Re: Integration in gnuplot IS possible!

[Alexandre F. <o.a...@gm...>]

The Pieter-Tjerk is fairly better :D
redefining it this make the same thing but you ask for a maximum integration
distance
instead a maximum
intf(x0,a,h) = (h<=delta) ? f(x0+a/2)*a : ( intf(x0,a/2,delta) +
intf(x0+a/2,a/2,delta) )

when you use gnuplot i think you want to plot something, this version if you
say
plot intf(x0, x - x0, delta)
ensures that any integration interval will be larger than delta, and that
the
recurrence steep will be the minimum (with this function structure)
if you plot with 1024 samples the integration function intf(x0, a, delta) is
called
1397077 times, and the function f(x) will be evaluated 350548 times and the
max
recurrence depth will be 10


to integrate with the same acuracy the Daniel's scheme will call the intf*
functions and f(x) are called about 523 thounsand times. and the max
recurrence deepth is 1024

my scheme calls f(x) 1024 times and intf(x) 1024 times, but use some global
variables.

excuse-me i accidentally replied only to 3snoW

here goes the my scheme.
It's not encouraged the use of global variables, but in such case i think
here we a better solution, not THE better solution

# Characteristic for the integration
n_samps = 100;
a = 0.0;
b = 5.0;
# initialization
aux = 0.0;
h = (b-a)/n_samps;
set samples n_samps
set xrange [a to b]
# the function
f(x) = sin(5*x)/(0.1+x)

#the integrator scheme
intf(x) = (aux = (aux + f(x)*h))
# plot it
plot f(x), intf(x)
# another function
f(x) = sin(x)*x
replot

for the 2D is also possible. the only thing you need is to reinit the aux
variable when x=a
this scheme is as poor as the former, therefore it's O(nsamples) and why to
use recurrence if you can use memorization?
intf can also have other integration schemes, with the advantage that you
have to implement only once
for example simpson's rule or any other method

intf(x) = (aux = (aux + (f(x-h)+4*f(x-0.5*h)+f(x))*h/6))

this example make the h function to be called three times more.
the ideal to generate plots is to derive integration schemes open in
f(x-h) and closed in f(x), but i will not make this now :D