EY W 1 errors are set to 1 7 5 S
187. from the null hypothesis Based on considerations such as those given above as well as considerable computational experience it is generally believed that tests like the Kolmogorov or Smirnov Cramer Von Mises which is similar but more complicated to calculate are probably the most powerful for the kinds of phenomena generally of interest to high energy physicists This is especially true for two dimensional data where the Chisquare Test is of little practical use since it requires either enormous amounts of data or very big bins The Confidence Level for 1 dimensional data Using the terms introduced above the confidence level is just the probability of rejecting the null hypoth esis when it is in fact true That is if you accept the two histograms as compatible whenever the value of PROB is greater than 0 05 then truly compatible histograms should fail the test exactly 596 of the time The value of PROB returned by HDIFF is calculated such that it will be uniformly distributed between zero and one for compatible histograms provided the data are not binned or the number of bins is very large compared with the number of events Users who have access to unbinned data and wish exact confidence levels should therefore not put their data into histograms but should save them in ordinary Fortran arrays and call the routine TKOLMO which is being introduced into the Program Library On the other hand since HBOOK is a convenient way of collecting data and
188. gical unit value for the results HOUTPU or the error messages HERMES Input parameters LOUT logical unit number of the file with the printed output LERR logical unit number of the file with error messages 88 Chapter 4 Advanced features for booking editing operations 10 20 Example of printing options SUBROUTINE HEXAM4 TEST PRINTING OPTIONS gt R Brun DATA 0 1 Get hist 110 from data base CALL HRGET 110 hexam dat Book 2 new histograms CALL HBOOK1 1000 TEST OF PRINTING OPTIONS 40 1 41 0 CALL HBOOK1 2000 TEST OF BIG BIN 20 XMIN XMAX O CALL HIDOPT 1000 ERRO Fills new IDs DO 10 I 1 40 J 2 I 1 W HI 110 J HI 110 751 CALL HFILL 1000 FLOAT I 0 W CONTINUE DO 20 I 1 20 W SQRT HI 110 J CALL HIX 2000 I X CALL HF1 2000 X W CONTINUE Set various printing options CALL HIDOPT 110 BLAC CALL HIDOPT 110 NPLO CALL HIDOPT 110 NPST CALL 110 1 CALL HMAXIM 110 100 CALL HIDOPT 110 1EVL CALL HIDOPT 110 NPCH CALL 110 1 CALL 1000 NPCH CALL 1000 CALL 1000 15 1 CALL HIDOPT 1000 LOGY CALL 1000 CALL 1000 INTE CALL 1000 PERR CALL 1000 ROTA CALL 1000 CALL 2000 5 CALL
189. grams if there is saturation since it does not have enough information in this case 6 2 2 Statistical Considerations The Kolmogorov Test The calculations in routine HDIFF are based on the Kolmogorov Test See e g 11 pages 269 270 It is usually superior to the better known Chisquare Test for the following reasons It does not require a minimum number of events per bin and in fact it is intended for unbinned data this is discussed below It takes account not only of the differences between corresponding bins but also the sign of the difference and in particular it is sensitive to a sequence of consecutive deviations of the same sign In discussing the Kolmogorov test we must distinguish between the two most important properties of any test its power and the calculation of its confidence level 6 2 Statistical differences between histograms 105 The Power The job of a statistical test is to distinguish between a null hypothesis in this case that the two histograms are compatible and the alternative hypothesis in this case that the two are not compatible The power of a test is defined as the probability of rejecting the null hypothesis when the alternative is true In our case the alternative is not well defined it is simply the ensemble of all hypotheses except the null so it is not possible to tell whether one test is more powerful than another in general but only with respect to certain particular deviations
190. h the normal output W This switch controls the weights to applied to the data during the fit O weights on histogram contents are already defined via HBARX or HPAKE If not they are taken to be equal to the square root of the contents 1 weights are equal to 1 T This switch controls the system defined elementary functions set to use 0 Monomials will be selected as the standard elementary functions 1 Chebyshev polynomials with a definition region 1 1 7 4 Parametrization 129 C R 4 W N This This 0 Legendre polynomials with a definition region 1 1 shifted Chebyshev polynomials with a definition region 0 1 Laguerre polynomials with a definition region 0 00 Hermite polynomials with a definition region oo 00 switch controls the kind of regressor used in the fit Regressors are products of standard polynomials see preceeding switch Regressors are products of user defined elementary functions The user should write a DOUBLE PRECISION function HELEFT IEF X where is the elementary function code in the sense explained above 10 times the function code plus 1 The function code number can vary from 1 to PNEF number of user supplied elementary functions PNEF has to be specified by the user before calling HPARAM via a call to the routine HSETPR described below The seconf parameter X is the point where the function should be calculated Regressors are user defined in this case the variable P
191. hannels in Y zero for a 1 dimensional histogram YMI Lower edge of first Y channel YMA Upper edge of last Y channel NWT Number of machine words for the title If there is no title NWT Is returned as 0 LOC Address of the histogram in the common PAWC 5 14 Statistics 101 5 14 Statistics VARIAB HSTATI ID ICASE CHOICE NUM Action This function of type REAL returns the mean value standard deviation or number of equivalent events of a 1 dimensional distribution Underflows and overflows are not included in the calculation Input parameters ID Histogram identifier ICASE 1 Mean value 2 Standard deviation 3 Number of equivalent events CHOICE See HUNPAK NUM See HUNPAK If HIDOPT CID STAT has been called the results are based on the information stored at filling time Otherwise the results are based on the channel contents only If z and represent the value and contents of event i then one has the following relations T H H Expectation value E x Dini Wi Ti 2 Wi Mean value E x Central moment of order n M n E x E x Standard deviation 1 2 SE Number of equivalent events Chapter 6 Operations Histograms 6 1 Arithmetic Operations Histograms can be added subtracted divided or multiplied provided their number of channels are the same CALL HOPERA ID1 CHOPER ID2 ID3 C1 C2 Action Fills an histogram I3 with values such that logically operands a
192. he different p are allowed to float independently they return a set of values for which the fitted number of events is generally less than the actual total number as downward fluctuations have a smaller assigned error and are given higher weight Weighted Events In some problems it is necessary to apply weights to the Monte Carlo data before comparing it with the real data An example occurs when events are detected with some efficiency which differs from bin to bin and the form of which is known exactly Rather than reject MC events on a random basis it is more effective to include them all weighted by the appropriate efficiency Another such instance arises if MC data has been generated according to one function but another one is desired For example data on p BE cos 0 may have been generated using some form of the Bethe Bloch Equation dE and with hindsight it is realised that some other form F 0 m is more correct This be accomo dated by weighting each bin by Fo p 0 mj Wji FF In such a case the predicted number of events in each bin is modified and Equation 7 8 becomes m pata Asa 7 19 j 1 The likelihood function of Equation 7 9 is unchanged The differentials of Equation 7 10 become 0 Vj 7 20 jmd 42 and the differentials with respect to the give the equivalents of Equations 7 14 and 7 15 7 21 1 140 Chapter 7 Fit
193. he error on the resulting histogram is calculated supposing that the contents of the two input histograms ID1 and ID2 are uncorrelated This is valid also for projections slices and bands of 2 dimensional histograms If histogram ID3 is packed the number of bits allocated per channel cell has to be sufficient to store the results 102 6 2 Statistical differences between histograms 103 6 2 Statistical differences between histograms CALL HDIFF ID1 1D2 PROB CHOPT Action Statistical test of compatibility in shape between two histograms using the Kolmogorov test The histograms are compared and the probability that they could come from the same parent distribution is calculated The comparison may be done between two 1 dimensional histograms or between two 2 dimensional histograms For further details on the method see 6 2 2 below Input parameters 1 Identifier of first histogram to be compared ID2 Identifier of second histogram to be compared A character string specifying the options desired D Debug printout produces a blank line and two lines of information at each call in cluding the identifier numbers ID the number of events in each histogram the value of PROB and the maximum Kolmogorov distance between the two histograms For 2 dimensional histograms there are two Kolmogorov distances see below If option N is specified there is a third line of output giving the probalility PROB for shape a
194. histogram bin contents Its dimension should be at least equal to the number of channels in histogram ID Remark If the HBARX option was not set for the given histogram then it is activited by a call to HPAKE 64 Chapter 4 Advanced features for booking editing operations 4 2 3 Filling histograms using character variables Routines for which using routine HLABEL alphanumeric labels were associated with the histogram channels are filled with the routines HFC1 and HFC2 These allow on top of by bin number to fill an histogram by specifying a alphanumeric channel identifier CALL HFC1 ID IBIN CLAB W CHOPT Action Fills a channel in a one dimensional histogram ID One dimensional histogram identifier IBIN Number of the bin to be filled Gf Z 0 Character variable containing the label describing the bin if IBIN 0 CHOPT Character variable specifying the option desired gt default as S N filling order i e the order of the labels on the plot is given by the sequence in which they are presented in the successive calls to the routine this method can be very time consuming since all channels must be scanned at each call S automatic sort U if the channel does not exist then the underflow channel is incremented by default a new channel is created for each new label Remarks If IBINZO then the channel IBIN is filled CLAB may then be undefined When a label is encountered wh
195. ic function to a number of value pairs with associated errors Input parameters N Number of points to be fitted NDIM Declared first dimension of array X Dimension of the distribution X Array of dimension N containing the X coordinates of the points to be fitted Y Array of dimension N containing the Y coordinates of the points to be fitted EY Array of dimension N containing the errors on the Y coordinates of the points to be fitted FUN Parametric function to be declared EXTERNAL CHOPT Character variable specifying the desired options B Some or all parameters are bounded The arrays STEP PMIN and PMAX must be speci fied By default all parameters vary freely D user provides the derivatives of the function analytically by specifying the user routine HDERIV By default derivatives are computed numerically E Perform a detailed error analysis using the minuit routines L the logaritnic Likelihood fitting method By default the chisquared method is used M Invoke interactive MINUIT 902 Quiet mode No printing User function value is taken from HCFITD FITPAD 24 FITFUN see section 7 1 5 All calculations are performed in double precision 116 Chapter 7 Fitting parameterization and smoothing V Verbose mode Results are printed after each iteration By default only final results are printed W Set the event weights equal to one By default weights taken according to
196. ical unit number associated to the file CHTOP Character variable specifying the name of the top directory associated with unit LUN maxi mum 8 characters This is an arbitrary name used to identify the file on unit LUN in subsequent calls to HR routines CHFILE Character variable specifying the name of the file to be opened CHOPT Character variable specifying the options selected Medium Disk default G Global Section see chapter 9 mode gt Existing HBOOK file default W Create a new file Q Override default number of records for new file with contents of IQUEST 10 X The file is will be in exchange format U Update an existing file P Preserve case of file name Unix F Use fortran I O LREC Record length in machine words recommended value is 1024 If LREC 0 the actual record length is returned on exit 168 Chapter 8 Memory Management input output Routines Output parameters ISTAT Return code ISTAT O indicates success LREC Only when LREC 0 on input The actual record length of the file on disk Remarks HROPEN uses C IO unless it is called with option F In that case should be called to close the file instead of HREND On fortran I O is the default On Unix the filename CHFILE will be translated to lowercase unless option P is given If LREC 0 on input HROPEN will automatically determine the record length of existing files maximum number of records is by default 32
197. ice or band of a 2 dimensional histogram on the line printer in the standard representation Input parameters ID Histogram identifier ID 0 means edit all existing histograms CHOICE Character variable that selects subhistograms irrelevant for the one dimensional case See routine HUNPAK for possible values CHOICE is equivalent to CHOICE HIST NUM Serial order of the slice or band NUM 0 is the same as NUM 1 Routine HPHIST ignores the option HIDOPT ID ROTA 86 Chapter 4 Advanced features for booking editing operations CALL HPROT ID CHOICE NUM Action Analogous to HPHIST but with a presentation down the page Parameters special values and remarks are the same as for HPHIST CALL HPSCAT ID Action Edits a 2 dimensional histogram as a scatter plot Input parameter ID Histogram identifier 2 dimensional ID 0 means to edit all histograms Remark 2 dimensional histogram with identifier ID might have been booked as a table and will be output as a scatter plot Projections are not printed see HPHS CALL HPTAB ID Action Edits a 2 dimensional histogram as a table Input parameter ID Histogram identifier 2 dimensional ID 0 means to edit all histograms Remark 2 dimensional histogram with identifier ID might have been booked as a scatterplot but it will be output as a table The following two routines can be used to save space when the program does no
198. ich is not yet known then for options N and S a new channel is added dynamically while for option U the underflow channel is incremented Routine HLABEL can be called before or after HFC1 CALL HFC2 ID IBINX CLABX IBINY CLABY W CHOPT Action Fills for a two dimensional histogram the channel identified by position IBINX or label CLABX and position IBINY or label CLABY with weight W ID Two dimensional histogram identifier IBINX Number of the X bin to be filled if Z 0 CLABX Character variable containing the label describing the X bin if IBINX 0 IBINY Number of the Y bin to be filled if Z 0 CLABY Character variable containing the label describing the Y bin Gf IBINY 0 W Weight of the event to be entered into the histogram CHOPT Character variable specifying the option desired gt default as S 4 2 Filling Operations 65 W filling order see S automatic sort default U ifthe channel does not exist then the underflow channel is incremented by default a new channel is created for each new label Remarks For efficiency reasons routine HLABEL must be called before HFC2 If IBINXZO then the channel described by IBINX is filled CLABX may then be undefined If IBINYZO then the channel described by IBINY is filled CLABY may then be undefined If the channel described by IBINX or CLABX does not exist the underflow channel is incremented Idem for IBINY and CLABY
199. ich type of histogram it is and unpacking and packing bits if more than one channel is to be stored in one computer word To reduce the overall filling time there are several actions that can be taken 4 2 Filling Operations 61 Bypass part of the logic that finds out the characteristics of the histogram to fill This can be achieved by using instead of HFILL the special filling entries described in this section Avoid packing more than one channel in a computer word For these reasons it is recommended to use always HFILL at the development stage and replace it later with HF1 HF2 etc only when a rather stable program is going to be used extensively Calls to HFILL and HF1 or HF2 cannot be mixed on the same ID CALL HF1 ID X WEIGHT Action Analogous to HFILL on a 1 dimensional histogram but HBARX and HIDOPT ID STAT are ignored Input parameters ID histogram identifier X value of the abscissa WEIGHT event weight CALL HF1E ID X WEIGHT ERRORS Action Analogous to HF1 but also the errors are accumulated Input parameters ID histogram identifier X value of the abscissa WEIGHT content is incremented by WEIGHT ERROR the error is incremented by ERROR 2 HFIE Fills a 1 D histogram SUBROUTINE HFI E ID X W E ID Histogram identifier X Value of the abscissa W Content is incremented by W E Errors is incremented by E 2 CALL HF2 ID X Y WEIGHT Action Analogous to HFIL
200. ill be returned when the two content values are identical since no statistical test could claim they came from different distributions Other notes The normalization scaling used unless N option selected is based on channel contents for all channels requested including overflow underflow provided you select one of the overflow underflow options Negative bin contents are flagged as bad bins in 5 C options Statistical methods and numerical notes For simplicity this is written as if the N option were in effect The methods used for the S and C options are correct for unweighted events and Poisson statistics for 1 or 2 dimensional histograms Errors may result in either the 5 and C options for small tolerances if bin contents are greater than the largest allowed integer For the 8 option with unweighted events the test which is uniformly most powerful treats N 2 sum of the two bin contents as having chosen via a binomial distibution which histogram to enter The binomial parameter p is given by the relative normalization of the histograms 0 5 if the total number of entries in each histogram was the same For DIFFS values greater than TOL the first two digits are correct For values less than TOL the two digits to the right of the first non zero TOL digit are significant i e for TOL 0 0001 0 000xxx are significant One can force higher accuracy by setting TOL smaller or even 0 but calculation time will increase and warni
201. ing the right parameter errors with limits The best way to be absolutely sure of the errors is to use independent calculations and compare them or compare the calculated errors with a picture of the function Theoretically the covariance matrix for a physical function must be positive definite at the minimum although it may not be so for all points far away from the minimum even for a well determined physical problem Therefore if MIGRAD reports that it has found a non positive definite covariance matrix this may be a sign of one or more of the following A non physical region its way to the minimum MIGRAD may have traversed a region which has unphysical behaviour which is of course not a serious problem as long as it recovers and leaves such a region An underdetermined problem If the matrix is not positive definite even at the minimum this may mean that the solution is not well defined for example that there are more unknowns than there are data points or that the parameterization of the fit contains a linear dependence If this is the case then MINUIT or any other program cannot solve your problem uniquely and the error matrix will necessarily be largely meaningless so the user must remove the underdeterminedness by reformulating the parameterization MINUIT cannot do this itself Numerical inaccuracies It is possible that the apparent lack of positive definiteness is in fact only due to excessive roundoff errors in
202. ion B splines smoothing of a 1 dimensional histogram Input parameters ID Identifier of an existing 1 dimensional histogram IC Superimposition flag IC 0 is identical to IC 1 1 Replaces original contents by the value of the spline 2 Superimposes the spline function when editing N Number of knots when N lt O then 13 K Degree of the splines when K gt 3 then K 3 Output Parameter 2 chisquare x between original and smoothed histogram Remarks HSPLII can be called several times for the same histogram identifier ID for any value of the parameters If the distribution to be smoothed exibits NP statistically relevant peaks then a rule of thumb to define the number of knots is N 4 NP 6 for a spline of degree 3 7 5 Smoothing 133 CALL HSPLI2 ID NX NY KX KY Action B splines smoothing of a 2 dimensional histogram Input parameters ID Identifier of an existing 2 dimensional NX Number of knots in the X interval when NX lt O then 13 NY Number of knots in the Y interval when NY lt 0 then 13 KX Degree of the spline in X when KX gt 3 then 3 KY Degree of the spline in Y when gt then KY 3 Remark he original contents of the histogram are replaced by the value of the spline approximation See the remark about the number of knots for routine HSPLII S HSPFUN Action Performs a B spline smoothing of a 1 dimensional histogram and returns
203. ion while HPLEND closes the metafile See the HPLOT user s guide 2 for more details The result of the job and the resulting PostScript file can be compared to the lineprinter output in Figure 1 4 Example of a simple HPLOT program PROGRAM HPTEST COMMON PAWC H 80000 DIMENSION X 3 CHARACTER 8 CHTAGS 3 DATA CHTAGS X Z CALL HLIMIT 80000 Reopen data base UNIT 10 file hplot meta form formatted status unknown CALL 10 TEST1 100 3 3 0 CALL HBOOK2 20 TEST2 30 3 3 30 3 3 250 CALL HBOOKN 30 N TUPLE 3 1000 CHTAGS DO 10 I 1 10000 CALL RANNOR A B 1 X 2 B X 3 A A B B CALL HFN 30 X 10 CONTINUE 14 CALL CALL CALL CALL CALL CALL CALL END HPR0J1 10 30 0 0 1 999999 1 HPR0J2 20 30 0 0 1 999999 1 2 HPLINT 0 HPLCAP 10 HPLOT 0 0 HPLEND HINDEX Chapter Introduction 1 6 HPLOT interface for high quality graphics Output Generated Version 1 13 05 of HIGZ started HBOOK CERN VERSION 4 13 HISTOGRAM AND PLOT INDEX 06 02 92 NO TITLE ID B C ENTRIES DIM NCHA LOWER UPPER ADDRESS LENGTH 1 TEST 10 32 10000 1 X 100 0 300 01 0 300 01 78388 144 2 5 2 20 8 10000 2 X 30 0 300 01 0 300 01 78240 298 Y 30 0 300E 01 0 300 01 77963 268 3 N TUPLE 30 N 77914 39 MEMORY UTILISATION MAXIMUM TOTAL SIZE OF COMMON PAWC 80000 28 t
204. ion in terms of elementary functions regressors Let us suppose that we have collected NP sets of NDIM 1 data being yi x1 v NDprM With 1 lt i lt NP the i set Here yi is the value observed at the coordinates 714 wprw NDIM must be greater or equal to 1 and itis the dimensionality of our parametrization problem that is the number of independent 126 Chapter 7 Fitting parameterization and smoothing variables that we want to use in order to parametrize our data In the case of a histogram NDIM is clearly 1 x is the centre of a histogram channel y is the contents of the corresponding channel and NP is the number of channels of the histogram In the case of a scatter plot NDIM is 2 x and are the ordinate and abscissa of the centre of a cell y is the contents of the cell and NP is NX NY the total number of cells In case of histograms or scatter plots the entry HPARAM should be used For data which are not contained in an HBOOK histogram or scatter plot and for higher dimensionality sets NDIM lt 10 the entry HPARMN has to be used We could express a possible expansion of our data in elementary functions in the following way y F t enco Fuco 214 ZNDIMA U1 ec F t NP ENDIM NP t enco Fnco 1 NP 2NDIM NP UNP where we are summing NCO elementary functions each one multiplied by its own coefficient In other words we are pretending that our data points are fitted by
205. ional histograms More statistical information Comprehensive booking and filling with user supplied functions of one or two real variables Dynamic creation of ordinary Fortran arrays HARRAY 2 4 rename reset and delete CALL HCOPY ID1 ID2 CHTITL Action Generates histogram ID2 as a copy of ID1 apart from the title Input parameter description 1 existing identifier ID2 non existing identifier CHTITL new title CHTITL means that the old title is kept 2 4 Copy rename reset delete 19 CALL HCOPYR ID1 ID2 CHTITL IBINX1 IBINX2 IBINY1 IBINY2 CHOPT Action Generates histogram ID2 as a copy of a range of the channels of ID1 and optionally copies the stored errors on the channels If ID2 already exists it is deleted and re created The new histogram is created with the same bin width in X and Y for 2 D histograms as in the original histogram bin number range is allowed to exceed the range of the original histogram in which case the new histogram will contain bins with zero contents This possibility is to allow users to copy a histogram into one of a larger scale Input parameter description Existing identifier ID2 New identifier CHTITL New title CHTITL means that the old title is kept IBINX1 Binin X from which to start the channel IBINX2 Binin X on which to end the channel copy IBINY1 Binin Y from which to start the channel copy 2 D his
206. itting method By default the chisquared method is used M Invoke interactive minuit W Theresults of the fit are not stored bin by bin with the histogram By default the function is calculated at the centre of each bin in the specified range 902 Quiet mode No printing R Restricted area of the 1 D histogram IFTLOW IQUEST 11 specifies the lower limit of the minimization domain IFTUP IQUEST 12 specifies the upper limit of the minimization domain 7 1 Fitting 115 mode Results are printed after each iteration By default only final results are printed W Set event weights to one By default weights are taken according to statistical errors NP Number of parameters PAR Array of dimension NP with initial values for the parameters STEP Array of dimension NP with initial step sizes for the parameters B option only PMIN Array of dimension NP with the lower bounds for the parameters B option only PMAX Array of dimension NP with the upper bounds for the parameters B option only Output parameters PAR Array of dimension NP with the final fitted values of the parameters SIGPAR Array of dimension NP with the standard deviations on the final fitted values of the parameters CHI2 Chisquared of the fit 7 1 3 Fitting one or multi demensional arrays CALL N NDIM NVAR X Y EY FUN CHOPT NP PAR STEP PMIN PMAX SIGPAR CHI2 Action Fits a given parametr
207. ize of the file A simple rule of thumb in the case of no data compression is to have NWPAWC gt NCOL LREC where NWPAWC is the total number of words allocated by HLIMIT LREC is the block size of the file in machine words as given in the call to HROPEN and NCOL is the number of columns 3 3 2 Describing the columns of a CWN CALL HBNAME ID CHBLOK VARIABLE CHFORM CALL HBNAMC ID CHBLOK VARIABLE CHFORM Action Describe the variables to be stored in a CWN non character and character variables respec tively Input parameters ID Identifier of the Ntuple as in the call to HBNT CHBLOK Character variable of maximum length 8 characters specifying the name by which the block of variables described by CHFORM is identified VARIABLE The first variable that is described in CHFORM Variables must be in common blocks but may not be in a ZEBRA bank For example given the common block CEXAM described below one would call HBNAME with the argument IEVENT In the case of character variables the routine HBNAMC must be used In all other cases one should use HBNAME CHFORM Can be either a character string describing the variables to be stored in block CHBLOK or CLEAR To clear the addresses of all variables in the Ntuple SET To set the addresses in which to write the values of all variables in block CHBLOK The last two forms are used before reading back the Ntuple data using HGNT HGNTB HGNTV or HGNTF See also HUWFUN With CHFOR
208. ked projections slices bands are filled as well Input parameter description ID X Y histogram identifier value of the abscissa value of the ordinate WEIGHT event weight positive or negative Remarks If one full word per channel is reserved at booking time WEIGHT is taken with its floating point value In case of packing i e more than one channel per word WEIGHT must be positive and will be truncated to the nearest integer WEIGHT O will give meaningless results See section 4 2 on page 60 for alternative filling routines 18 Chapter 2 One two dimensional histograms Basics 2 3 Editing CALL HISTDO Action Outputs all booked histograms to the line printer An index is printed at the beginning specifying the characteristics and storage use of each histogram Remark If a histogram is empty a message declares this condition and the histogram is not printed CALL HPRINT ID Action Outputs a given histogram to the line printer ID Histogram identifier Remarks CALL HPRINT O is equivalent to CALL HISTDO apart from not printing the index When a histogram is empty a message declares this condition and the histogram is not printed Some available booking options are shortly listed below For a full description see chapter 4 Creation of histograms with non equidistant bins Creation of profile histograms Rounded scale Projections and slices of 2 dimens
209. lacian of event density is statistically significant The data must be statistically independent i e events weighted or unweighted drawn randomly from a parent probability distribution or differential cross section e g you cannot further smooth a previously smoothed distribution For histograms the chi squared CHISQ is that of the fit to the original histogram assuming gaus sian errors on the original histogram even for low statistics including the error on zero being 1 It is calculated like this even for a Poisson likelihood fit in that case the maximum likelihood may not correspond to the minimum chi squared but CHISQ can still be used with NDF the no of degrees of freedom as a goodness of fit estimator For Ntuples an internally generated and temporary histogram is used to calculate CHISQ in the same way 7 6 Random Number Generation 135 7 6 Random Number Generation R HRNDM1 ID Action Returns a random number distributed according to the contents of 1 dimensional histogram Input parameter ID Identifier of an existing 1 dimensional histogram according to whose distribution random numbers have to be generated Remark The first time HRNDM1 is called on a given histogram with identifier ID the channel contents of the original histogram are replaced by the integrated channel contents normalized to 1 The histogram ID must be booked with 1 bin word VMX 0 If the histogram ID does not exist zero
210. length larger or equal to N N Number of histograms to be compared N 0 Means compare all existing 1 dimensional histograms Remark This routine can be called as often as desired to recompute the histogram scales 84 Chapter 4 Advanced features for booking editing operations CALL HNORMA ID XNORM Action Normalizes the total contents of a 1 dimensional histogram when printing it Original contents are left intact Input parameters ID Histogram identifier ID 0 Meams apply normalization factor to all existing histograms XNORM Normalization factor to be applied to histogram when printing XNORM 0 is illegal Remarks Ifa function is superimposed it is not affected by the normalization The histogram can have error bars The normalization factor can be redefined at any time CALL HSCALE ID FACTOR Action The contents scale for a scatter plot is multiplied by a given factor Input parameters ID Histogram identifier ID 0 Means apply scaling factor to to all existing 2 dimensional histograms FACTOR Scaling factor to be applied to the contents scale FACTOR 0 means automatic scaling The range will be from the minimum to the maximum of the actual contents In a scatter plot the contents scale starts at O and increases in steps of 1 The content of each channel is represented by one character using the following scheme Value Character Range 0 lt a lt l 1 1 lt lt 2 2 lt x lt 3 3 3
211. les labelled X Y 227 The Ntuple data when the initial size of 1000 words is exhausted will be written to the directory on disk specified in the call to HBOOKN i e EXAM2 NTUPLE and the data in memory are replaced with those newly read A one and a two dimensional projection of X and X Y are then made onto histograms 10 and 20 respectively before they are printed and written on the HBOOK RZ file At the end the current and parent directories are listed The contents of the latter shows that the data written in the first job HTEST are indeed still present in the file under the top directory EXAM2 The call to RZSTAT shows usage statistics about the RZ file Example of adding data to a HBOOK RZ file PROGRAM HTEST1 PARAMETER NWPAWC 20000 COMMON PAWC H NWPAWC DIMENSION X 3 CHARACTER 8 CHTAGS 3 DATA CHTAGS X Y gt Z CALL HLIMIT NWPAWC Reopen data base LRECL 0 CALL HROPEN 1 EXAM2 HTEST DAT U LRECL ISTAT CALL HMDIR NTUPLE S7 CALL HBOOK1 10 TEST1 100 3 3 0 CALL HBOOK2 20 TEST2 30 3 3 30 3 3 250 CALL 30 N TUPLE 3 EXAM2 NTUPLE 1000 CHTAGS DO 10 I 1 10000 CALL RANNOR A B 1 X 2 B X 3 A A B B CALL HFN 30 X 10 CONTINUE CALL HPR0J1 10 30 0 0 1 999999 1 CALL HPR0J2 20 30 0 0 1 999999 1 2 CALL HPRINT O CALL HROUT O ICYCLE CALL HLDIR C CALL HCDIR 9 CALL HLDIR
212. lot routines 4 1 6 Function Representation CALL HBFUN1 ID CHTITL NX XMI XMA FUN Action Books 1 dimensional histogram and fills it with the values of the external function FUN X computed at the centre of each bin One computer word per channel is used The first five parameters are as for 58 Chapter 4 Advanced features for booking editing operations Input parameters ID histogram identifier integer non zero CHTITL histogram title character variable or constant up to 80 characters NX number of channels XMI lower edge of first channel XMA upper edge of last channel FUN real function of one variable to be declared EXTERNAL in the calling subroutine and to be supplied by the user CALL HBFUN2 ID CHTITL NX XMI XMA NY YMI YMA FUN Action Books a 2 dimensional histogram and fills it with the values of the external function FUN X Y computed at the centre of each bin One computer word per channel is used The first eight parameters are as for HBOOK2 Input parameters ID histogram identifier integer CHTITL histogram title character variable or constant up to 80 characters NX number of channels in X XMI lower edge of first X channel XMA upper edge of last X channel NY number of channels in Y YMI lower edge of first Y channel YMA upper edge of last Y channel FUN real function of two variables to be declared EXTERNAL in the calling subroutine and to be supplied by the us
213. luctuation in weights The result is that HDIFFB rejects to many bins in this case Comparisons for profile histograms assume Gaussian statistics for the 5 and C mode comparisons of the channel mean Fewer that 25 or so events will result in DIFFS values which are too large The result is that HDIFFB rejects too many event in these low statistic cases Chapter 7 Fitting parameterization and smoothing 71 Fitting The fitting routines in HBOOK are based on the Minuit package 12 Minuit is conceived as a tool to find the minimum value of a multi parameter function and analyze the shape of the function around the minimum The principal application is foreseen for statistical analysis working on chisquare or log likelihood functions to compute the best fit parameter values and uncertainties including correlations between the parameters It is especially suited to handle difficult problems including those which may require guidance in order to find the correct solution In the case of x minimization the final fitted parameter values correspond to the minimum of the function as defined below dus 3 29 FORD Aton At 1 where following definitions used n Number of channels cells in the 1 dimensional or 2 dimensional histogram HFITH HFITHN or number of points of the distribution HFITV C I Contents of channel cell I Error C I 1 Coordinate s of centre of channel cell or coordinate v
214. ly until the convergence criteria for the fit are reached The user has the choice to specify that the criteria are met either when the residual variance stops decreasing or when the multiple correlation coefficient reaches the value specified via the input parameter R2MIN see later Once the list of all possible regressors has been established at each step the one which gives the highest drop in the residual sum of squares is added to the expansion In addition all previously chosen regressors are tested for possible rejection using standard test statistics F tests as it can happen that a regressor becomes superfluous at a later stage of the fitting process 7 4 Parametrization 127 The routines offer three choices for the regressors standard elementary functions user given elementary functions or user given regressors In the first two cases each regressor is the product of NDIM elementary functions one for each variable the constant function may be included in the set This means that in the first two cases we will have a matrix of NDIM NCO elementary functions and the array of regressors will be the result of the scalar product of the NDIM columns of this matrix In the last case each regressor is user defined and we have just NCO regressors to be specified as user functions see below The NCO regressors have to be linearly combined with the NCO coefficients contained in the output array COEFF to obtain the parametrization Each element
215. m degrees of the standard polynomials for each independent variable are given by MAXPOW array of dimension NDIM This input parameter is mandatory and there is no default provided for it total degree of a regressor made up from the product of standard polynomials may be limited by setting PSEL via HSETPR to a positive value NDIM PSEL controls the exclusion of the combinations of standard polynomials which give the higher order regressors see the description of this parameter Each initial regressor whose code is passed to the logical function HSELBF written by the user may be accepted or rejected according to user criteria argument ITERM under control of IC below may be used as input to the routines to contain the list of the codes of the acceptable regressors As soon as the best parametrization is obtained the user may call the function HRVAL X which is of type DOUBLE PRECISION and which returns the value of the parametrization computed at point X where X is an array of dimension NDIM The program can handle up to 10 dimensions i e NDIM lt 10 Up to 50 regressors may appear in the final expression This is controlled by the PNCX parameter set by the routine HSETPR see below 128 Chapter 7 Fitting parameterization and smoothing Memory requirements a 1 dimensional histogram with 100 channels and with the maximum number of regressors PNCX set to 10 requires in DOUBLE PRECISION version less than
216. mber of 1 dimensional histograms N Number of 1 dimensional histograms CALL HID2 IDVECT N Action Returns the number and identifiers of all existing 2 dimensional histograms see HID1 CALL HIDALL IDVECT N Action Returns the number and identifiers of all existing histograms see HID1 93 94 Chapter 5 Accessing Information 5 4 Number of entries CALL HNOENT ID NOENT Action Provides the number of entries of a memory resident histogram plot or Ntuple value returned includes also the contents of the overflow and underflow bins Input parameter ID Histogram identifier Output Parameter NOENT Number of entries in the given histogram 5 5 Histrogram attributes Contents CALL HKIND ID KIND CHOPT Action Returns the attributes of a histogram Input parameters ID Histogram identifier CHOPT Character variable specifying desired option gt default only KIND 1 is filled according to the following convention 1 unknown kind of histogram 0 identifier ID does not exits 1 one dimensional plot 2 two dimensional plot 3 table 4 Ntuple 8 profile histogram N B The gt A More complete information on histogram all status bits characterizing the his togram are expanded into the vector KIND 32 using the following conventions 5 6 Contents 95 KIND 1 KIND 17 HBIGBI KIND 2 HBOOK2 KIND 18 HNORMA KIND 3 HTABLE KIND 19 HSCALE KIND 4 NTUPLE KIN
217. minuit package acts on a multiparameter Fortran function to which one must give the generic name FCN In the paw hbook implementation the function FCN is called HFCNH when the command Histo Fit paw or the routine HFITH are invoked It is called when the command Vector Fit or the routine HFITV are invoked The value of FCN will in general depend on one or more variable pa rameters To take a simple example suppose the problem is to fit a polynomial through a set of data points with the command Vector Fit Routine HFCNV called by HFITV calculates the chisquare between a polynomial and the data the variable parameters of would be the coefficients of the polynomials Routine HFITV will request MINUIT to minimize HFCNV with respect to the parameters that is find those values of the coefficients which give the lowest value of chisquare 7 2 1 Basic concepts The transformation for parameters with limits For variable parameters with limits MINUIT uses the following transformation Pnt arcsin Pat a sin Pint 1 so that the internal value can take on any value while the external value can take on values only between the lower limit a and the upper limit b Since the transformation is necessarily non linear it would transform a nice linear problem into a nasty non linear one which is the reason why limits should be avoided if not necessary In addition the transformation does require some computer tim
218. moothing Histograming is the least expensive and most popular density estimator but has several statistical draw backs To name only two it fails to identify structures that are much narrower than the bin size and exhibits sharp discontinuities statistical fluctuations among adjacent low population bins The first problem is usually solved by adapting the bin width to the experimental resolution or by re binning after looking at the histogram To filter out the statistical fluctuations smoothing algorithms can be applied Three such techniques are implemented in HBOOK the so called 353QH the method of B splines HSPLI1 HSPLI2 HSPFUN and multiquadric smoothing HQUAD Before trying them out references 13 14 15 16 and 16 should be consulted and results taken with care 132 Chapter 7 Fitting parameterization and smoothing CALL HSMOOF ID ICASE CHI2 Action Routine to smooth a 1 dimensional histogram according to algorithm 353QH TWICE see 13 Input parameters ID Histogram identifier ICASE Oand 1 replace original histogram by smoothed version 2 superimposes as a function when editing Output Parameter 2 chisquare x2 between original and smoothed histogram Remark The mean value and standard deviation are recalculated if ICASE 1 The routine can be called several times for the same histogram identifier ID for ICASE 1 or 2 CALL HSPLH 2 Act
219. ms 89 Sun 156 TABL 14 table 2 Taylor expansion 110 TCP IP 159 test Kolmogorov 90 TKOLMO 92 two dimensional histogram 13 type character type 4 integer 4 parameter 4 real 4 underflow 88 INDEX Unix 142 147 148 150 156 157 VAX see VMS VAX VMS 148 155 VMS 151 155 VMX 4 13 VMX 142 W 58 weight 14 XZRZOP 144 ZEBRA 139 142 146 149 151 RZ package 146 151 193
220. n particular it is written when the histogram is stored in a file with HROUT Naming the parameters of a fit CALL ID CHPNAM Action Modify the names of the fitted parameters in the data structure associated with the given his togram Input parameter ID Histogram identifier CHPNAM CHARACTER array specifying the name s to be given to the parameter s of the fit truncated to 8 characters NPAR Number of parameters specified 7 1 Fitting 117 Retrieving fitted parameters CALL HGFIT ID NFPAR NPFITS FITCHI FITPAR FITSIG FITNAM Action Retrieve the fitted parameters values from the data structure associated with a given histogram Input parameter ID Histogram identifier Output parameters NFPAR Number of parameters NPFITS Number of data points used in the fit FITCHI x ofthe fit FITPAR Array of dimension at least NFPAR containing the value of the fitted parameters FITSIG Array of dimension at least NFPAR containing the standard deviations of values of the fitted parameters FITNAM Character array of dimension at least NFPAR containing the names of the fitted parameters truncated to 8 characters See also HFINAM above 7 1 5 user parametric function When routines HFITH and HFITV are invoked a user parametric function FUN specified as an argument to those routines is called during the minimization procedure If the option is specified with these routi
221. n reading a RWN due to the overhead introduced by the type checking and compression mechanisms and because the data is not stored sequentially on disk The performance increase with a CWN will most clearly show up when using paw where one typically histograms one column with cuts on a few other columns The advantages of having different data types and data compression generally outweighs the performance penalty incurred when reading a complete CWN 26 Chapter 3 Ntuples 3 31 Booking CWN The booking is performed in two stages Firstly a call to HBNT is made to declare the Ntuple identifier and title Secondly one or more calls are made to HBNAME or HBNAMC to describe the variables that are to be stored in the Ntuple Routine HBNAMC is used to define CHARACTER variables while all other variable types are defined with routine HBNAME CALL HBNT ID CHTITL CHOPT Action Books a CWN Input parameters ID Identifier of the Ntuple CHTITL Character variable specifying the title associated to the Ntuple CHOPT Character variable specifying the desired options gt for disk resident Ntuples default D idemas 2 W for memory resident Ntuples The CWN will be stored in the current HBOOK directory The variables to be stored in the Ntuple will be specified with routine HBNAME or HBNAMC described below When the CWN will be filled with HENT the memory buffers associated with each column will be written to the file and direc
222. n with respect to the two parameters whose external numbers are par1 and par2 Other variable parameters of the function if any will have their values fixed at the current values during the contour tracing The optional parameter devs default value 2 gives the number of standard deviations in each parameter which should lie entirely within the plotting area Optional parameter ngrid default value 25 unless page size is too small determines the resolution of the plot i e the number of rows and columns of the grid at which the function will be evaluated EXIT End of Interactive MINUIT Control is returned to paw FIX parno Causes parameter parno to be removed from the list of variable parameters and its value will remain constant at the current value during subsequent minimizations etc until another command changes its value or its status HELP SET SHOw Causes MINUIT to list the available commands The list of SET and SHOw commands must be requested separately 122 Chapter 7 Fitting parameterization and smoothing HESse maxcalls Instructs MINUIT to calculate by finite differences the Hessian or error matrix That is it calculates the full matrix of second derivatives of the function with respect to the currently variable parameters and inverts it printing out the resulting error matrix The optional argument maxcalls specifies the approximate maximum number of function calls after which the calculation will b
223. nd normalization alone separately F1 Histogram ID1 has no errors it is a function F2 Histogram ID2 has no errors it is a function W Include a comparison of the relative normalization of the two histograms in addition to comparing the shapes The output parameter PROB is then a combined confidence level taking into account absolute contents g Overflow requests that overflow bins be taken into account also valid for 2 dim Underflow requests that underflow bins be taken into account also valid for 2 dim For 2 dimensional histograms only IL Left include X underflows in the calculation R Right include X overflows in the calculation B Bottom include Y underflows in the calculation include Y overflows in the calculation Output Parameter PROB The probability of compatibility between the two histograms Remark Options 0 and U can also refer to 2 dimensional histograms so that for example the string UT means that underflows in X and Y and overflows in Y should be included in the calculation he histograms ID1 and ID2 must exist and already have been filled before the call to HDIFF They must also have identical binning lower and upper limits as well as number of bins 104 Chapter 6 Operations Histograms The probability is returned as a number between zero A values close to one indicates very similar histograms and a value near
224. nd perform unconstrained fit If the histogram or Ntuple is un weighted perform a Poisson likelihood fit otherwise a least squares fit see MODE 4 4 force an unconstrained least squares fit in all cases This is a linear least squares problem and therefore the most efficient possible since it allows a single step calculation of the best fit and covariances But note it assumes gaussian errors even for low statistics including the error on zero being 1 SENSIT Sensitivity parameter It controls the sensitivity to statistical fluctuations see Remarks SENSIT 0 is equivalent to SENSIT 1 SMOOTH Smoothness parameter It controls the radius of curvature of the multiquadric basis functions SMOOTH 0 is equivalent to SMOOTH 1 Output parameters NSIG no of significant points or centres found i e no of basis functions used CHISQ chi squared see Remarks NDF no of degrees of freedom FMIN minimum function value FMAX maximum function value IERR error flag 0 if all s OK Hopefully helpful error messages are printed where possible Remarks Empty bins are taken into account Poisson statistics are used for the unweighted case The multiquadric basis functions are A where is the radial distance from its centre and A is a scale parameter and also the curvature at the centre Centres also referred to as significant points are located at points where the 2nd differential or Lap
225. ne PAW gt hrout 0 save all histograms from PAWC to the local file PAW gt rshell module OP3 MT2 PAW server connects to another OS9 monitoring task PAW gt Output 56 os9 listing Change output file on client PAW gt rshell ldir list all histograms in MT2 on file os9 listing PAW gt Output 56 Change output file to default unit 6 file os9 listing is closed Chapter 10 Tabular Overview Table 10 1 Routine calling sequences Calling Sequence CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL HARRAY ID NWORDS LOC HBANDX ID YMI YMA VMX HBANDY ID XMI XMA VMX HBARX ID HBARY ID HBAR2 ID HBFUN1 ID CHTITL NX XMI XMA FUN HBFUN2 ID CHTITL NX XMI XMA NY YMI YMA FUN HBIGBI ID NCOL HBINSZ CYES N0 HBNAMC ID CHBLOK IADDR CHFORM HBNAME ID CHBLOK IADDR CHFORM HBNT ID CHTITL CHOPT HBOOKB ID CHTITL NCX XBINS VMX HBOOKN ID CHTITL NVAR CHRZPA NPRIME CHTAGS HBOOKNC ID CHTITL NVAR BLOCK TUPLE CHTAGS HBOOK1 ID CHTITL NX XMI XMA VMX HBOOK2 ID CHTITL NX XMI XMA NY YMI YMA VMX HBPRO ID VMX HBPROF ID CHTITL NCX XLOW XUP YMIN YMAX CHOPT HBPROX ID VMX HBPROY ID VMX HBSET OPTION IVAL IERR HBSLIX ID NSLI VMX HBSLIY ID NSLI VMX HCDIR CHPATH CHOPT HCOMPA IDVECT N HCONVOL ID1 ID2
226. ned 1 dimensional histograms Weight distributions which just change the shape of the Monte Carlo spectra i e not efficiency distributions must be normalised so that i The best estimate of the fraction of each Monte Carlo distribution present in the data distribution is returned with an error estimate where required Input parameters IDD Data histogram identifier IDM Array of dimension NSRC containing Monte Carlo histogram identifiers IDW Array of dimension NSRC containing weight histogram identifiers W option only NSRC Number of Monte Carlo sources Must be greater than 1 CHOPT F Fix one or more of the fractions Default is for all fractions to vary freely L Set limits on the fractions as given FLIM Default is no limits W Use weight histograms provided For non existent weight histograms and if the W option is not requested a dummy weight histogram in which all entries are 1 is booked S Scan the likelihood function with respect to each fit parameter before and after the fit If the N option is specified the function will only be scanned once for each parameter W Do not perform the fit P Use the parameter start points and initial step sizes provided in START and STEP If the P option is not specified then the start point for each free parameter is 1 5 NSRC Ny where Xy is the sum of the fixed fractions and Ny is the number of fixed fracti
227. nes the user function is calculated in double precision in the case of HFITHN with the predefined functions G E Pn double precision is always used In this case you must reference the common block HCFITD which contains the parameter values in double precision and store the resulting function value in variable FITFUN as shown in the example below Example of user function double FUNCTION UFIT X The dimension of DPAR MUST be 24 DOUBLE PRECISION DPAR 24 FITFUN COMMON HCFITD DPAR FITFUN FITFUN DPAR 1 DPAR 2 SQRT X DPAR 3 X UFIT FITFUN END Even is you do not want to use a double precision function value i e you do not specify the U option you should still compute the fit function as accurately as possible using double precision variables in strategic places This function should also be protected against possible arithmetic exception conditions like under or overflows and negative arguments for square roots or logarithms 118 Chapter 7 Fitting parameterization and smoothing User specified derivatives CALL HDERIV DERIV Action User provided subroutine which calculates the derivatives of the parameters of the function being fitted This routine must be called from the user function FUN when option D is selected with HFITH or HFITN Input parameter DERIV Array containing the derivatives of the function being fitted 7 2 Basic concepts of MINUIT The
228. ng datatoaHBOOKRZfile 1 5 Output generated by HPLOT on printer with graphics capabilities 3 1 Schematic structure ofa RWN Ntuple 32 Schematic structure of a CWN wm geo ob EU RR ee Bxampleofttheuseof HLABEL uu cA BG W oed ERR Rede 7 11 Monte Carlo distributions left and data distribution right 8 1 The layout of the PAWC dynamicstore 8 2 The ZEBRA data structure used for two dimensional histograms 8 3 Different kinds of HBOOK directories ee g acide 91 Visualise histograms in global section 92 Visualise histograms in Unix shared memory 9 3 Visualising histograms on OS9 modules from PAW List of Tables The CERN personnel Ntupl o uus nog RR ue wU ee ee Q 4 1 Available HBOOK options 2 0 62 ee oo Rom wee ed 10 1 HBOOK Routine calling sequences 4 cs coce s s dw RR ERG xa 174 174 174 175 176 177 178 179 180 181 Chapter 1 Introduction Data processing is an important aspect of particle physics experiments since the volume of data to be handled is quite large a single LEP experiment producing of the order of a terabyte of data per year As a result every particle physics laboratory has a large data processing centre even though more than 50 of the
229. ng messages will be issued A Gaussian approximation is used when there are 25 or more events in each bin and TOL 0 001 The C option for unweighted events in the data histogram simply calculates the Poisson probability of finding n the ID2 bin value given a mean equal to the bin value of ID1 A Gaussian approximation is used when the the mean is 106 or larger and TOL is 0 001 or larger Given the expected mean the choice of TOL implies bounds on n i e n within these bounds passes An error occurs when the approximations used in calculating DIFFS give an incorrect value for n lt or ns No such errors occur for mean lt 10 and TOL gt 10 The errors in n lt or ny are less than 2 for mean lt 10 TOL gt 1079 or mean lt 107 TOL gt 10 There is a maximum n beyond which DIFFS returns zero so bins with gt Nmax always fail For mean lt 107 this is irrelevant for values of TOL gt 1077 110 Chapter 6 Operations Histograms For the profile histogram S option HDIFFB calculates the test probability that both bin means were produced from a population with the same mean The C option calculates the probability of finding the value in ID1 given a Gaussian with u and given by the ID2 contents Small numbers of entries for either test give DIFFS values which are too large and HDIFFB will reject too many events in profile histograms For weighted events the 8 and C options use a Gaussian approximation This res
230. numerical calculations in the user function or not enough precision This is unlikely in general but becomes more likely if the number of free parameters is very large or if 7 2 Basic concepts of MINUIT 121 the parameters are badly scaled not all of the same order of magnitude and correlations are also large In any case whether the non positive definiteness is real or only numerical is largely irrelevant since in both cases the error matrix will be unreliable and the minimum suspicious An ill posed problem For questions of parameter dependence see the discussion above on positive definiteness Possible other mathematical problems are the following Excessive numerical roundoff especially careful of exponential and factorial functions which get big very quickly and lose accuracy Starting too far from the solution function may have unphysical local minima especially at infinity in some variables 7 2 4 MINUIT interactive mode With the routines HFITH or HFITV and the M option HBOOK goes into interactive mode and gives control to the MINUIT program In this case the user may enter MINUIT control statements directly Overview of available MINUIT commands CLEar Resets all parameter names and values to undefined Must normally be followed by PARAMETER command or equivalent in order to define parameter values CONtour par2 devs ngrid Instructs MINUIT to trace contour lines of the user functio
231. ommands A RWN should not be used if there are more than about 100 columns or when your queries only references a small number of columns A RWN can only contain floating point data It is created with HBOOKN and filled with HEN Routines HGN HGNF are used to retrieve information about one row Figure 3 1 shows schematically how a RWN is laid out in memory row after row The buffer size in memory NWBUFF is specified as the primary allocation parameter NWBUFF of the HBOOKN routine Of course you must have reserved sufficient space in the PAWC common when calling the HBOOK initialization routine HLIMIT The lower line shows how the information is written to an RZ file The length of the input output buffer LRECL is specified as an argument of the routine HROPEN It is evident that if you have a small Ntuple and a lot of memory you can fit the complete Ntuple in memory thus speeding up the Ntuple operations In a Column Wise Ntuple CWN the elements of each column are stored sequentially Data in such an Ntuple can be accessed in a much more flexible and powerful manner than for a RWN The CWN storage mechanism has been designed to substantially improve access time and facilitate compression of the data thereby permitting much larger event samples several hundreds of Mbytes to be interactively processed e g using paw Substantial gains in processing time can be obtained especially if your queries only reference a few columns A CWN is not limi
232. on Fixed term regression all selected regressors will appear in the final expression N This switch controls the normalization of the X range during the computation 0 1 2 3 No normalization of X range X scaled in the range 1 1 X scaled in the range 0 1 X scaled in the range 0 The value of R2MIN is used to determine the satisfactory end of the fitting process If 0 lt R2MIN lt 1 this value will be compared to the current sum of the squares of the residuals to determine whether the fit should be stopped or continued If R2MIN gt 1 the fitting process will be halted when the residual variance is minimal Various parameters which are relevant for the parametrization can be set via the routine HSETPR CALL HSETPR CHNAME VALUE Input parameters CHNAME Name of the parameter to be set of type CHARACTER VALUE Value assigned to parameter CHNAME of type REAL Possible values for CHNAME are PNEF gt PNBF gt PSEL This parameter specifies to the system the number of elementary functions that are supplied by the user in case the switch B of the IC parameter is set to 1 The system will build PNBF basic regressors made up by products of NDIM elementary functions possibly user selected as specified by the switch C of the parameter IC This parameter must be specified in case user regressors are used B switch of IC set to 2 or in case the ITERM contains on input the selected regressors
233. ons and the initial step size is 0 01 142 Chapter 7 Fitting parameterization and smoothing E Perform a detailed error analysis using the MINUIT routines HESSE and MINOS IFIX Array of dimension NSRC containing 1 if a parameter is to be fixed in the fit 0 otherwise option only FRAC Array of dimension NSRC with the values at which parameters are to be fixed F option only FLIM Array of dimension 2 NSRC with the lower then upper limits on the parameters L option only START Array of dimension NSRC with the start values for each parameter P option only if P option is chosen then default start values are used if values in START are negative STEP Array of dimension NSRC with initial step values for each parameter P option only if P option is chosen then default step values are used if values in STEP are negative UP UP value for the error estimate E option only Default 0 5 if user supplies negative or zero value for UP when E option is chosen See the Minuit manual for definition of UP Output parameters PAR Array of dimension NSRC with the final fitted values of the parameters DPAR Array of dimension NSRC with the errors on the final fitted values of the parameters CALL HMCINI IDDATA IDMC IDWT NSRC CHOPT IERR Action Initialisation routine for function HMCLNL needs to be called each time a new set of histograms is introduced generally once at the beginning of each fit
234. operating system Access to remote files from workstation PAW gt rlogin CERNVM connect to CERNVM gt rshell file HRZTEST HBOOK PAW server connects HRZTEST HBOOK A to LUN11 PAW gt histo plot 10 plot histogram 10 from CERNVM PAW gt histo fit 20 G fit histo 20 with a gaussian and plot it PAW gt rlogin VXCRNA connect to VXCRNA PAW gt rshell file DISK DL PAW HEXAM DAT 3 PAW server on VXCRNA connects file to LUN11 PAW gt histo plot 110 plot histogram 110 from VXCRNA PAW gt rshell file HRZTEST DAT PAW server on VXCRNA connects file to LUN12 PAW gt histo plot 110 s plot histogram 110 from HRZTEST DAT on VXCRNA on the existing picture PAW gt rshell 1d list all files connected on VXCRNA PAW gt cdir CERNVM Change current PAW directory to CERNVM PAW gt histo plot 110 plot histogram 110 from CERNVM PAW gt histo plot VXCRNA 110 plot histogram 110 from VXCRNA PAW gt cdir PAWC current directory to local memory PAW gt histo list list all histograms in PAWC PAW gt Histo delete 0 delete all histograms in memory PAW gt hrin VXCRNA O read all histograms from VXCRNA file HRZTEST DAT to PAWC PAW cdir CERNVM change directory to CERNVM PAW gt rshell file NEW DAT D 1024 N creates a new file on the D disk PAW gt hrout 0 write all histograms from PAWC to CERNVM file NEW DAT D 180 Chapter 9 Global sections shared m
235. or basic elementary functions C switch of IC parameter set to 2 The parameter is ignored in the other cases This is the total number of user defined regressors or elementary functions which the system will use for the parametrization process Please note that in case of user given regressors if the C switch of the IC parameter is either 0 or 1 the logical function HSELBF ELEF will always be called in order to verify the inclusion of the regressor IELEF in the list for the current fitting operation This parameter is used only in case of system supplied elementary functions It is the maxi mum limit for the sum of the terms POW I 1 in each regressor where is the power of the system supplied elementary function for the I variable 1 lt I lt NDIM and MAXPOW CI is the user supplied maximum value for the degree of the system supplied elemen tary functions for the I variable This value must be 0 lt VALUE lt NDIM Note that setting PSEL to 0 selects the constant term for all the regressors Setting PSEL to a value gt NDIM has the effect of removing any limitation on the total degree of the regressors leaving MAXPOW I as the only effective limitation on the degree of the the elementary functions This means that the total degree of the regressors can be equal to the sum of the NDIM elements of MAXPOW I The system supplied default is 1 7 5 Smoothing 131 PFLV This parameter determines the F test significance l
236. ou want to read using HGNTV If you call HBNAME for all blocks you should have a PAWC which is at least the same size as the one you used to create the Ntuple If not you will run out of memory Also changing the buffer size will not help because the buffer used for reading will be the same size as the buffer used to write the Ntuple There is a special option in HBNAME with which you can tell HBNAME to only set the address for a single variable in a block this option is used by PAW to reduce memory usage To set the address for a single variable call HBNAME or HBNAMC as follows CALL HBNAME ID BLOCK IADDR SET NTVAR This will tell HGNTV to restore the Ntuple variable NTVAR in address IADDR Using this form of HB NAME will only reserve buffer space for the variables you plan to read and not for all variables in the block However you have to be careful that when you change the list of variable for HGNTV to also add or remove the correct HBNAME calls CALL HGNTF ID IROW IERR Action Retrieve information about all variables specified in a previous call to either HGNT HGNTB or HGNTV in an Ntuple row This routine is much faster than either HGNT HGNTB or HGNTV Input parameters ID Identifier of the Ntuple IROW Number of the row about which information is required Output parameter IERR Error return code 0 if row was found The information is restored at the addresses specified by HBNAME or HBNAMC for CHARACTER dat
237. presentation system paw 3 is to create one Ntuple Instead of histograming the 200 variables directly and therefore losing the exact values of the variables for each event and their correlations the variables are first stored in an Ntuple One can of course fill the histograms at the same time An Ntuple is like a table where the 200 variables mentioned above are the columns and each event is a row The storage requirement is proportional to the number of columns in one event and can become significant for large event samples An Ntuple can thus be regarded as a standard way of storing a DST Once the events are stored in this form it becomes easy in particular with paw to make 1 or more dimensional projections of any of the NVAR variables of the events and to change the selection mecha nisms or the binning and so on Before running the system on a large number of events the selection mechanisms can be rapidly tested on a small sample 31 CWN and RWN Two kinds of Ntuples In a Row Wise Ntuple RWN the elements of each row usually corresponding to an individual event are stored contiguously in an HBOOK RZ file This storage method is similar to that of a conventional DST where events are stored sequentially and it is particularly suited for small Ntuples up to a few Mbytes with only a few columns You can even use an RWN for larger Ntuples up to about 20 Mbytes when you know you want to reference almost all columns in your query c
238. presents the smallest probability considered as an acceptable match TOL 0 05 will cause DIFFS to reject the bin as bad if there is less than a 5 probability the two bins came from the same distribution Under option A TOL is the degree of precision of match required for the test to be considered as passed TOL 2 0 means that a data bin differing from the reference mean by less than 2 0 times the reference error is compatible NBINS The number of bins in the comparison For a 1 dimensional histogram this is the number of bins plus 0 1 or 2 depending on whether the overflow and underflow channels are included For a 2 dimensional histogram this will have the total number of bins plus room for overflow bins along any of the axes requested For more detail see the discussion of DIFFS below CHOPT string allowing specification of the following options N Use the absolute contents of each histogram thus including the normalization of the his togram as well as its shape in the comparison By default for the S and C options in 1 and 2 dimensional histograms the means are adjusted for the relative numbers of entries including any overflow or underflow bins requested in ID1 and ID2 No adjustment is ever made for profile histograms 0 Overflow requests that overflow bins be taken into account Underflow requests that underflow bins be taken into account R Right overflow bin For a 2 dimensional histogram it includes the X Axis overflow
239. ract any infor mation that cannot be obtained with the entries previously described 8 2 1 Space requirements The argument NWPAWC must be given a value large enough to accomodate in memory all histograms 1 D and 2 D and all Ntuple headers and buffers i e NF N1 N2 NT NWPAWC gt 10000 Sp i M 51 i Seli M Sw i i 1 1 1 1 8 2 Memory size control 159 Figure 8 2 The zebra data structure used for two dimensional histograms ZEBRA structure for HBOOK tables LCID pointer to histogram table ID Histogram attributes parameters title LSCAT Sum of contents for 2 D NX NY LPROX Contents PROX Errors PROX LPROY Contents PROY Errors PROY Contents SLIX I Errors SLIX I LSLIY same as LSLIX Contents BANX 1 Errors BANX 1 LBANY same as LBANX 160 Chapter 8 Memory Management input output Routines NF Number of open files Sp i 100 LREC where LREC is the buffer size for file 7 as specified in a call to HROPEN N1 Number of 1 D histograms S i Space occupied by 1 D histogram i e 40 NCHAN 2 PACK IERR NCHAN 10 IFUN NCHAN 10 NCHAN Number of channels in histogram PACK Packing factor 1 by default See parameter of HBOOKI IERR 1 if HBARX called 0 otherwise IFUN 1 if the histogram has an associated function HFUNC fits or smoothing N2 Number of 2 D histograms S t Space occupied by 2 D histogram
240. rations Histograms are output on the line printer by calling HISTDO or HPRINT according to the following specifications 4 3 Editing operations 79 One dimensional histograms One histogram per page is printed writing the global title date title drawing the contour of the his togram in the range between the minimum and the maximum content with the contents scale adjusted to fit on one page followed by channel number contents and low edge of each channel plus some statistics about the histogram itself entries mean value standard deviation and so on If the number of channels is greater than 100 the histogram is printed on several pages Two dimensional histograms They can use more than one page according to the number of channels in X and Y and in X and Y both channel number and lower edge of each channel are printed The plot statistics reported at the bottom consists of a table of 9 numbers corresponding to the total contents in each of the following classes Ni underflow X overflow Y N2 Xinsiderange overflow Y N3 overflow X overflow Y N1 N2 N3 underflow X Y inside range N4 N5 N6 N5 Xinside range inside range N7 N8 N9 N6 overflow X Y inside range N7 underflow X underflow Y N8 Xinsiderange underflow Y overflow underflow Y Any of these numbers can in fact be smaller than the real sum of the contents in the case of saturation of a cell For information on ho
241. re the bin contents ID3 C1 ID1 OPERATION C2 ID2 Input parameters ID1 ID2 Operand histogram identifiers CHOPER Character variable specifying the kind of operation to be performed ID3 compute binomial errors E compute error bars on the resulting histograms correctly assuming that the input his tograms ID1 and ID2 are independent For instance BE will generate binomial errors for the division of ID1 by ID2 Identifier of the histogram containing the result after the operation C1 C2 Multiplicative constants Remark ID1 ID2 and ID3 must have the same number of channels If histogram ID3 is not empty its contents are overwritten The output histogram ID3 can be either one of the input histograms ID1 or ID2 If histogram does not exist it is created by HOPERA with the same specification as for histogram ID1 The mean value standard deviation etc are calculated from the contents of the resulting histogram ID3 unless the STAT option is active and the operation is an addition or subtraction in which case they are computed exactly A division by zero gives zero Negative results for bin contents in a packed histogram are meaningless The number of entries in the resulting histogram ID3 is set to the sum of the entries in histograms ID1 and ID2 When an operation is performed on two 1 dimensional histograms with the sum of the squares of the weights stored option HBARX t
242. rs whose numbers parno are specified If none are specified Minos errors are calculated for all variable parameters Minos errors may be expensive to calculate but are very reliable since they take account of non linearities in the problem as well as parameter correlations and are in general asymmetric The optional argument maxcalls specifies the approximate maximum number of function calls per parameter requested after which the calculation will be stopped for that parameter RELease parno If parno is the number of a previously variable parameter which has been fixed by a command FIX parno then that parameter will return to variable status Otherwise a warning message is printed and the command is ignored Note that this command operates only on parameters which were at one time variable and have been FIXed It cannot make constant parameters variable that must be done by redefining the parameter with a PARAMETER command 7 2 Basic concepts of MINUIT 123 REStore code If no code is specified this command restores all previously FIXed parameters to variable status If code 1 then only the last parameter FIXed is restored to variable status SCAn parno numpts from to Scans the value of the user function by varying parameter number 1 leaving all other parameters fixed at the current value If parno is not specified all variable parameters are scanned in sequence The number of points numpts in the
243. rst fifteen iterations have been captured and are shown at the bottom right of Fig 9 2 9 4 Access to remote files from PAW session 179 9 4 Access to remote files from PAW session When running it is often necessary to access files e g files which reside on a different computer Therefore a PAW server is provided which works using a conventional Client Server model The client PAW typically runs on a workstation When the PAW command RLOGIN is invoked a PAW server is automatically started on the remote machine normally a mainframe or data server Once the RLOGIN REMOTE command has been executed the PAW Current Directory is set to REMOTE The PAW client can now instruct the PAW server to attach a file using the RSHELL command e g 11 file pawtest dat If an histogram with HBOOK ID 10 is on the remote file than the PAW com mand Histo Plot 10 will plot this histogram on the local workstation The histogram resides on PAWC like other histograms coming from local files The RSHELL command may be used to communicate with the PAW server The expression typed fol lowing RSHELL is passed to the server The current implementation of the PAW server recognizes the commands rshell file filename Server connects filename rshell cdir 11111 rshell 1 rshell 1d Server changes current directory Server lists current directory Server lists all connected files rshell message Server pass message to
244. s the user a choice of several minimization algorithms The MIGRAD Other algorithms are available with Interactive MINUIT as described on Page 121 algorithm is in general the best min imizer for nearly all functions It is a variable metric method with inexact line search a stable metric updating scheme and checks for positive definiteness Its main weakness is that it depends heavily on knowledge of the first derivatives and fails miserably if they are very inaccurate If first derivatives are a problem they can be calculated analytically inside the user function and communicated to paw via the routine HDERIV If parameter limits are needed in spite of the side effects then the user should be aware of the following techniques to alleviate problems caused by limits Getting the right minimum with limits If MIGRAD converges normally to a point where no parameter is near one of its limits then the existence of limits has probably not prevented MINUIT from finding the right minimum On the other hand if one or more parameters is near its limit at the minimum this may be because the true minimum is indeed at a limit or it may be because the minimizer has become blocked at a limit This may normally happen only if the parameter is so close to a limit internal value at an odd multiple of that MINUIT prints a warning to this effect when it prints the parameter values The minimizer can become blocked at a limit because at a limit
245. scan is 40 by default and cannot exceed 100 The range of the scan is by default 2 standard deviations on each side of the current best value but can be specified as from from to to After each scan if a new minimum is found the best parameter values are retained as start values for future scans or minimizations The curve resulting from each scan is plotted on the output unit in order to show the approximate behaviour of the function This command is not intended for minimization but is sometimes useful for debugging the user function or finding a reasonable starting point SEEK maxcalls devs Causes a Monte Carlo minimization of the function by choosing random values of the variable parame ters chosen uniformly over a hypercube centered at the current best value The region size is by default 3 standard deviations on each side but can be changed by specifying the value of devs SET ERRordef up Sets the value of up default value 1 defining parameter errors MINUIT defines parameter errors as the change in parameter value required to change the function value by up Normally for chisquared fits up 1 and for negative log likelihood up 0 5 SET LIMits parno lolim uplim Allows the user to change the limits on one or all parameters If no arguments are specified all limits are removed from all parameters If parno alone is specified limits are removed from parameter parno If all arguments are specified then par
246. sional density estimators under the form of histograms scatter plots and tables and to handle Ntuples Some interesting features of HBOOK are basic operations require the knowledge of just a few subroutine calls that can be learned in half an hour reading a few pages of documentation The internal structure of the package is also such that the options that are not directly called by the user program are not loaded in memory Histograms and plots are represented on the line printer in a standard format that contains the picture and some numerical information Several options are available to modify the presentation mainly in the case of one dimensional histograms By default one histogram per page is printed writing a possible common title date individual title drawing the countour of the histogram between the minimum and maximum channel content with the contents scale adjusted to fit in one page followed by channel number contents and scale and some statistical information entries mean value standard deviation and so on If the number of channels is greater than 100 the histogram is printed on several pages Printing options permit to add or suppress some information choose a different graphic presenta tion and modify the mapping of histograms on output pages Histograms can also be printed with channels oriented along rows instead of columns to avoid splitting the ones with many channels Logarithmic contents s
247. sixties and early seventies a large fraction of particle physicists were active in bubble chamber physics The number of events they treated varied between a few hundreds neutrino to several tens of thousands e g strong interaction spectroscopy Normally users would reduce there raw measurement tapes after event reconstruction onto Data Summary Tapes DST and extract from there mini and micro DSTs which would then be used for analysis In those days a statistical analysis program SUMX 4 would read each event and compile information into histograms two dimensional scatter diagrams and ordered lists Facilities were provided via data cards to select subset of events according to criteria and the user could add routines for computing event by event quantities not immediately available Although the idea and formalism of specifying cuts and selection criteria in a formal way were a very nice idea the computer technology of those days only allowed the data to be analysed in batch mode on the CDC or IBM mainframes Therefore it was not always very practical to run several times through the data and a more lightweight system HBOOK 5 6 easier to learn and use was soon developed It was in the middle seventies when larger proton and electron accelerators became available that counter experiments definitively superseded bubble chambers and with them the amount of data to be treated was now in the multi megabyte range Thousands of raw d
248. stograms are used to display the mean value of Y and its RMS for each bin in X Profile histograms are in many cases an elegant replacement of two dimensional histograms the inter relation of two measured quantities X and Y can always be visualized by a two dimensional histogram or scatter plot its representation on the line printer is not particularly satisfactory except for sparse data If Y is an unknown but single valued approximate function of X this function is displayed by a profile histogram with much better precision than by a scatter plot The following formulae show the cumulated contents capital letters and the values displayed by the printing or plotting routines small letters of the elements for bin J HO EY LY I MI h I H 3 L 3 82 vE L h 3 2 e J sQ VLQ The first five parameters are similar to Only the values of Y between YMIN and will be considered The value of L J in the formula L J l corresponds to the number of entries between YMIN and YMAX in bin J To fill a profile histogram one must use CALL HFILL ID X Y 1 H J is printed as the channel contents The errors displayed s J if CHOPT S spread option or e J if CHOPT gt error on mean Profile histograms can be filled with weights The computation of the errors and the text below is based on a proposal by Stephane Coutu Stephane Coutu coutu
249. t print tables and rotated 1 dimensional histograms CALL HPHS ID Action Analogous to HPRINT but ignore tables and HIDOPT ID ROTA CALL HPHST ID Action Analogous to HPRINT but ignore HIDOPT ID ROTA 4 3 Editing operations 87 4 3 7 Printing after System Error Recovery The operating systems of some computers define CP time limits for job execution and abort the job with a system error when this occurs In most of the cases users recover from the time limit error transfering control to a summary subroutine that will eventually edit the histograms calling e g HISTDO This can be inconvenient if the time limit condition has been reached in HISTDO or other printing routines because the printing will restart from the beginning To avoid this HBOOK can be instructed to start printing just where it stopped before CALL HPONCE Action In case of system error recovery during histogram editing a possible recovery editing will start where the original printing stopped Remark If HPONCE has been called before printing then a histogram that has been output completely will no longer be printed 4 3 8 Changing Logical unit numbers for output and message files The output file containing the histograms is by default the line printer file where also error messages will be written The names of the result and error files can be redefined using CALL HOUTPU LOUT and CALL HERMES LERR Action Replaces the lo
250. ted MULTIDIMENSIONAL PARAMETRIZATION gt K gt K gt K gt K gt K gt gt K gt K K gt K k k k k k k k k k ok KOR OR ORO R FIT CHARACTERISTICS AND OPTIONS ID 1 DIM 1 WORKING SPACE IN PAWC 5045 0 USER DEFINED BASIC FUNCTIONS 0 USER DEFINED ELEMENTARY FUNCTIONS MAX NUMBER OF REGRESSORS 15 MAX POWERS OF POLYNOMIALS IN EACH DIM 14 AMOUNT OF OUTPUT 1 WEIGHTING TYPE 0 CLASS OF POLYNOMIALS 3 CLASS BASIC FUNCTIONS 0 BASIC FUNCTION SELECTION MODE O REGRESSION MODE O X NORMALIZATION TYPE O POWER LIMITOR 1 00 F TEST LEVEL 1 00 PARAMETRIZATION SUPERIMPOSED ON HISTOGRAM FORTRAN CODE FPARAM WRITTEN ON UNIT 31 FITTING PROCESS WILL STOP WHEN THE RESIDUAL VARIANCE HITS A MINIMUM 15 CANDIDATE BASIC FUNCTIONS WERE RETAINED FOR THE FIT NUMBER OF POINTS TO FIT 95 SUM OF SQUARES OF Y VALUES 5000 0 MACHINE PRECISION 0 22 15 FITTING PROCESS STOPPED AS RESIDUAL VARIANCE HITS MINIMUM R2 0 98543 12 REGRESSORS INCLUDED FINAL RESULTS OF THE FIT ITERATION RSS R2ADJ REGRESSOR COEFF VALUE TERM OF PARAMETRIZATION 7 7 Fitting with finite Monte Carlo statistics 1 hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh hhh REGR 1 1 10 15 20 25 3 72 841 0 98350 1 2 3 4 5 6 7 8 9 10
251. ted to floating point data but can contain all basic data types real integer unsigned integer logical or character A CWN is created with routines HBNT HBNAME or HBNAMC and filled with HENT and HENTB Information about one row block column can be retrieved with routines HGNT HGNTB HGNTV and HGNTF 20 3 1 CWN and RWN Two kinds of Ntuples 21 Header created by HBOOKN Buffer filled by HFN LRECL HBOOK RZ direct access file NWBUFF Figure 3 1 structure of a RWN Ntuple Header created by HBNT HBNAME Buffers filled by HFNT NWBUFF _ gt i LRECL gt HBOOK RZ direct access file Figure 3 2 Schematic structure of a CWN Ntuple Figure 3 2 shows the layout of a CWN Ntuple The buffer size for each of the columns NWBUFF was set equal to the record length LRECL defined with routine HROPEN A CWN requires a large value for the length of the common PAWC in any case larger than the number of columns times the value NWBUFF i e NWPAWC gt NWBUFF NCOL You can however expect important performance improvements by setting the buffer size NWBUFF equal to a multiple of the record length LRECL via routine HBSET In both figures xi yi Zi ti etc represent the columns of event i 22 Chapter 3 Ntuples 3 2 Row Wise Ntuples RWN 3 2 1 Booking a RWN CALL ID CHTITL NVAR CHRZPA NWBUFF CHTAGS Action Books a RWN in memory
252. ters CHTITL Character variable containing the title associated with the Ntuple NVAR The original contents is overwritten by the actual dimension of the Ntuple If ID1 does not exist or is not an Ntuple NVAR 0 is returned CHTAG Character array of dimension NVAR which contains the tag names of the Ntuple elements RLOW Array of dimension NVAR which contains the lowest value for each Ntuple element RHIGH Array of dimension NVAR which contains the highest value for each Ntuple element 3 5 1 Retrieve the contents of a RWN into an array CALL HGN ID IDN IDNEVT X IERROR Action Copy the contents of a RWN event into an array Input parameters ID Identifier of the Ntuple IDN Must be initialized to zero before the first call to HGN IDNEVT Event number Output parameters IDN Internal HBOOK pointer X Array to contain variables for the event chosen IERROR Error return code This routine returns in the vector X the contents of the row IDNEVT or Ntuple ID The vector X must be of size NVAR as specified in the call to HBOOKN If more than one row of the Ntuple is to be processed it is more efficient to call first HGNPAR and then HGNF CALL HGNPAR ID CHROUT Action Obtains the address and parameters of Ntuple ID Input parameters ID Identifier of the Ntuple CHROUT Character variable containing the name of the calling subroutine printed in case of errors This routine sets some internal pointers and must be called
253. tes and maps the global section using SYS CRMPSC Open the file using SYS SETDFPROT to set protection loose Input parameters global name Name of the section to be mapped base common First word of COMMON to be mapped size size of the COMMON in words The function value returned is equal to the global section length pages if the procedure was successful or an errorcode lt 0 if an error occurred HCREATEG DIR is a LOGICAL which if defined gives the directory for the mapping file of the global section In this case the file is not deleted upon closing VALUE hmapg global_name base_common offset Action Function to dynamically map to an existing global section The function maps to the global section using SYS MGBLSC allocating pages in the pO region with the sec m_expreg option Input parameters global_name Name of the section to be mapped base_common First word of reference COMMON to be mapped offset Offset with respect to BASE_COMMON of the mapped section in words i e BASE_COMMON OFFSET is the first word The function value returned is equal to the global section length pages if the procedure was successful or is an errorcode lt 0 if an error occurred VALUE hfree global size base common offset Action Function to dynamically delete unmap global section space using the service SYS DELTVA Input parameters global size Size of the section to be freed pages base common First word of reference
254. the derivative seen by the minimizer OF OPy is zero no matter what the real derivative P is OF OF OP OF lt 0 OF ext o Pint OP ext Getting the right parameter errors with limits In the best case where the minimum is far from any limits MINUIT will correctly transform the error matrix and the parameter errors it reports should be accurate and very close to those you would have got without limits In other cases which should be more common since otherwise you wouldn t need limits the very meaning of parameter errors becomes problematic Mathematically since the limit is an absolute constraint on the parameter a parameter at its limit has no error at least in one direction The error matrix which can assign only symmetric errors then becomes essentially meaningless 7 2 3 Interpretation of Parameter Errors There are two kinds of problems that can arise the reliability of MINUIT s error estimates and their statistical interpretation assuming they are accurate Statistical interpretation For discussuion of basic concepts such as the meaning of the elements of the error matrix or setting of exact confidence levels see 111 120 Chapter 7 Fitting parameterization and smoothing Reliability of MINUIT error estimates MINUIT always carries around its own current estimates of the parameter errors which it will print out on request no matter how accurate they are at any given point in the
255. the probability is quantized For example the probability might be 0 053 for 4 entries and 0 021 for 3 If TOL 0 05 only bins with 3 or fewer entries would be flagged as bad When to use the S option The 8 option should be used when both histograms are filled with statistical data for example a momen tum distribution from two successive data runs Using the 8 option when comparing data to a function or known reference yields poor results because it attributes errors to both histograms In this case the C option should be selected When to use the C option The C option assumes that the reference histogram contains the theoretically expected values with no or negligible errors Examples might be a flat distribution hand inserted as the expectation for a phi distribution or a long data run to be compared with shorter data runs When to use the option The A option can be used as an equivalent to the C option by choosing TOL in terms of standard deviations instead of probability and returns z values in DIFFS for each bin The option is intended for setting by hand absolute minima and maxima restrict an efficiency between 80 and 100 load the reference histogram with a mean of 0 9 via HPAK and the error bar of 0 1 via and use HDIFFB with TOL 1 0 and the A option The N option should also be selected for this application Comparison of Weighted versus Unweighted events This is in general undesirable as
256. the unbinned data to be ordered which is easy in one dimension but is not well defined i e not scale invariant in higher dimensions Paradoxically the binning which was a nuisance in one dimension is now very useful since it enables us to define an obvious ordering In fact there are 106 Chapter 6 Operations Histograms two obvious orderings horizontal and vertical which give rise to two in general different Kolmogorov distance measures Routine HDIFF takes the average of the two distances to calculate the probability value PROB which gives very satisfactory results The precautions necessary for 1 dimensional data also apply to this case 6 3 Bin by bin histogram comparisons CALL HDIFFB ID1 ID2 TOL NBINS CHOPT NBAD DIFFS Action Compare two histograms bin by bin For each bin return the probability that the contents are from the same distribution For details of the method see below The comparison may be done between two 1 dimensional histograms two 2 dimensional histograms or between two profile histograms Input parameters 1 first histogram to be compared reference histogram options and ID2 The second histogram to be compared data histogram in options and 1 1 1 2 are a pair of 1 D 2 D or profile histograms booked with the same number of bins TOL The tolerance for a passing the test Under options 5 and C TOL is a number between 0 and 1 which re
257. ting parameterization and smoothing di 1 fad 1 The solution of these 4 sets of equations proceeds as before Notice that as one would expect if w is the same for all 2 then this merely amounts to a scaling of the Monte Carlo strength So far this assumes that the weight is the same for all events from a given source in a given bin the quantity w This may not be the case if either a the bin size is so large that the weight factor varies significantly within the bin or b the weight factor depends not only on the variable s 2 used in making the comparison but also on some other variable s call it z which is not binned and used in the comparison perhaps it does not exist in the real data In either case the weights of different events from the same source in the same bin can be different In such a case the Equations 7 19 7 22 still apply with w equal to the ideal average weight for source 7 in bin This may be a known quantity more likely it has to be estimated using the actual weights attached to the MC data values themselves At this point one has to worry whether the discrepancy between the average actual weight and the true average weight should be included in the fitting procedure estimation and errors Now in practice this method of weighting only works satisfactorily if the weights do not differ very much The variance of a sum of weights from Poisson sources is w 18 and
258. tion Possible keywords are G to fit gaussian PAR 1 exp 0 5 x PAR 2 PAR C3 2 1 corresponds to the normalization PAR 2 corresponds to the mean value and PAR 3 corresponds to the half width of the Gaussian E to fit exponential exp PAR 1 2 Pn tofit polynomyal PAR 1 PAR 2 x PAR 3 2 PAR n 1 x n Any combination of these keywords with the 2 operators or is allowed e g p4 g a com bination of a 4th degree polynomial and a gaussian which needs eight parameters or p2 g g a second degree polynomyal and 2 gaussians needing 9 parameters The order of the parame ters in PAR must correspond to the order of the basic functions For example in the first case above PAR 1 5 apply to the polynomial of degree 4 and PAR 6 8 to the gaussian while in the second case PAR 1 3 apply to the polynomial of degree 2 PAR 4 6 to the first gaussian and PAR 7 9 to the second gaussian Blanks are not allowed in the expression CHOPT B Some or all parameters are bounded The arrays STEP PMIN and PMAX must be speci fied By default all parameters vary freely D user is assumed to compute derivatives analytically using the routine HDERIV default derivatives are computed numerically E Perform a detailed error analysis using the minuit routines HESSE and MINOS F Force storing of the result of the fit bin by bin with the histogram CIL the logaritmic Likelihood f
259. tion culminating in the current version HBOOK 4 Many people have contributed to the design and development of HBOOK through discussions com ments and suggestions For many years and up to November 1994 Ren Brun has been responsible for the HBOOK program Paolo Palazzi was involved in the original design D Lienart has been in charge of the parametrization part Fred James is the author of routine HDIFF and of the minimization package Minuit which forms the basis of the fitting routines The idea of Profile histograms has been taken from the HYDRA system The Column wise Ntuple routines were implemented by Fons Rademakers The multi dimensional quadratic fit package HQUAD is the work of John Allison J Linnemann and his colleagues of the DO experiment contributed the routine HDIFFB Pierre Aubert is the author of the routines to associate labels with histograms Roger Barlow and Christine Beeston OPAL have developed the HMCMLL package Julian Bunn is the author of the HNFORM routine Preliminary remarks This manual serves at the same time as a Reference manual and as a User Guide for the HBOOK system After a short introductory chapter where the basic ideas are explained the following chapters describe in detail the calling sequences for the different user routines In this test examples are in monotype face and strings to be input by the user are underlined In the index the page where a routine is defined is in bold page numbers wher
260. tion to exclude some of the regressors or of the elementary functions according to the value of the B switch he has selected The input array ITERM contains a list of selected regressors or elementary functions according to the value of the switch B The array has to be at least NDIM PNBF words and the variable PNBF maximum number of elementary functions or regressors should have been set via a call to HSETPR In the case of elementary functions the element ITERM IDIM IBF 1 NDIM is the function of the variable to be multiplied by the coefficent number IBF given a maximum expected number of PNBF coefficents This can be of course reduced by the fitting program under considerations of linear dependency as stated above returning only NCO coefficents thus after the fit ITERM will identify which regressors were actually used In the case of user defined regressors only the first PNBF position of the ITERM array need to be filled and the array will contain directly the code of the selected user defined regressors This switch controls the system selection mechanism for the regressors 130 0 1 2 Chapter 7 Fitting parameterization and smoothing Stepwise regression the regression is calculated as explained before and selected regressors may be eliminated in a further step of the procedure Forward regression The backward stage is suppressed a regressor included at one time will always remain in the regression later
261. togram vertically 1EVL Force an integer value for the steps in the Y axis AEVL Steps for the Y axis are automatically computed 2PAG Histogram is printed over two pages 1PAG Histogram is printed in one single page A star indicates that the option is the default setting Table 4 1 List of available HBOOK options which can be set by HIDOPT 82 Chapter 4 Advanced features for booking editing operations CALL HSTAF If CHOPT YES statistics are computed at filling time the histograms created via HBOOKI or HBOOK2 after CALL HSTAF YES will have the IDOPT option STAT automatically activated This is very useful when histograms are created in an indirect way like in the command NT PLOT The way to activate this option in paw is PAW gt OPTION HSTA PAW NT PLOT 10 x IDH 100 43 3 Graphic Choices 1 dimensional histogram A histogram is normally represented by drawing its contour with a channel being represented by one character along the printed line at a displacement corresponding to the bin contents but alternative graphic presentations are available If some contents are negative a dotted line is drawn at 0 CALL HPCHAR CHOPT CHAR Action Selects a printing character different from the default for histograms that are not drawn contour only or for superimposed functions Input parameters CHOPT Printing option for which the character applies It can be
262. tograms only IBINY2 Binin Y on which to end the channel copy 2 D histograms only CHOPT causes the stored errors on each bin to be be copied as well CALL HRENID IDOLD IDNEW Action Renames a histogram or Ntuple Input parameter description IDOLD Old histogram identifier IDNEW New histogram identifier CALL HRESET ID CHTITL Action Resets the contents of all channels of a histogram and its projections or Ntuple to zero and changes optionally the title Input parameter description ID identifier of a histogram ID 0 resets all existing histogram contents CHTITL new title CHTITL means that the old title is kept CALL HDELET ID Action Deletes a histogram and releases the corresponding storage space Input parameter description ID identifier of a histogram ID 0 deletes all existing histograms See section 1 4 in the introductory chapter for a simple example of how to book fill and print histograms Chapter 3 Ntuples To introduce the concept of Ntuples let us consider the following example A Data Summary Tape DST contains 10000 events Each event consists of many variables say NVAR 200 for which we would like to make some distributions according to various selection criteria One possibility is to create and fill 200 histograms on an event by event basis while reading the DST An alternative solution particularly interesting during interactive data analysis with the data
263. tory corresponding to the current working directory when HBNT was called Remember that when routine HROPEN is called the current working directory is automatically set to the top directory of that file It is therefore convenient to call HBNT immediately after HROPEN If this was not the case routine HCDIR must be called prior to HBNT to set the current working directory When the Ntuple has been filled via calls to HENT the resident buffers in memory as well as the Ntuple header must be written to the file with a call to HROUT Before calling HROUT the current working directory must be set to the current directory when HBNT was called CALL HBSET CHOPT IVAL IERR Action Set global Ntuple options Input parameters CHOPT Character variable specifying the parameter to set BSIZE Set the buffer size For each variable column a buffer of BSIZE words is created in memory The default for BSIZE is 1024 IVAL Value for the parameter specified with CHOPT Output parameters IERR Error return code O means no errors 3 3 More general Ntuples Column Wise Ntuples CWN 27 If the total memory in PAWC allocated via HLIMIT is not sufficient to accomodate all the column buffers of BSIZE words then HBNT will automatically reduce the buffer size in such a way that all buffers can fit into memory It is strongly recommended to allocate enough memory to PAWC in such a way that each column buffer is at least equal to the block s
264. tput buffers for HRIN and HROUT COMMON PAWC NWPAW IXPAWC IHDIV IXHIGZ IXKU FENC 5 LMAIN HCV 9989 DIMENSION IQ 2 Q 2 LQ 8000 EQUIVALENCE LQ 1 LMAIN IQC1 LQ 9 Q 1 IQC1 link work free HBOOK HIGZ KUIP system _ area area space div div div div Figure 8 1 The layout of the PAWC dynamic store 8 1 1 use of ZEBRA Inside the hbook division the various data elements are stored as a zebra data structure one for each identifier In fact all identifiers histogram or Ntuple numbers are stored in an ordered array in a zebra bank and access to the information associated with the hbook data is via the reference link at the same offset as the identifier in the data part of the bank The data structure for a given element depends on its characteristics In any case the top bank for a given element contains the title and other constants 157 158 Chapter 8 Memory Management input output Routines while the data themselves are stored in another bank hanging from the previous one Sometimes other banks are created e g for automatic binning for storing the limits of the elements of a Ntuple and when a Ntuple is kept in memory for containing the overflow of the data for projections slices and bands in the 2 dim case of for containing the errors associated to a bin This means that each hbook identifier has a whole set of attributes associated with its existence and when a histogram or Nt
265. ults in DIFFS values which are too low HDIFFB rejects too many bins for weighted events particularly for small numbers of equivalent events Error messages of HDIFFB Warning Zero tolerance The passed value TOL is less than or equal to 0 TOL 0 be used to force highest accuracy in the 8 option Warning Only one comparison at a time please More than one type of comparison was selected Only one of options 5 C and may be used default S option will be used Warning Different binning The XMIN values for a 1 dimensional histogram or the XMIN and or YMIN values on a 2 dimensional histogram are different This may give inaccurate results Warning Weighted or saturated events in 2 dimensions HBOOK does not compute error bars for two dimensional histograms thus weighted event are not allowed and HDIFFB can not compute the correct statistics An answer is still given but it is probably not right The only reliable case is a weighted 2 dimenension histogram as the reference histogram for the C option Sum of histogram contents is zero The sum of the content bins 1s zero Histograms must be the same dimension A 1 dimensional and a 2 dimensional histogram have been specified In order for the routine to work both must be the same dimensionality Both histograms must be the standard or profile type Two different types of histograms have been specified Both must be profile or non profile You
266. umerically this does not present a problem They not coupled and each equation clearly has one and only one solution in the allowed region for t i e the region where the A are all positive which lies between t 1 Pmaz and t 1 Pmaz being the largest of the p t 0 is a suitable place to start and Newton s method readily gives a solution Special considerations apply when there are no events from one or more of the MC sources more details of the solution can be found in 17 Other points concerning the solution Some nice points emerge from the algebra The Equations 7 10 can be written more simply as odu s 0 Vj 7 16 Also replace a by 1 Aj aj pj Aji from Equation 7 12 and the equations then reduce to 7 17 i i These are telling us that the estimates of the for some source will change the shape of the distribution from that of the MC data a but will not change the overall total number 7 7 Fitting with finite Monte Carlo statistics 139 Equation 7 11 can be multiplied by and summed over j to give Y d Aji 0 j summing over i and using Equation 7 17 gives 2 4 2 i i j Np gt p N 7 18 which nicely returns the normalisation and makes clear the significance of p It is Interesting that such an automatic normalisation does not occur in the minimisation technique of Equation 7 4 If t
267. uple is written to backup store and later reread the complete data structure containing all characteristics and attributes are retrieved Figure 8 2 shows the zebra data structure for a two dimensional histogram The precise layout of this bank should be of no concern to the user It is only shown here as an example of the underlying zebra structure of hbook Note the use of the data part of the bank for storing attributes e g title number of bins number of entries as well as of the link part for storing the addresses to access the associated data points scatter plot contents X and Y projections slices and bands and their associated errors 8 2 Memory size control CALL NWPAW Action Defines the maximum total size NWPAW of common PAWC Remark HLIMIT must be called before any other hbook routine hbook is compiled with a COMMON PAWC dimensioned to 10000 words If NWPAW 10000 then the default value of 10000 is assumed If zebra has already been initialised HLIMIT must be called with a negative argument e g CALL HLIMIT NWPAW CALL HLOCAT ID LOC Action Returns the pointer in common PAWC to the zebra 10 structure which contains the description of a given histogram Input parameter ID histogram identifier Output Parameter LOC Pointer to the zebra bank containing the histogram information This routine can be useful to access directly the memory area of a given histogram to ext
268. ure containing 3 4 Making projections of a RWN 33 the column names is always created in the current directory in memory PAWC or PAWC subdir However the call to HBNT remembers the current directory on disk in the case below the CD on disk is 0 When you fill the Ntuple HENT fills a buffer in memory When this buffer is full HENT knows what is the CD on disk The buffer is written into that directory Note that your current directory on disk may be somewhere else HENT will temporarely change the CD to K0 and will reset the CD to what it was before calling HENT At the end of your job you have to save the header and the current buffer in memory on the disk file For that you have to Change the directory in memory where you book the Ntuple If you do not have subdirectories this operation is not necessary Change the directory on disk where you specified it in HBNT In the case below KO Issue a call to HROUT or HREND Creating a disk resident Ntuple call HCDIR PAWC HROPEN sets the directory to 0 call to HCDIR is needed call HROPEN 50 KO mydir KO rz N 1024 ISTAT if ISTAT ne 0 write 6 Error in HROPEN call HBNT 1000 Ntuple D call HLDIR PAWC T Now you can see the header in PAWC call HLDIR KO T OK nothing yet on KO HBNAME describes the Ntuple call HBNAME 1000 Event EvtNo Run
269. usly not valid between programs The first call clears all the addresses stored by HBOOK for the specified Ntuple and the second one sets the addresses for the variables in block CHBLOK starting at variable VARIABLE The second call should be repeated for every block of which data has to be retrieved The routine HUWFUN will generate these calls automatically in the skeleton user function CALL ID CHBLOK IROW IERR Action Retrieve information about a named block in an Ntuple row Input parameters ID Identifier of the Ntuple CHBLOK Character variable specifying the block that is to be retrieved IROW Number of the row about which information is required Output parameter TERR Error return code 0 if row was found The information is restored at the addresses specified by HBNAME or HBNAMC for CHARACTER data 38 Chapter 3 Ntuples CALL HGNTV ID CHVAR NVAR IROW IERR Action Retrieve information about the named variables in an Ntuple row Input parameters ID Identifier of the Ntuple CHVAR Array of character variables specifying the variables that are to be retrieved NVAR Number of character variables specified in CHVAR IROW Number of the row about which information is required Output parameter IERR Error return code 0 if row was found The information is restored at the addresses specified by HBNAME or HBNAMC for CHARACTER data You should only call HBNAME for the blocks that contain variables y
270. v2 33 3 322 143 22 2 4 2 2 UND 23 2 UNI LOW EDGE 32222211111 1111122222 086420864208642024680246802468 ENTRIES 10000 PLOT SATURATION AT 255 12 SCALE 2 3 A B STATISTICS STEP 1 MINIMUM O akak ak ak ak ak aK aK aK k aK aK NTUPLE ID 30 ENTRIES 10000 N TUPLE akak ak ak ak ak ak aK aK aK aK Var numb Name Lower Upper FE 1 X 422027E 01 0 386411 01 2 Y 411076 01 0 378366E 01 3 2 0 485187E 04 0 179518E 02 aK aK ak ak ak aK aK aK aK aK aK K gt Directory EXAM2 NTUPLE 30 N N TUPLE 10 1 TEST1 20 2 TEST2 gt Directory EXAM2 100 1 Test of HRNDM1 110 1 Filled according to HTFUN1 200 2 Test of HRNDM2 210 22 Fill according to HTFUN2 NREC NWORDS QUOTA FILE DIR NAME 34 34066 21 21 EXAM2 NTUPLE 41 40438 26 26 EXAM2 Figure 1 4 Adding data to a HBOOK RZ file 1 6 HPLOT interface for high quality graphics 13 1 6 HPLOT interface for high quality graphics hplot is a package of Fortran subroutines for producing hbook output suitable for graphic devices or in PostScript It is designed to produce drawings and slides of a quality suitable for presentations at conferences and scientific publications It do
271. value of point 98 Chapter 5 Accessing Information 5 8 Associated function VARIAB ID I Action Function returning the value of the associated function that has been stored in a given histogram channel The function value will be zero if no associated function exists Input parameters ID Histogram identifier I Channel bin number 5 9 Abscissa to channel number CALL HXI ID X I and CALL HXYIJ ID X Y I J Action Return the number of the channel cell which contains a given value in X 1 dimensional case or a given pair of X Y 2 dimensional case Input parameters ID Histogram identifier X X value Y Y value 2 dimensional case i e HXYIJ only Output Parameters I Channel number in X dimension Under Overflows give I 0 or I NCHANX 1 respectively J Channel number in Y dimension 2 dimensional case i e HXYIJ only Under Overflows give 750 or 1 respectively CALL HIX ID I X and CALL HIJXY ID I J X Y Action Returns the X coordinate of the lower edge of a given channel 1 dimensional case or the X Y coordinate pair if a given cell 2 dimensional case Input parameters ID Histogram identifier I Channel or cell number X dimension with 1 lt I lt NCHANX J Cell number in Y dimension with 1 lt J lt NCHANY 2 dimensional case i e HIJXY only Output Parameters X X coordinate of lower edge of channel or cell Y Y coordinate of lower edge of cell 2
272. w to suppress the plot statistics see HIDOPT ID NPST All projections bands and slices follow the plot they refer to as 1 dimensional histograms in the order in which they were booked Histograms are printed with the channels oriented along computer printer output columns so if they extend to more than 100 channels they will be chopped into pieces of 100 channels each and printed one after the other on separate pages The same is true for 2 dimensional histograms the limit for tables being related to the maximum value that has to be stored in each channel see remarks about HTABLE Using the entries described in this chapter it is possible to modify the standard output format adding or suppressing some information choosing a different printed presentation and modifying the mapping of histograms onto computer output pages One dimensional histograms can also be printed with channels oriented along rows instead of columns to avoid chopping up those having more than 100 channels editing entries must be executed before calling HISTDO or HPRINT Some of them can be executed any time after the booking others require that the histogram is already full so it is good practice to group them perhaps in one single subroutine and execute them just before printing 4 31 Index and General Title It is sometimes convenient to print just the index of plots without printing all the plots themselves 80 Chapter 4 Advanced features for booking
273. zero means that it is very unlikely that the two arose from the same parent distribution By default no options selected with the comparison is done only the shape of the two histograms without consideration of the difference in number of events and ignoring all underflow and overflow bins 6 2 1 Weights and Saturation Weighted 1 dimensional histograms Itis possible to compare weighted with weighted histograms and weighted with unweighted histograms but only if HBOOK has been instructed to maintain the necessary information by appropriate calls before filling to HBARX However it is not possible to take into account underflow or overflow bins if the events are weighted Saturated 1 dimensional histograms If there is saturation more than the maximum allowed contents in one or more bins the probability PROB is calculated as if the bin contents were exactly at their maximum value ignoring the saturation This usually will result in a higher value of PROB than would be the case if the memory allowed the full contents to be stored but not always It should therefore be realized that the results of HDIFF are not accurate when there is saturation and it is the user s responsability to avoid this condition 2 dimensional histograms Routine HDIFF cannot work if the events are weighted since in the current version of HBOOK the necessary information is not maintained HDIFF will also refuse to compare 2 dimensional histo

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