reset
#
# fit polynomial to data
#
f(x) = c0 + c1*sqrt(1-x**2) + 2*c2*(1-x**2)
c0 = 1500; c1 = 6000; c2 = -500;
FIT_LIMIT = 1e-10
fit f(x) 'ld_19_7_02_1.txt' using 1:3 via  c0, c1, c2
#
# plot it
#
set xrange [-1.1:1.1]
set yrange [0:1.2]
set key 0.1,0.3
set xlabel "r/R"
set ylabel "Intensity"
set pointsize 1.0
plot "ld_19_7_02_1.txt" \
       using 1:($3/f(0)) \
       title 'Fit result' \
       with points pointtype 7, \
       f(x)/f(0) \
       title '' with lines linetype 1
#
#  normalize the parameters
#
a0 = c0 / f(0)
a1 = c1 / f(0)
a2 = c2 / f(0)
print "parameters a0, a1, a2...", a0, a1, a2