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
TITLE OF ID1
HBOOK ID = 1 DATE 18/05/92 NO = 14
172 -
168 I
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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
\finalnewpage
TITLE OF ID = 2
HBOOK ID = 2 DATE 18/05/92 NO = 15
84 -
82 - I
80 I I
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72 I I II I I
70 I I- II I I -
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36 I I I-
34 I I--II
32 I I
30 -I I
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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
\finalnewpage
{\scriptsize
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
}
\finalnewpage
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
\finalnewpage
{\scriptsize
**********************************************
* *
* 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
{\scriptsize
****************************************
* *
* 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
}
\finalnewpage
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
\finalnewpage
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