gnuplot-beta

Newton's method in gnuplot...

[Philipp K. J. <ja...@ie...>]

f(x) = cos(x)
steps=0; x=0.5; eps=1e-6

while( abs(f(x)) > 1e-10 ) {
x = x - eps*f(x)/( f(x+eps) - f(x) )
steps = steps + 1
}

print steps, x

Re: Newton's method in gnuplot...

[Christoph B. <us...@be...>]

Zitat von "Philipp K. Janert" <ja...@ie...>:
> f(x) = cos(x)
> steps=0; x=0.5; eps=1e-6
>
> while( abs(f(x)) > 1e-10 ) {
> x = x - eps*f(x)/( f(x+eps) - f(x) )
> steps = steps + 1
> }
>
> print steps, x

g(x) = cos(x)
h(x) = (abs(g(x)) < 1e-10) ? x : h(x - eps*g(x)/(g(x + eps) - g(x)))
x=0.5; eps=1e-6
print h(x)

Should we now remove recursion?

Don't get me wrong, I really appreciate, that you raised this discussion.

Only, in my opinion you cannot completely sort out "programming features".
Yes, the loops allow you to do some kind of programming, but it also allows
you to greatly improve your gnuplot scripts when working e.g. with many data
files:

files = system('ls *.dat')
plot for [f in files] f

That makes your script much more flexible, e.g. when dealing with a lot of
similar measurement sets which then basically requires only a single script
for plotting.

Christoph

Re: Newton's method in gnuplot...

[Petr M. <mi...@ph...>]

>> f(x) = cos(x)
>> steps=0; x=0.5; eps=1e-6
>>
>> while( abs(f(x)) > 1e-10 ) {
>> x = x - eps*f(x)/( f(x+eps) - f(x) )
>> steps = steps + 1
>> }
>>
>> print steps, x
>
> g(x) = cos(x)
> h(x) = (abs(g(x)) < 1e-10) ? x : h(x - eps*g(x)/(g(x + eps) - g(x)))
> x=0.5; eps=1e-6
> print h(x)
>
> Should we now remove recursion?

newton.gp:
f(x) = cos(x)
steps=0; x=0.5; eps=1e-6
call "newton_inside.gp"
print steps, x

newton_inside.gp:
x = x - eps*f(x)/( f(x+eps) - f(x) )
steps = steps + 1
if (abs(f(x)) < 1e-10 ) exit
call "newton_inside.gp"

Should we remove if and call? :-)

I really like the current loops. They help with easy tasks a lot.

> files = system('ls *.dat')
> plot for [f in files] f
>
> That makes your script much more flexible, e.g. when dealing with a lot of
> similar measurement sets which then basically requires only a single script
> for plotting.

Gnuplot is mainly for plotting, and "for" helps a lot!

---
Petr

[offlist] Re: Newton's method in gnuplot...

[Philipp K. J. <ja...@ie...>]

On Thu, 30 Oct 2014 09:44:48 +0100
Christoph Bersch <us...@be...> wrote:

> Zitat von "Philipp K. Janert" <ja...@ie...>:
> > f(x) = cos(x)
> > steps=0; x=0.5; eps=1e-6
> >
> > while( abs(f(x)) > 1e-10 ) {
> > x = x - eps*f(x)/( f(x+eps) - f(x) )
> > steps = steps + 1
> > }
> >
> > print steps, x
> 
> g(x) = cos(x)
> h(x) = (abs(g(x)) < 1e-10) ? x : h(x - eps*g(x)/(g(x + eps) - g(x)))
> x=0.5; eps=1e-6
> print h(x)

Clever, that! I didn't think of this.

Re: [offlist] Re: Newton's method in gnuplot...

[Philipp K. J. <ja...@ie...>]

Apologies for the spam - this was supposed to go
to Christoph only.

It IS clever, though! ;-)

> 
> > Zitat von "Philipp K. Janert" <ja...@ie...>:
> > > f(x) = cos(x)
> > > steps=0; x=0.5; eps=1e-6
> > >
> > > while( abs(f(x)) > 1e-10 ) {
> > > x = x - eps*f(x)/( f(x+eps) - f(x) )
> > > steps = steps + 1
> > > }
> > >
> > > print steps, x
> > 
> > g(x) = cos(x)
> > h(x) = (abs(g(x)) < 1e-10) ? x : h(x - eps*g(x)/(g(x + eps) - g(x)))
> > x=0.5; eps=1e-6
> > print h(x)
> 
> Clever, that! I didn't think of this.
>