Re: Integration in gnuplot IS possible!

[3snoW <vas...@gm...>]

Daniel J Sebald wrote:
> 
> On 06/15/2011 07:35 PM, 3snoW wrote:
>>
>> Hello,
>> I'm not sure if this qualifies as "Dev", If it doesn't I'm sorry.
> [snip]
>> Let me know if you have any ideas to make it better or if you find any
>> bug
>> using it! I hope this was helpful!
> 
> Very creative.  Of course, this is straightforward rectangular 
> approximation to integration.  It will have problems with functions that 
> change quickly near discontinuities and so on so won't have the 
> precision of, say, adaptive integral techniques.  Nonetheless, it works 
> (sort of, see note at end), assuming the initial condition is that the 
> integral passes through zero at a.
> 
> [snip]
> 
> Notice how accuracy is lost moving outward.  So you might want to 
> experiment with making h another parameter in the function.  Generalizing, 
> 
> intf(a,x,N)=x>a?intfAux1(a,x-(x-a)/N/2,(x-a)/N)*(x-a)/N:intfAux2(a,x+(a-x)/N/2,(a-x)/N)*(x-a)/N; 
> 
> I can't push N high enough to get good resolution before a stack 
> overflow occurs. 
> 
> An internal integration feature is probably the only good way to address 
> this sort of thing. 
> 
> Dan 
> 
Hi Dan,

The reason I was using f(x)-f(a) in the intfAux functions and then add
f(a)*(x-a) is because I originally was using a fixed small step h instead of
dividing the interval in 90 small parts. That way, if f(a) was not 0, the
integral would have a discontinuity every time x was a multiple of h, so, as
a workaround to this problem, I set it to integrate f(x)-f(a), and
compensated adding f(a)*(x-a). But since I switched to dividing into 90
equal parts, this is no longer a problem. 

I didn't make the integration method more sophisticated because of the
'stack overflow' issue. Adaptive integral techniques would most likely
consume 'stacks' at a much higher rate, and in the end you would have a
worse integration because of the lack of resolution. I'm thinking of maybe
upgrading this to the trapezoidal integration or even a superior order
technique, but for now I think this works fine for any 'well behaved'
function.

Lastly, the generalized function that includes N as a parameter is a good
idea, but I'll call it Nintf instead of intf, because that way I can have
both functions. Thank you for your contribution, it was really constructive!
I'll update the config.ini file with your changes.

3snoW
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