gnuplot-info

[Gnuplot-info] How to plot a discontinous function

[Federico B. <fed...@gm...>]

Hi I'm trying to plot a discontinuous function like this

f(x) = a1*x**2+b1*x+c1  for x in [t11,t12]
f(x) = a2*x**2+b2*x+c2  for x in [t21,t22]
f(x) = a3*x**2+b3*x+c3  for x in [t31,t32]
....
....
...
where t11<=t12<=t21<=t22, etc

and I don't know how to do it.
I've tried defining as many functions as intervals and making the
function undefined (1/0) outside its interval and plotting each
function (with persistent plot) but it doesn't work when the intervals
are small.
Thanks
Federico

-- 
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I go into another room and read a good book.

Re: [Gnuplot-info] How to plot a discontinous function

[Hans-Bernhard B. <HBB...@t-...>]

On 04.10.2010 21:47, Federico Bergero wrote:
> Hi I'm trying to plot a discontinuous function like this
>
> f(x) = a1*x**2+b1*x+c1  for x in [t11,t12]
> f(x) = a2*x**2+b2*x+c2  for x in [t21,t22]
> f(x) = a3*x**2+b3*x+c3  for x in [t31,t32]
> ....
> ....
> ...
> where t11<=t12<=t21<=t22, etc
>
> and I don't know how to do it.

Several ways possible.  You could combine all functions into one using 
the ? operator:

	f(x) = (x < t21) ? f1(x) : (x < t31) ? f2(x) : f3(x)

Or you can plot each function individually, like you appear to be doing now.

> I've tried defining as many functions as intervals and making the
> function undefined (1/0) outside its interval and plotting each
> function (with persistent plot)

Using multiplot for that is wrong.  Just

	plot f1(x), f2(x), f3(x)

> but it doesn't work when the intervals
> are small.

So up the 'set samples'.

Better yet, switch to parametric mode, map a common t interval [0:1] to 
your individual t ranges, and then:

	x1(t) = t11+t*(t12-t11)
	...

	plot x1(t), f1(x1(t)), x2(t), f2(x2(t)), ...

Re: [Gnuplot-info] How to plot a discontinous function

[Jon <dev...@gm...>]

Pretty good hints! Thanks,


2010/10/5 Hans-Bernhard Bröker <HBB...@t-...>

> On 04.10.2010 21:47, Federico Bergero wrote:
> > Hi I'm trying to plot a discontinuous function like this
> >
> > f(x) = a1*x**2+b1*x+c1  for x in [t11,t12]
> > f(x) = a2*x**2+b2*x+c2  for x in [t21,t22]
> > f(x) = a3*x**2+b3*x+c3  for x in [t31,t32]
> > ....
> > ....
> > ...
> > where t11<=t12<=t21<=t22, etc
> >
> > and I don't know how to do it.
>
> Several ways possible.  You could combine all functions into one using
> the ? operator:
>
>        f(x) = (x < t21) ? f1(x) : (x < t31) ? f2(x) : f3(x)
>
> Or you can plot each function individually, like you appear to be doing
> now.
>
> > I've tried defining as many functions as intervals and making the
> > function undefined (1/0) outside its interval and plotting each
> > function (with persistent plot)
>
> Using multiplot for that is wrong.  Just
>
>        plot f1(x), f2(x), f3(x)
>
> > but it doesn't work when the intervals
> > are small.
>
> So up the 'set samples'.
>
> Better yet, switch to parametric mode, map a common t interval [0:1] to
> your individual t ranges, and then:
>
>        x1(t) = t11+t*(t12-t11)
>        ...
>
>        plot x1(t), f1(x1(t)), x2(t), f2(x2(t)), ...
>
>
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