Feb1.doc
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File  Function - A Lorentzian
f  x 
1
 x  x0 
1 

 w 
for\TLORENT.FOR
cpp\BLILOREN.C
The code for using the bli to produce a Lorentzian (is
given in for\TLORENT.ZIP cpp\cloren.zip
The output is for\loren.out but you need viw to find that
x=0 is line 63
-19.8413
-15.8730
-11.9048
-7.93651
-3.96825
0.284217E-13
1.98413
3.96825
5.95238
7.93651
11.9048
2
0.597528E-03
0.867610E-03
0.137258E-02
0.249093E-02
0.583801E-02
0.262741E-01
0.128281
0.566860
0.500839E-01
0.160250E-01
0.454596E-02
Consider three items of interest. First the name Lorent
in Fortran implies an integer. Second I found this by
going to watfor. This implies that the code
for\TLORENT.FOR has the line
C$INCLUDE BLI
This line is also included by Watcom which includes
the subroutine bli twice.
I used only 128 points in the above. The plot
closer to the peak is
This is a set of decidedly not equally spaced points.
Linear interpolation
The simplest interpolation scheme is based on
the expansion
f  x  
(1.1)
f A  x   f  x0    x  x0 

x  x x
0
Approximate
f  x  
f  x1   f  x0 
(1.2)


x  x x
x1  x0
0
So that this becomes
f  x1   f  x0 
f A  x   f  x0    x  x0 
(1.3)
x1  x0
This has the feature that is easy to rememeber and in
addtion fA(x0)f(x0), fA(x1)f(x1) making fA(x)
continuous if in all cases x0<=x<=x. In code that is
f  43  f  42 
f A  x   f  42    x  x0 
(1.4)
1.98413
0  x  1.98413
The function AlorenA(x) must have a part that looks at
the file for\loren.out for a given x and returns the fact
that
x(63) <= x <= x(64). This is the locate routine.
Locate.doc
Addition to function in practice
The practical function also needs to use static variables,
../Progdet/PANDA.mht#static_variables so that it can
store data in along with code. These enable the
function to read and organize its files on the first call
for use on later calls.
FUNCTION FUN1(X)
DIMENSION XP(137),DP(137)
SAVE NC,NDAT,XP,DP
DATA NC/0/
Feb1.doc
5
IF(NC.EQ.0)THEN
NC=1
OPEN(1,FILE=’loren.out’)
NDAT=1
READ(1,*,ERR=10)XP(NDAT),DP(NDAT)
NDAT=NDAT+1
IF(NDAT.LE.137)THEN
GOTO 5
ELSE
PRINT*,' FROM FUN1 NDAT > 137 '
READ(*,*)ITEST
ENDIF
NDAT=NDAT-1
ENDIF
CALL LOCATE(X,XP,NDAT,J)
FUN1=DP(J)+(X-XP(J))*(DP(J+1)2 DP(J))/(XP(J+1)-XP(J))
RETURN
END
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