gnuplot-info

[Gnuplot-info] complicated function expressions

[Marek W. G. <gu...@if...>]

I'm trying to plot two identical functions, f(x) and g(x).  f(x) is defined as
a single, looong expression, while g(x) is defined as a composition of several
simpler functions.  Yet, as you can see in the picture attached - f(x) and g(x)
look differently.  g(x), made of smaller chunks of code, is correct.
Why are they different?
Is there any limit for the length of the expression defining a function??

Intrigued,
Marek Gutowski

gnuplot> show funct

         User-Defined Functions:
 
f(x)=(pi*(1.0-0.5/(x**2))+2.0*atan(2.0*x)/(x**2)-2.0*(1.0+0.25/(x**2))*atan(4.0*x)-10.0*atan(0.25/x)+4.0*(1.0+0.25/(x**2))*atan(0.5/x)+2.0*log((1.0+4.0*x**2)/(1.0+16.0*x**2)))/(-2.0*pi)
         f1(x)=pi*(1.0-0.5/(x**2))
         f2(x)=2.0*atan(2.0*x)/(x**2)
         f3(x)=-2.0*(1.0+0.25/(x**2))*atan(4.0*x)
         f4(x)=-10.0*atan(0.25/x)
         f5(x)=4.0*(1.0+0.25/(x**2))*atan(1.0/(2.0*x))
         f6(x)=2.0*log((1.0+4.0*x**2)/(1.0+16.0*x**2))/x
         g(x)=-(f1(x)+f2(x)+f3(x)+f4(x)+f5(x)+f6(x))/(2.0*pi)

gnuplot> plot [0.0001:10.0] g(x) w l 3, f(x) w l 6

I am working with
         G N U P L O T
         Version 4.0 patchlevel 0
         last modified Thu Apr 15 14:44:22 CEST 2004
         System: Linux 2.6.18-6-k7

Yes, I know there is a newer version but my Debian Linux is rather conservative
and I stick strictly to the stable distribution.  The processor is Athlon XP2000+
-- 
Marek W. Gutowski
Institute of Physics, ON-3.2, Al. Lotnikow 32/46
02-668 Warszawa, POLAND, tel. +48-22-0228436601 ext. 3122
 >> To talk or not to talk?  Yes, talk, plain ASCII please <<
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Re: [Gnuplot-info] complicated function expressions

[<Tam...@Al...>]

There are two options:
- user error
- software error

The first one is much more likely.
Thoroughly inspect your equations and you will find that they are _not_
equivalent.
Hint: look at f6(x)

Tammo 

> -----Original Message-----
> From: gnu...@li... 
> [mailto:gnu...@li...] On Behalf 
> Of Marek W. Gutowski
> Sent: Friday, February 15, 2008 10:35 AM
> To: gnu...@li...
> Subject: [Gnuplot-info] complicated function expressions
> 
> I'm trying to plot two identical functions, f(x) and g(x).  
> f(x) is defined as a single, looong expression, while g(x) is 
> defined as a composition of several simpler functions.  Yet, 
> as you can see in the picture attached - f(x) and g(x) look 
> differently.  g(x), made of smaller chunks of code, is correct.
> Why are they different?
> Is there any limit for the length of the expression defining 
> a function??
> 
> Intrigued,
> Marek Gutowski
> 
> gnuplot> show funct
> 
>          User-Defined Functions:
>  
> f(x)=(pi*(1.0-0.5/(x**2))+2.0*atan(2.0*x)/(x**2)-2.0*(1.0+0.25
> /(x**2))*atan(4.0*x)-10.0*atan(0.25/x)+4.0*(1.0+0.25/(x**2))*a
> tan(0.5/x)+2.0*log((1.0+4.0*x**2)/(1.0+16.0*x**2)))/(-2.0*pi)
>          f1(x)=pi*(1.0-0.5/(x**2))
>          f2(x)=2.0*atan(2.0*x)/(x**2)
>          f3(x)=-2.0*(1.0+0.25/(x**2))*atan(4.0*x)
>          f4(x)=-10.0*atan(0.25/x)
>          f5(x)=4.0*(1.0+0.25/(x**2))*atan(1.0/(2.0*x))
>          f6(x)=2.0*log((1.0+4.0*x**2)/(1.0+16.0*x**2))/x
>          g(x)=-(f1(x)+f2(x)+f3(x)+f4(x)+f5(x)+f6(x))/(2.0*pi)
> 
> gnuplot> plot [0.0001:10.0] g(x) w l 3, f(x) w l 6
> 
> I am working with
>          G N U P L O T
>          Version 4.0 patchlevel 0
>          last modified Thu Apr 15 14:44:22 CEST 2004
>          System: Linux 2.6.18-6-k7
> 
> Yes, I know there is a newer version but my Debian Linux is 
> rather conservative and I stick strictly to the stable 
> distribution.  The processor is Athlon XP2000+
> --
> Marek W. Gutowski
> Institute of Physics, ON-3.2, Al. Lotnikow 32/46
> 02-668 Warszawa, POLAND, tel. +48-22-0228436601 ext. 3122  >> 
> To talk or not to talk?  Yes, talk, plain ASCII please << 
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> 


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