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 HBOOK1.

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 user.

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(ID,'PFUN')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.

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 $\chi 2$ , as defined below, will be printed along with the statistical information at the bottom of the histogram.

$\chi 2=\; \sum$_i=1^n_ch {(C(i)-F(i))²∑_j=1ⁿⁱ W_ji ²}

with:

$n$ch	number of channels of histogram
$C(i)$	contents of channel $i$
$F(i)$	value of function at centre of channel $i$
$ni$	number of entries in channel $i$ i
$W$ji	weight of event $j$ in channel $i$ , i.e.
	square root of contents $C(i)$ or
	as given by HBARX/HPAKE