+------------------------------------------------------------------------------+ |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, i.e., 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.
Remarks:
Example of fits
SUBROUTINE HEXAM5 *.==========> *. OPERATIONS ON HISTOGRAMS AND FITTING *..=========> (R.Brun, modified by M.Goossens) COMMON/HFPAR/PAR(6) COMMON/HFGAUS/AG,BG,CG 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 TITL1/'TITLE OF ID1'/ *.___________________________________________ * * GET hist 110 from data base * CALL HRGET(110,'hexam.dat',' ') CALL HRGET(210,'hexam.dat',' ') * * CALL HBOOK1(1,TITL1,100,0.,1.,0.) CALL HCOPY(1,2,'TITLE OF ID = 2') * * Gets information from ID=110 and fills new IDs 1,2 * CALL HUNPAK(110,X,'HIST',1) CALL UCOPY(X,Y,100) CALL VZERO(X(51),50) CALL HPAK(1,X) CALL HPHIST(1,'HIST',1) CALL VZERO(Y,50) 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,' ') * * 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 * PAR(1) = 40. PAR(2) = 20. PAR(3) = 0.4 PAR(4) = 0.6 PAR(5) = 0.1 PAR(6) = 0.1 * CALL HFITH(3,HFUNF,'V',6,PAR(1),ST,PMI,PMA,SIGPAR,CHI2) * CALL HPHIST(3,'HIST',1) * * * Fits a two-dimensional distribution (xf,yf) with HFITN * initialize parameters. Prints results of the last * iteration. * Errors EY automatically computed as SQRT(yf) * NY=0 DO 10 J=1,40 DO 5 I=1,100 CONT=HIJ (210,I,J) IF (CONT.EQ.0.) GOTO 5 NY=NY+1 YF(NY)=CONT EY(NY)=SQRT(CONT) CALL HIJXY (210,I,J,X1,X2) XF(NY,1)=X1+0.005 XF(NY,2)=X2+0.0125 5 CONTINUE 10 CONTINUE PAR(1) = 3. PAR(2) = 1. PAR(3) = 0.3 PAR(4) = 0.7 PAR(5) = 0.07 PAR(6) = 0.12 * 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) WRITE(31,*) ' COVARIANCE MATRIX' WRITE(31,*) ' *****************' DO 20 I=1,6 WRITE(31,'(6(D12.4,1X))') (COV(I,J),J=1,I) 20 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.) 30 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 A1,A2,C1,C2,XM1,XM2,XS1,XS2,X1,X2 * Force double precision calculation C1 = PAR(1) C2 = PAR(2) XM1 = PAR(3) XM2 = PAR(4) XS1 = PAR(5) XS2 = PAR(6) * A1=-0.5*((X-XM1)/XS1)**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 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 FUNCTION HFUNGA (X) COMMON/HFGAUS/AG,BG,CG DOUBLE PRECISION AG,BG,CG HFUNGA=AG*EXP(-0.5*((X-BG)/CG)**2) END
Output Generated
TITLE OF ID1 HBOOK ID = 1 DATE 18/05/92 NO = 14 172 - 168 I 164 I 160 -I 156 II - 152 II-I 148 I I- 144 --I I 140 I I- 136 I I 132 I I 128 I I- 124 -I I 120 -I I 116 I I 112 I I 108 I I 104 -I I- 100 I I 96 I I - 92 I I-I 88 -I I 84 I I - 80 I I I 76 I I I 72 I I I- 68 I I-II 64 I I 60 - I I 56 I-I I 52 I I- 48 -I I- 44 I I 40 I I- 36 I I 32 I I - 28 -I I- - I 24 --I I-I I 20 -I I I- 16 I I-II 12 -I I 8 - --I I 4 -----I-I I CHANNELS 100 0 1 10 0 1 2 3 4 5 6 7 8 9 0 1 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 CONTENTS 100 1111111111111 10 112224658012445755432099687543222121 1. 211246268181476068282127104785115522257716498 LOW-EDGE 1. 111111111122222222223333333333444444444455555555556666666666777777777788888888889999999999 *10** 1 0 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789 * ENTRIES = 100 * ALL CHANNELS = 0.2825E+04 * UNDERFLOW = 0.0000E+00 * OVERFLOW = 0.0000E+00 * BIN WID = 0.1000E-01 * MEAN VALUE = 0.3087E+00 * R . M . S = 0.7466E-01 TITLE OF ID = 2 HBOOK ID = 2 DATE 18/05/92 NO = 15 84 - 82 - I 80 I I 78 - I I - 76 I - I I I 74 I-I -I I I 72 I I II I I 70 I I- II I I - 68 I I II-I -I-I 66 - I I-I I-I I 64 - I I I- 62 I-I I I 60 I I -I I 58 I I I I 56 I I I I 54 I I-I I - 52 - I I I 50 I-I I-I 48 I I 46 I I 44 I I - 42 -I I- I 40 -I I I 38 I I I 36 I I I- 34 I I--II 32 I I 30 -I I 28 - I I - 26 I -I I- I 24 I I I I 22 I- I I I-- 20 II I I-I I - 18 II-I I I 16 I I-I 14 I I 12 I I-- 10 I I 8 I I - - 6 I I-I-I 4 I I- 2 I I CHANNELS 100 0 1 10 0 1 2 3 4 5 6 7 8 9 0 1 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 CONTENTS 10 221233455666557776678686676664543343222221111 1. 71850922032539736953183588893942434650812591167574 LOW-EDGE 1. 111111111122222222223333333333444444444455555555556666666666777777777788888888889999999999 *10** 1 0 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789 * ENTRIES = 100 * ALL CHANNELS = 0.2175E+04 * UNDERFLOW = 0.0000E+00 * OVERFLOW = 0.0000E+00 * BIN WID = 0.1000E-01 * MEAN VALUE = 0.7102E+00 * R . M . S = 0.1063E+00 MINUIT RELEASE 90.10 INITIALIZED. DIMENSIONS 100/ 50 EPSMAC= 0.89E-15 ********** ** 1 **SET EPS 0.1000E-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. 0.10E-03 PARAMETER DEFINITIONS: NO. NAME VALUE STEP SIZE LIMITS 1 'P1 ' 40.000 12.000 no limits 2 'P2 ' 20.000 6.0000 no limits 3 'P3 ' 0.40000 0.12000 no limits 4 'P4 ' 0.60000 0.18000 no limits 5 'P5 ' 0.10000 0.30000E-01 no limits 6 'P6 ' 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= 0.21E-05 STRATEGY= 1 ERROR MATRIX ACCURATE EXT PARAMETER STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 P1 154.37 3.8591 0.97447 -0.16735E-03 2 P2 74.934 2.1210 0.51925 0.16237E-03 3 P3 0.30351 0.15347E-02 0.76783E-03 -0.91430 4 P4 0.70017 0.29587E-02 0.17713E-02 0.19339 5 P5 0.69299E-01 0.12334E-02 0.28758E-03 0.39057 6 P6 0.11985 0.27357E-02 0.62656E-03 0.52392 CHISQUARE = 0.9164E+00 NPFIT = 95 TITLE OF ID1 HBOOK ID = 3 DATE 18/05/92 NO = 16 172 - 168 I 164 I 160 -I 156 I*** 152 *I-I 148 I I* 144 -*I I 140 I I* 136 * I 132 I I* 128 I I- 124 *I I 120 -I I* 116 I I 112 * I 108 I I * 104 -I I- 100 I I 96 * I * 92 I I-I 88 -I I 84 * I - - - 80 I I*I - I I - 76 I I I I--****** I 72 *I I I- I**- II I**I - 68 I I-*I - ** I-II-I--**I 64 I I --I* I *- 60 * I * I * -I * 56 I-I I I*I-I I*- 52 I I- --* I-* 48 *I *- I* I* 44 I I -* I-* - 40 I *- ** I ** 36 *I I *I I--I* 32 I * - *-I I* 28 *-I I* - I -**-I I-*- 24 *-I I***I**- I I *-- 20 -I I *-II-I I-I** - 16 * I-I I** 12 **I I** 8 - *-I I**** 4 ************I I* CHANNELS 100 0 1 10 0 1 2 3 4 5 6 7 8 9 0 1 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 CONTENTS 100 1111111111111 10 112224658012445755432099687543222121221233455666557776678686676664543343222221111 1. 21124626818147606828212710478511552225771649871850922032539736953183588893942434650812591167574 LOW-EDGE 1. 111111111122222222223333333333444444444455555555556666666666777777777788888888889999999999 *10** 1 0 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789 * ENTRIES = 200 * ALL CHANNELS = 0.5000E+04 * UNDERFLOW = 0.0000E+00 * OVERFLOW = 0.0000E+00 * BIN WID = 0.1000E-01 * MEAN VALUE = 0.4834E+00 * R . M . S = 0.2184E+00 * CHISQUAR = 0.8156E+02 ********************************************** * * * Function minimization by SUBROUTINE HFITV * * Variable-metric method * * ID = 0 CHOPT = V * * * ********************************************** Convergence when estimated distance to minimum (EDM) .LT. 0.10E-03 PARAMETER DEFINITIONS: NO. NAME VALUE STEP SIZE LIMITS 1 'P1 ' 3.0000 0.90000 no limits 2 'P2 ' 1.0000 0.30000 no limits 3 'P3 ' 0.30000 0.90000E-01 no limits 4 'P4 ' 0.70000 0.21000 no limits 5 'P5 ' 0.70000E-01 0.21000E-01 no limits 6 'P6 ' 0.12000 0.36000E-01 no limits ********** ** 4 **SET PRINT 0.0000 ********** ********** ** 5 **MIGRAD 1160. 1.000 ********** MACHINE ACCURACY LIMITS FURTHER IMPROVEMENT. MIGRAD MINIMIZATION HAS CONVERGED. MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX. EIGENVALUES OF SECOND-DERIVATIVE MATRIX: -0.1596E+01 -0.6458E+00 0.3800E+00 0.7478E+00 0.1277E+01 0.5837E+01 MINUIT WARNING IN HESSE ============== MATRIX FORCED POS-DEF BY ADDING 1.6018 TO DIAGONAL. MIGRAD TERMINATED WITHOUT CONVERGENCE. FCN= 1709.709 FROM MIGRAD STATUS=FAILED 197 CALLS 198 TOTAL EDM= 0.41E+02 STRATEGY= 1 ERR MATRIX NOT POS-DEF EXT PARAMETER APPROXIMATE STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 P1 2.4709 0.73263E-01 0.00000 4.1109 2 P2 1.8247 0.37237E-01 0.00000 8.5400 3 P3 0.27725 0.24789E-02 0.00000 -125.59 4 P4 0.70933 0.51778E-02 0.00000 132.72 5 P5 0.90472E-01 0.47875E-02 0.00000 -302.38 6 P6 0.21181 0.75383E-02 0.00000 -63.830 CHISQUARE = 0.9282E+00 NPFIT = 1848 COVARIANCE MATRIX ***************** 0.5367E-02 0.9472E-03 0.1387E-02 0.4548E-05 -0.9488E-06 0.6145E-05 -0.1520E-04 -0.2581E-04 0.1647E-05 0.2681E-04 -0.2597E-03 -0.7556E-04 -0.2361E-06 0.2208E-05 0.2292E-04 0.1100E-03 -0.3230E-04 -0.1566E-05 0.1904E-05 -0.2129E-04 0.5683E-04 ********************************************** * * * Function minimization by SUBROUTINE HFITH * * Variable-metric method * * ID = 5 CHOPT = * * * ********************************************** Convergence when estimated distance to minimum (EDM) .LT. 0.10E-03 FCN= 69.87250 FROM MIGRAD STATUS=CONVERGED 64 CALLS 65 TOTAL EDM= 0.38E-05 STRATEGY= 1 ERROR MATRIX ACCURATE EXT PARAMETER STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 P1 199.30 3.5192 0.84934 -0.13509E-03 2 P2 0.39761 0.14150E-02 0.10059E-02 -1.6362 3 P3 0.98783E-01 0.10313E-02 0.24990E-03 -1.7442 CHISQUARE = 0.1075E+01 NPFIT = 68 EXAMPLE NO = 5 -------------- HBOOK ID = 5 DATE 18/05/92 NO = 17 230 - 220 - I 210 I I 200 ****** - 190 **I I--*I- 180 *I I I *I 170 * I-I I-I* 160 *I-I I* 150 *I I* 140 -I I* 130 -*I I *-- 120 *-I I--*I 110 *I I 100 *I *- 90 *I * 80 *I I* 70 *I I-* 60 *-I I *-- 50 *-I I-I*I 40 -*I **- 30 -** I-** 20 *** I-*** 10 ****************I I************************************ CHANNELS 100 0 1 10 0 1 2 3 4 5 6 7 8 9 0 1 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 CONTENTS 100 111111111211211121111111 10 1 112233456889131356586199288608541122964655231111 1. 1 2224268062313614000760053587389243868095597245890427768955738341 11 1 LOW-EDGE 1. 111111111122222222223333333333444444444455555555556666666666777777777788888888889999999999 *10** 1 0 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789 * ENTRIES = 5000 * ALL CHANNELS = 0.5000E+04 * UNDERFLOW = 0.0000E+00 * OVERFLOW = 0.0000E+00 * BIN WID = 0.1000E-01 * MEAN VALUE = 0.3984E+00 * R . M . S = 0.9985E-01 * CHISQUAR = 0.6987E+02
Example of parametrization and smoothing
SUBROUTINE HEXAM6 *.==========> *. PARAMETRIZATION - SMOOTHING *..=========> ( 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) * * CALL HCOPY(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 Generated
**************************************** * * * MULTIDIMENSIONAL PARAMETRIZATION * * * **************************************** 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 OF BASIC FUNCTIONS = 0 BASIC FUNCTION SELECTION MODE = 0 REGRESSION MODE = 0 X-NORMALIZATION TYPE = 0 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 = 0.22E-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 13 72.841 0.98350 1 40.320 0 2 -32.156 20 3 29.461 60 4 -20.018 80 5 7.7912 100 6 -18.482 50 7 -7.0469 110 8 -9.0691 10 9 4.4675 130 10 6.4382 90 11 -3.9874 140 12 3.1189 30 REGRESSOR STANDARD DEVIATION CONFIDENCE INTERVAL 1 0.70650 [ 39.144 , 41.495 ] 2 1.0509 [ -33.904 , -30.407 ] 3 0.85147 [ 28.044 , 30.877 ] 4 0.90853 [ -21.530 , -18.506 ] 5 0.82336 [ 6.4213 , 9.1611 ] 6 1.0259 [ -20.189 , -16.775 ] 7 0.78401 [ -8.3514 , -5.7425 ] 8 1.0731 [ -10.854 , -7.2836 ] 9 0.68036 [ 3.3355 , 5.5995 ] 10 0.83660 [ 5.0463 , 7.8301 ] 11 0.85716 [ -5.4135 , -2.5612 ] 12 1.1372 [ 1.2267 , 5.0110 ] DOUBLE PRECISION FUNCTION FPARAM (X) DOUBLE PRECISION COEFF,P,P0,P1,P2,HELEFT,HBASFT DIMENSION X(1),COEFF(12),IBASFT( 1,12) DATA COEFF/ 0.40319615E+02,-0.32155589E+02, 0.29460772E+02, +-0.20017895E+02, 0.77912196E+01,-0.18481896E+02, +-0.70469122E+01,-0.90690550E+01, 0.44674803E+01, + 0.64381900E+01,-0.39873663E+01, 0.31188760E+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 (NUM.NE.0) THEN IF (ITYP.EQ.0) THEN P0=1. P1=2*X (I)-1. DO 10 J=2,NUM P2=2*(2*X (I)-1.)*P1-P0 P0=P1 10 P1=P2 P=P*P1 END IF IF (ITYP.EQ.1) P=P*HELEFT(NUM,X (I)) IF (ITYP.EQ.2) THEN P=HBASFT(NUM,X ) GOTO 20 END IF END IF 15 CONTINUE 20 FPARAM=FPARAM+COEFF(K)*P 25 CONTINUE RETURN END THIS HISTOGRAM IS FILLED ACCORDING TO THE FUNCTION HTFUN1 HBOOK ID = 1 DATE 17/12/91 NO = 18 172 - 168 I 164 I 160 -I 156 II - 152 I**I 148 * *- 144 -*I * 140 I I- 136 * * 132 I I 128 *I I* 124 -I I 120 -I I* 116 * I 112 I I 108 I I * 104 -I I- 100 * I 96 I I * 92 I I-I 88 *I I 84 I I*- - - 80 I I I - I I - 76 *I I I I-******** I 72 I I *- **I- II I *I - 68 I I-II - *I I-II-I--**I 64 I I --I* I *- 60 * I * I** -I * 56 I-I I * I-I I*- 52 I I* -*I I-* 48 *I I- * I* 44 * I * *I I-* - 40 I I- *I I *I 36 * *I * *I I--*- 32 I I - *-I ** 28 *-I I* - I - *-I I-*- 24 * --I I*I I ** I I **- 20 -* ****II-I I-I **- 16 * * I-I I-** 12 *I I-* 8 * -***I I**** 4 ******-I I* CHANNELS 100 0 1 10 0 1 2 3 4 5 6 7 8 9 0 1 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 CONTENTS 100 1111111111111 10 112224658012445755432099687543222121221233455666557776678686676664543343222221111 1. 21124626818147606828212710478511552225771649871850922032539736953183588893942434650812591167574 LOW-EDGE 1. 111111111122222222223333333333444444444455555555556666666666777777777788888888889999999999 *10** 1 0 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789 * ENTRIES = 5000 * ALL CHANNELS = 0.5000E+04 * UNDERFLOW = 0.0000E+00 * OVERFLOW = 0.0000E+00 * BIN WID = 0.1000E-01 * MEAN VALUE = 0.4834E+00 * R . M . S = 0.2184E+00 * CHISQUAR = 0.7284E+02 THIS HISTOGRAM IS FILLED ACCORDING TO THE FUNCTION HTFUN1 HBOOK ID = 2 DATE 17/12/91 NO = 19 185 I 180 I 175 0 170 II I 165 IIII 160 0IIII 155 III I0I 150 III**I0I 145 00* I*II 140 I* I *0I 135 I*I III 130 III *I 125 I* * 120 0I I 115 I*I I* 110 II I 105 0 0*I 100 I* III 95 II I0* I I 90 * II I I I I I 85 I I *0I III I0 0 I 80 *I II 0I0I***II I0II 75 I*0 I I ****I0I***IIIII 70 * I I III**III0II 0 I**00I 65 II 0 * 00*II I I0I I 0I **0 I 60 00 I * III*II0 I I II I *II 55 *II 0I 0I*I 0I ** I 50 0 I I* III* I 0I* I 45 *I I0* I**I I 0* 0I 40 I I0 I*I II**0 35 *I I* I I I *I 00 * I 30 II0 0** 0 0I**0 II I**0II 25 I*0I I0I*****I0I 0I**0 I 20 *II I I 0 I0I I0 I**0 15 I*I 0 I I 0**0 10 I0 0*I I****0I 5 ******** II0** CHANNELS 100 0 1 10 0 1 2 3 4 5 6 7 8 9 0 1 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 CONTENTS 100 1111111111111 10 112224658012445755432099687543222121221233455666557776678686676664543343222221111 1. 21124626818147606828212710478511552225771649871850922032539736953183588893942434650812591167574 LOW-EDGE 1. 111111111122222222223333333333444444444455555555556666666666777777777788888888889999999999 *10** 1 0 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789 * ENTRIES = 5000 * ALL CHANNELS = 0.5000E+04 * UNDERFLOW = 0.0000E+00 * OVERFLOW = 0.0000E+00 * BIN WID = 0.1000E-01 * MEAN VALUE = 0.4834E+00 * R . M . S = 0.2184E+00 * CHISQUAR = 0.9674E+02